괄호 안의 항을 2, 3, 4 항으로 설정하는 기능 추가

app/(game)/number-parentheses/NumberParenthesesClient.tsx

@@ -8,6 +8,10 @@ export default function NumberParenthesesClient() {
     (state) => state.selectedProblemCount,
   );
   const setProblemCount = useGameStore((state) => state.setProblemCount);
+  const selectedMaxTermCount = useGameStore(
+    (state) => state.selectedMaxTermCount,
+  );
+  const setMaxTermCount = useGameStore((state) => state.setMaxTermCount);
   const initSession = useGameStore((state) => state.initSession);
 
   return (
@@ -16,10 +20,12 @@ export default function NumberParenthesesClient() {
       title="숫자 괄호 풀기"
       description="정수로 이루어진 괄호식을 풀며 음수 분배와 부호 변화를 연습합니다."
       notice="현재는 소괄호 숫자 문제만 선택할 수 있습니다."
-      playHref={`/number-parentheses/play?count=${selectedProblemCount}`}
+      playHref={`/number-parentheses/play?count=${selectedProblemCount}&terms=${selectedMaxTermCount}`}
       selectedProblemCount={selectedProblemCount}
+      selectedMaxTermCount={selectedMaxTermCount}
       onProblemCountChange={setProblemCount}
-      onStart={() => initSession(selectedProblemCount)}
+      onMaxTermCountChange={setMaxTermCount}
+      onStart={() => initSession(selectedProblemCount, selectedMaxTermCount)}
     />
   );
 }

app/(game)/number-parentheses/play/NumberPlayClient.tsx

@@ -16,7 +16,7 @@ import StageIndicator from "@/components/game/StageIndicator";
 import { DESKTOP_INPUT_DEVICE_QUERY } from "@/lib/input-device";
 import KatexRenderer from "@/components/math/KatexRenderer";
 import { useGameStore } from "@/store/gameStore";
-import type { ProblemCount } from "@/store/gameStore";
+import type { MaxTermCount, ProblemCount } from "@/store/gameStore";
 
 const REAL_NUMBER_PATTERN = /^-?\d+(?:\.\d+)?$/;
 
@@ -30,16 +30,22 @@ function parseAnswer(value: string) {
 
 interface NumberPlayClientProps {
   problemCount: ProblemCount;
+  maxTermCount: MaxTermCount;
 }
 
 export default function NumberPlayClient({
   problemCount,
+  maxTermCount,
 }: NumberPlayClientProps) {
   const session = useGameStore((state) => state.session);
   const selectedProblemCount = useGameStore(
     (state) => state.selectedProblemCount,
   );
   const setProblemCount = useGameStore((state) => state.setProblemCount);
+  const selectedMaxTermCount = useGameStore(
+    (state) => state.selectedMaxTermCount,
+  );
+  const setMaxTermCount = useGameStore((state) => state.setMaxTermCount);
   const initSession = useGameStore((state) => state.initSession);
   const submitAnswer = useGameStore((state) => state.submitAnswer);
   const nextProblem = useGameStore((state) => state.nextProblem);
@@ -48,8 +54,9 @@ export default function NumberPlayClient({
   const problemCardRef = useRef<HTMLDivElement>(null);
   const answerFormRef = useRef<NumberAnswerFormHandle>(null);
 
-  const [answerA, setAnswerA] = useState("");
+  const [answers, setAnswers] = useState<string[]>(() =>
-  const [answerB, setAnswerB] = useState("");
+    Array.from({ length: maxTermCount }, () => ""),
+  );
   const [activeInput, setActiveInput] = useState<ActiveAnswerInput>(0);
   const [inputError, setInputError] = useState("");
 
@@ -59,7 +66,8 @@ export default function NumberPlayClient({
   const isComplete = Boolean(
     session && session.currentIndex >= session.problems.length,
   );
-  const sessionNeedsInit = sessionProblemCount !== problemCount;
+  const sessionNeedsInit =
+    sessionProblemCount !== problemCount || session?.termCount !== maxTermCount;
   const correctCount =
     session?.results.filter((result) => result?.correct).length ?? 0;
   const totalCount = session?.problems.length ?? 0;
@@ -69,40 +77,53 @@ export default function NumberPlayClient({
       setProblemCount(problemCount);
     }
 
+    if (selectedMaxTermCount !== maxTermCount) {
+      setMaxTermCount(maxTermCount);
+    }
+
     if (sessionNeedsInit) {
-      initSession(problemCount);
+      initSession(problemCount, maxTermCount);
     }
   }, [
     initSession,
+    maxTermCount,
     problemCount,
+    selectedMaxTermCount,
     selectedProblemCount,
     sessionProblemCount,
     sessionNeedsInit,
+    setMaxTermCount,
     setProblemCount,
   ]);
 
   useEffect(() => {
-    setAnswerA("");
+    setAnswers(Array.from({ length: currentProblem?.terms.length ?? maxTermCount }, () => ""));
-    setAnswerB("");
     setActiveInput(0);
     setInputError("");
-  }, [currentProblem?.key]);
+  }, [currentProblem?.key, currentProblem?.terms.length, maxTermCount]);
 
   function handleSubmit(event: FormEvent<HTMLFormElement>) {
     event.preventDefault();
 
     if (currentResult || !currentProblem) return;
 
-    const parsedA = parseAnswer(answerA);
+    const parsedAnswers = answers.map(parseAnswer);
-    const parsedB = parseAnswer(answerB);
 
-    if (parsedA === null || parsedB === null) {
+    if (parsedAnswers.some((answer) => answer === null)) {
-      setInputError("두 칸 모두 실수로 입력하세요.");
+      setInputError("모든 항을 실수로 입력하세요.");
       return;
     }
 
     setInputError("");
-    submitAnswer({ a: parsedA, b: parsedB });
+    submitAnswer({ terms: parsedAnswers as number[] });
+  }
+
+  function handleAnswerChange(index: ActiveAnswerInput, value: string) {
+    setAnswers((currentAnswers) =>
+      currentAnswers.map((answer, answerIndex) =>
+        answerIndex === index ? value : answer,
+      ),
+    );
   }
 
   function handleNextProblem() {
@@ -184,10 +205,13 @@ export default function NumberPlayClient({
 
   const submitted = currentResult !== null;
   const isLastProblem = session.currentIndex === session.problems.length - 1;
-  const pendingAnswerLabels: [string, string] = [
+  const pendingAnswerLabels = currentProblem.terms.map((term, index) => {
-    String(currentProblem.a),
+    if (index === 0) return String(term);
-    String(currentProblem.operator === "-" ? -currentProblem.b : currentProblem.b),
+
-  ];
+    return String(
+      currentProblem.operators[index - 1] === "-" ? -term : term,
+    );
+  });
 
   return (
     <main className="min-h-screen bg-slate-50 px-6 py-10 text-slate-950">
@@ -214,9 +238,6 @@ export default function NumberPlayClient({
           ref={problemCardRef}
           className="rounded-md bg-white px-6 pt-6 pb-4 shadow-sm ring-1 ring-slate-200 sm:p-8"
         >
-          <p className="mb-4 text-sm font-semibold text-slate-500">
-            괄호를 풀어 두 항을 순서대로 입력하세요.
-          </p>
           <div className="text-3xl font-semibold text-slate-950 sm:text-4xl">
             <KatexRenderer latex={currentProblem.latexBefore} displayMode />
           </div>
@@ -231,14 +252,12 @@ export default function NumberPlayClient({
         {!submitted ? (
           <NumberAnswerForm
             ref={answerFormRef}
-            answerA={answerA}
+            answers={answers}
-            answerB={answerB}
             activeInput={activeInput}
             error={inputError}
             pendingAnswerLabels={pendingAnswerLabels}
             onActiveInputChange={setActiveInput}
-            onAnswerAChange={setAnswerA}
+            onAnswerChange={handleAnswerChange}
-            onAnswerBChange={setAnswerB}
             onInputFocus={scrollKatexToViewportTop}
             onSubmit={handleSubmit}
           />

app/(game)/number-parentheses/play/page.tsx

@@ -1,9 +1,10 @@
 import NumberPlayClient from "./NumberPlayClient";
-import type { ProblemCount } from "@/store/gameStore";
+import type { MaxTermCount, ProblemCount } from "@/store/gameStore";
 
 interface NumberPlayPageProps {
   searchParams?: {
     count?: string | string[];
+    terms?: string | string[];
   };
 }
 
@@ -15,8 +16,22 @@ function parseProblemCount(count?: string | string[]): ProblemCount {
   return count === "5" ? 5 : 10;
 }
 
+function parseMaxTermCount(terms?: string | string[]): MaxTermCount {
+  if (Array.isArray(terms)) {
+    return parseMaxTermCount(terms[0]);
+  }
+
+  if (terms === "3") return 3;
+  if (terms === "4") return 4;
+
+  return 2;
+}
+
 export default function NumberPlayPage({ searchParams }: NumberPlayPageProps) {
   return (
-    <NumberPlayClient problemCount={parseProblemCount(searchParams?.count)} />
+    <NumberPlayClient
+      problemCount={parseProblemCount(searchParams?.count)}
+      maxTermCount={parseMaxTermCount(searchParams?.terms)}
+    />
   );
 }

app/(game)/variable-parentheses/VariableParenthesesClient.tsx

@@ -10,6 +10,12 @@ export default function VariableParenthesesClient() {
   const setProblemCount = useVariableGameStore(
     (state) => state.setProblemCount,
   );
+  const selectedMaxTermCount = useVariableGameStore(
+    (state) => state.selectedMaxTermCount,
+  );
+  const setMaxTermCount = useVariableGameStore(
+    (state) => state.setMaxTermCount,
+  );
   const initSession = useVariableGameStore((state) => state.initSession);
 
   return (
@@ -18,10 +24,12 @@ export default function VariableParenthesesClient() {
       title="미지수 괄호 풀기"
       description="괄호 안의 한 항에 미지수 x가 들어간 식을 풀며 부호 변화를 연습합니다."
       notice="현재는 소괄호와 미지수 x 문제만 선택할 수 있습니다."
-      playHref={`/variable-parentheses/play?count=${selectedProblemCount}`}
+      playHref={`/variable-parentheses/play?count=${selectedProblemCount}&terms=${selectedMaxTermCount}`}
       selectedProblemCount={selectedProblemCount}
+      selectedMaxTermCount={selectedMaxTermCount}
       onProblemCountChange={setProblemCount}
-      onStart={() => initSession(selectedProblemCount)}
+      onMaxTermCountChange={setMaxTermCount}
+      onStart={() => initSession(selectedProblemCount, selectedMaxTermCount)}
     />
   );
 }

app/(game)/variable-parentheses/play/VariablePlayClient.tsx

@@ -12,15 +12,18 @@ import KatexRenderer from "@/components/math/KatexRenderer";
 import { formatVariableTermLatex } from "@/lib/engine/variable-parenthesis";
 import {
   useVariableGameStore,
+  type VariableMaxTermCount,
   type VariableProblemCount,
 } from "@/store/variableGameStore";
 
 interface VariablePlayClientProps {
   problemCount: VariableProblemCount;
+  maxTermCount: VariableMaxTermCount;
 }
 
 export default function VariablePlayClient({
   problemCount,
+  maxTermCount,
 }: VariablePlayClientProps) {
   const session = useVariableGameStore((state) => state.session);
   const selectedProblemCount = useVariableGameStore(
@@ -29,15 +32,21 @@ export default function VariablePlayClient({
   const setProblemCount = useVariableGameStore(
     (state) => state.setProblemCount,
   );
+  const selectedMaxTermCount = useVariableGameStore(
+    (state) => state.selectedMaxTermCount,
+  );
+  const setMaxTermCount = useVariableGameStore(
+    (state) => state.setMaxTermCount,
+  );
   const initSession = useVariableGameStore((state) => state.initSession);
   const submitAnswer = useVariableGameStore((state) => state.submitAnswer);
   const nextProblem = useVariableGameStore((state) => state.nextProblem);
   const resetSession = useVariableGameStore((state) => state.resetSession);
 
-  const [selectedChoiceIds, setSelectedChoiceIds] = useState<
+  const [selectedChoiceIds, setSelectedChoiceIds] = useState<(string | null)[]>(
-    [string | null, string | null]
+    () => Array.from({ length: maxTermCount }, () => null),
-  >([null, null]);
+  );
-  const [activeTermIndex, setActiveTermIndex] = useState<0 | 1>(0);
+  const [activeTermIndex, setActiveTermIndex] = useState(0);
 
   const sessionProblemCount = session?.problems.length ?? null;
   const currentProblem = session?.problems[session.currentIndex] ?? null;
@@ -45,7 +54,8 @@ export default function VariablePlayClient({
   const isComplete = Boolean(
     session && session.currentIndex >= session.problems.length,
   );
-  const sessionNeedsInit = sessionProblemCount !== problemCount;
+  const sessionNeedsInit =
+    sessionProblemCount !== problemCount || session?.termCount !== maxTermCount;
   const correctCount =
     session?.results.filter((result) => result?.correct).length ?? 0;
   const totalCount = session?.problems.length ?? 0;
@@ -55,40 +65,46 @@ export default function VariablePlayClient({
       setProblemCount(problemCount);
     }
 
+    if (selectedMaxTermCount !== maxTermCount) {
+      setMaxTermCount(maxTermCount);
+    }
+
     if (sessionNeedsInit) {
-      initSession(problemCount);
+      initSession(problemCount, maxTermCount);
     }
   }, [
     initSession,
+    maxTermCount,
     problemCount,
+    selectedMaxTermCount,
     selectedProblemCount,
     sessionProblemCount,
     sessionNeedsInit,
+    setMaxTermCount,
     setProblemCount,
   ]);
 
   useEffect(() => {
-    setSelectedChoiceIds([null, null]);
+    setSelectedChoiceIds(
+      Array.from({ length: currentProblem?.terms.length ?? maxTermCount }, () => null),
+    );
     setActiveTermIndex(0);
-  }, [currentProblem?.key]);
+  }, [currentProblem?.key, currentProblem?.terms.length, maxTermCount]);
 
-  function handleSelectChoice(termIndex: 0 | 1, choiceId: string) {
+  function handleSelectChoice(termIndex: number, choiceId: string) {
-    const nextSelectedChoiceIds: [string | null, string | null] = [
+    const nextSelectedChoiceIds = [...selectedChoiceIds];
-      ...selectedChoiceIds,
-    ];
     nextSelectedChoiceIds[termIndex] = choiceId;
 
     setSelectedChoiceIds(nextSelectedChoiceIds);
 
-    if (termIndex === 0) {
+    if (termIndex < nextSelectedChoiceIds.length - 1) {
-      setActiveTermIndex(1);
+      setActiveTermIndex(termIndex + 1);
       return;
     }
 
     if (currentResult || !currentProblem) return;
     if (
-      nextSelectedChoiceIds[0] === null ||
+      nextSelectedChoiceIds.some((selectedChoiceId) => selectedChoiceId === null)
-      nextSelectedChoiceIds[1] === null
     ) {
       return;
     }
@@ -140,16 +156,15 @@ export default function VariablePlayClient({
 
   const submitted = currentResult !== null;
   const isLastProblem = session.currentIndex === session.problems.length - 1;
-  const pendingChoiceLabels: [string, string] = [
+  const pendingChoiceLabels = currentProblem.terms.map((term, index) =>
-    formatVariableTermLatex(currentProblem.firstTerm),
     formatVariableTermLatex({
-      ...currentProblem.secondTerm,
+      ...term,
       coefficient:
-        currentProblem.operator === "-"
+        index > 0 && currentProblem.operators[index - 1] === "-"
-          ? -currentProblem.secondTerm.coefficient
+          ? -term.coefficient
-          : currentProblem.secondTerm.coefficient,
+          : term.coefficient,
     }),
-  ];
+  );
 
   return (
     <main className="min-h-screen bg-slate-50 px-6 py-10 text-slate-950">
@@ -173,9 +188,6 @@ export default function VariablePlayClient({
         </div>
 
         <div className="rounded-md bg-white px-6 pt-6 pb-4 shadow-sm ring-1 ring-slate-200 sm:p-8">
-          <p className="mb-4 text-sm font-semibold text-slate-500">
-            괄호를 풀어 첫째 항과 둘째 항의 답을 보기에서 고르세요.
-          </p>
           <div className="text-3xl font-semibold text-slate-950 sm:text-4xl">
             <KatexRenderer latex={currentProblem.latexBefore} displayMode />
           </div>

app/(game)/variable-parentheses/play/page.tsx

@@ -1,9 +1,13 @@
 import VariablePlayClient from "./VariablePlayClient";
-import type { VariableProblemCount } from "@/store/variableGameStore";
+import type {
+  VariableMaxTermCount,
+  VariableProblemCount,
+} from "@/store/variableGameStore";
 
 interface VariablePlayPageProps {
   searchParams?: {
     count?: string | string[];
+    terms?: string | string[];
   };
 }
 
@@ -15,10 +19,24 @@ function parseProblemCount(count?: string | string[]): VariableProblemCount {
   return count === "5" ? 5 : 10;
 }
 
+function parseMaxTermCount(terms?: string | string[]): VariableMaxTermCount {
+  if (Array.isArray(terms)) {
+    return parseMaxTermCount(terms[0]);
+  }
+
+  if (terms === "3") return 3;
+  if (terms === "4") return 4;
+
+  return 2;
+}
+
 export default function VariablePlayPage({
   searchParams,
 }: VariablePlayPageProps) {
   return (
-    <VariablePlayClient problemCount={parseProblemCount(searchParams?.count)} />
+    <VariablePlayClient
+      problemCount={parseProblemCount(searchParams?.count)}
+      maxTermCount={parseMaxTermCount(searchParams?.terms)}
+    />
   );
 }

components/game/FeedbackPanel.tsx

@@ -23,10 +23,11 @@ export default function FeedbackPanel({
   onNext,
 }: FeedbackPanelProps) {
   const nextButtonRef = useRef<HTMLButtonElement>(null);
-  const signedTerms = [
+  const signedTerms = problem.terms.map((term, index) => {
-    problem.a,
+    if (index === 0) return term;
-    problem.operator === "-" ? -problem.b : problem.b,
+
-  ] as const;
+    return problem.operators[index - 1] === "-" ? -term : term;
+  });
   const feedbackItems = signedTerms.map((term, index) => ({
     formulaLatex: `${formatSignedNumber(
       problem.multiplier,

components/game/NumberAnswerForm.tsx

@@ -14,7 +14,7 @@ import type { FocusEvent, FormEvent } from "react";
 import { DESKTOP_INPUT_DEVICE_QUERY } from "@/lib/input-device";
 import KatexRenderer from "@/components/math/KatexRenderer";
 
-export type ActiveAnswerInput = 0 | 1;
+export type ActiveAnswerInput = number;
 
 const ANSWER_INPUT_PATTERN = /^-?\d*(?:\.\d*)?$/;
 const KEYPAD_KEYS = [
@@ -36,13 +36,11 @@ export interface NumberAnswerFormHandle {
 }
 
 interface NumberAnswerFormProps {
-  answerA: string;
+  answers: string[];
-  answerB: string;
   activeInput: ActiveAnswerInput;
   error: string;
-  pendingAnswerLabels: [string, string];
+  pendingAnswerLabels: string[];
-  onAnswerAChange: (value: string) => void;
+  onAnswerChange: (index: ActiveAnswerInput, value: string) => void;
-  onAnswerBChange: (value: string) => void;
   onActiveInputChange: (input: ActiveAnswerInput) => void;
   onInputBlur?: () => void;
   onInputFocus?: () => void;
@@ -54,13 +52,11 @@ const NumberAnswerForm = forwardRef<
   NumberAnswerFormProps
 >(function NumberAnswerForm(
   {
-    answerA,
+    answers,
-    answerB,
     activeInput,
     error,
     pendingAnswerLabels,
-    onAnswerAChange,
+    onAnswerChange,
-    onAnswerBChange,
     onActiveInputChange,
     onInputBlur,
     onInputFocus,
@@ -75,17 +71,16 @@ const NumberAnswerForm = forwardRef<
   const [keypadOpen, setKeypadOpen] = useState(false);
   const [desktopInputDevice, setDesktopInputDevice] = useState(false);
 
-  const activeAnswer = activeInput === 0 ? answerA : answerB;
+  const activeAnswer = answers[activeInput] ?? "";
-  const activeLabel = activeInput === 0 ? "첫째 항" : "둘째 항";
+  const activeLabel = `${activeInput + 1}항`;
   const activeDescription = `${activeLabel}의 답을 입력하세요.`;
-  const activeEnterKeyHint = activeInput === 0 ? "next" : "done";
+  const lastInputIndex = answers.length - 1;
-  const activeAnswerChange =
+  const activeEnterKeyHint = activeInput < lastInputIndex ? "next" : "done";
-    activeInput === 0 ? onAnswerAChange : onAnswerBChange;
 
   function updateAnswer(value: string) {
     if (!ANSWER_INPUT_PATTERN.test(value)) return;
 
-    activeAnswerChange(value);
+    onAnswerChange(activeInput, value);
   }
 
   function handleInputFocus() {
@@ -154,16 +149,9 @@ const NumberAnswerForm = forwardRef<
     };
   }, []);
 
-  function setAnswer(input: ActiveAnswerInput, value: string) {
-    if (input === 0) {
-      onAnswerAChange(value);
-    } else {
-      onAnswerBChange(value);
-    }
-  }
-
   function toggleMinus() {
-    activeAnswerChange(
+    onAnswerChange(
+      activeInput,
       activeAnswer.startsWith("-") ? activeAnswer.slice(1) : `-${activeAnswer}`,
     );
     focusInput();
@@ -182,14 +170,14 @@ const NumberAnswerForm = forwardRef<
   function moveToInput(input: ActiveAnswerInput, reset = false) {
     onActiveInputChange(input);
     if (reset) {
-      setAnswer(input, "");
+      onAnswerChange(input, "");
     }
     focusInput();
   }
 
   function handleEnter() {
-    if (activeInput === 0) {
+    if (activeInput < lastInputIndex) {
-      moveToInput(1);
+      moveToInput(activeInput + 1);
       return;
     }
 
@@ -197,18 +185,11 @@ const NumberAnswerForm = forwardRef<
     focusInput();
   }
 
-  const answerButtons = [
+  const answerButtons = answers.map((value, index) => ({
-    {
+    index,
-      index: 0 as const,
+    label: `${index + 1}항`,
-      label: "첫째 항",
+    value,
-      value: answerA,
+  }));
-    },
-    {
-      index: 1 as const,
-      label: "둘째 항",
-      value: answerB,
-    },
-  ];
 
   return (
     <form
@@ -334,9 +315,9 @@ const NumberAnswerForm = forwardRef<
               onPointerDown={(event) => event.preventDefault()}
               onClick={handleEnter}
               aria-label={
-                activeInput === 0
+                activeInput < lastInputIndex
-                  ? "첫째 항 입력 완료 후 둘째 항으로 이동"
+                  ? "현재 항 입력 완료 후 다음 항으로 이동"
-                  : "둘째 항 입력 완료 후 제출"
+                  : "마지막 항 입력 완료 후 제출"
               }
               className="col-span-2 inline-flex h-12 items-center justify-center rounded-md bg-emerald-700 text-base font-semibold text-white shadow-sm transition hover:bg-emerald-800 focus:outline-none focus:ring-2 focus:ring-emerald-500 focus:ring-offset-2"
             >

components/game/ParenthesesPreparationClient.tsx

@@ -4,6 +4,7 @@ import Link from "next/link";
 import { useEffect, useRef } from "react";
 
 export type PreparationProblemCount = 5 | 10;
+export type PreparationMaxTermCount = 2 | 3 | 4;
 
 interface ParenthesesPreparationClientProps {
   eyebrow: string;
@@ -12,11 +13,33 @@ interface ParenthesesPreparationClientProps {
   notice: string;
   playHref: string;
   selectedProblemCount: PreparationProblemCount;
+  selectedMaxTermCount: PreparationMaxTermCount;
   onProblemCountChange: (count: PreparationProblemCount) => void;
+  onMaxTermCountChange: (count: PreparationMaxTermCount) => void;
   onStart: () => void;
 }
 
 const problemCounts: PreparationProblemCount[] = [5, 10];
+const maxTermCounts: PreparationMaxTermCount[] = [2, 3, 4];
+
+const buttonGroupClassName =
+  "inline-flex gap-1 rounded-md border border-slate-300 bg-white p-1 shadow-sm";
+
+function optionButtonClassName({
+  selected,
+  disabled = false,
+}: {
+  selected: boolean;
+  disabled?: boolean;
+}) {
+  return `h-10 min-w-16 rounded px-4 text-base font-semibold transition focus:outline-none focus:ring-2 focus:ring-emerald-500 focus:ring-offset-2 ${
+    selected ? "bg-emerald-700 text-white" : "text-slate-700 hover:bg-slate-100"
+  } ${
+    disabled
+      ? "cursor-not-allowed bg-slate-100 text-slate-400 hover:bg-slate-100"
+      : ""
+  }`;
+}
 
 const bracketKinds = [
   {
@@ -46,7 +69,9 @@ export default function ParenthesesPreparationClient({
   notice,
   playHref,
   selectedProblemCount,
+  selectedMaxTermCount,
   onProblemCountChange,
+  onMaxTermCountChange,
   onStart,
 }: ParenthesesPreparationClientProps) {
   const startLinkRef = useRef<HTMLAnchorElement>(null);
@@ -74,7 +99,7 @@ export default function ParenthesesPreparationClient({
               문제 수
             </legend>
             <div
-              className="inline-flex gap-1 rounded-md border border-slate-300 bg-white p-1 shadow-sm"
+              className={buttonGroupClassName}
               role="group"
               aria-label="문제 수 선택"
             >
@@ -87,11 +112,7 @@ export default function ParenthesesPreparationClient({
                     type="button"
                     onClick={() => onProblemCountChange(count)}
                     aria-pressed={selected}
-                    className={`h-10 min-w-16 rounded px-4 text-base font-semibold transition focus:outline-none focus:ring-2 focus:ring-emerald-500 focus:ring-offset-2 ${
+                    className={optionButtonClassName({ selected })}
-                      selected
-                        ? "bg-emerald-700 text-white"
-                        : "text-slate-700 hover:bg-slate-100"
-                    }`}
                   >
                     {count}
                   </button>
@@ -100,39 +121,63 @@ export default function ParenthesesPreparationClient({
             </div>
           </fieldset>
 
-          <fieldset className="space-y-3">
+          <div className="flex flex-col gap-6 sm:flex-row sm:items-start">
-            <legend className="text-sm font-semibold text-slate-700">
+            <fieldset className="space-y-3">
-              괄호 종류
+              <legend className="text-sm font-semibold text-slate-700">
-            </legend>
+                괄호 종류
-            <div
+              </legend>
-              className="inline-flex gap-1 rounded-md border border-slate-300 bg-white p-1 shadow-sm"
+              <div
-              role="group"
+                className={buttonGroupClassName}
-              aria-label="괄호 종류 선택"
+                role="group"
-            >
+                aria-label="괄호 종류 선택"
-              {bracketKinds.map((bracketKind) => (
+              >
-                <button
+                {bracketKinds.map((bracketKind) => (
-                  key={bracketKind.label}
+                  <button
-                  type="button"
+                    key={bracketKind.label}
-                  disabled={bracketKind.disabled}
+                    type="button"
-                  aria-pressed={bracketKind.selected}
+                    disabled={bracketKind.disabled}
-                  aria-label={`${bracketKind.name} ${
+                    aria-pressed={bracketKind.selected}
-                    bracketKind.disabled ? "준비 중" : "선택됨"
+                    aria-label={`${bracketKind.name} ${
-                  }`}
+                      bracketKind.disabled ? "준비 중" : "선택됨"
-                  className={`h-10 min-w-16 rounded px-4 text-base font-semibold transition focus:outline-none focus:ring-2 focus:ring-emerald-500 focus:ring-offset-2 ${
+                    }`}
-                    bracketKind.selected
+                    className={optionButtonClassName({
-                      ? "bg-emerald-700 text-white"
+                      selected: bracketKind.selected,
-                      : "text-slate-700 hover:bg-slate-100"
+                      disabled: bracketKind.disabled,
-                  } ${
+                    })}
-                    bracketKind.disabled
+                  >
-                      ? "cursor-not-allowed bg-slate-100 text-slate-400 hover:bg-slate-100"
+                    {bracketKind.label}
-                      : ""
+                  </button>
-                  }`}
+                ))}
-                >
+              </div>
-                  {bracketKind.label}
+            </fieldset>
-                </button>
+
-              ))}
+            <fieldset className="space-y-3">
-            </div>
+              <legend className="text-sm font-semibold text-slate-700">
-          </fieldset>
+                괄호 안 최대 항 수
+              </legend>
+              <div
+                className={buttonGroupClassName}
+                role="group"
+                aria-label="괄호 안 최대 항 수 선택"
+              >
+                {maxTermCounts.map((count) => {
+                  const selected = selectedMaxTermCount === count;
+
+                  return (
+                    <button
+                      key={count}
+                      type="button"
+                      onClick={() => onMaxTermCountChange(count)}
+                      aria-pressed={selected}
+                      className={optionButtonClassName({ selected })}
+                    >
+                      {count}
+                    </button>
+                  );
+                })}
+              </div>
+            </fieldset>
+          </div>
 
           <div className="flex flex-wrap gap-3">
             <Link

components/game/ScoreSummary.tsx

@@ -15,50 +15,54 @@ interface ScoreSummaryProps {
   onRestart: () => void;
 }
 
-function formatAnswerPairLatex(first: number, second: number) {
+function formatAnswerLatex(terms: number[]) {
-  const operator = second < 0 ? "-" : "+";
+  return terms
+    .map((term, index) => {
+      if (index === 0) return `${term}`;
 
-  return `${first} ${operator} ${Math.abs(second)}`;
+      const operator = term < 0 ? "-" : "+";
+      return `${operator} ${Math.abs(term)}`;
+    })
+    .join(" ");
 }
 
 function renderUserAnswerPair(result: GradeResult) {
-  const secondOperator = result.userAnswer[1] < 0 ? "-" : "+";
-  const firstCorrect = result.userAnswer[0] === result.correctAnswer[0];
-  const secondCorrect = result.userAnswer[1] === result.correctAnswer[1];
-
   return (
     <span className="inline-flex flex-wrap items-center gap-x-2 gap-y-1">
-      <span className={firstCorrect ? undefined : "text-red-700"}>
+      {result.userAnswer.map((term, index) => {
-        <KatexRenderer latex={`${result.userAnswer[0]}`} output="mathml" />
+        const operator = term < 0 ? "-" : "+";
-      </span>
+        const correct = term === result.correctAnswer[index];
-      <span className={secondCorrect ? undefined : "text-red-700"}>
+        const displayLatex =
-        <KatexRenderer
+          index === 0 ? `${term}` : `${operator} ${Math.abs(term)}`;
-          latex={`${secondOperator} ${Math.abs(result.userAnswer[1])}`}
+
-          output="mathml"
+        return (
-        />
+          <span key={index} className={correct ? undefined : "text-red-700"}>
-      </span>
+            <KatexRenderer latex={displayLatex} output="mathml" />
+          </span>
+        );
+      })}
     </span>
   );
 }
 
 function renderCorrectAnswerPair(result: GradeResult) {
-  const secondOperator = result.correctAnswer[1] < 0 ? "-" : "+";
-  const firstCorrect = result.userAnswer[0] === result.correctAnswer[0];
-  const secondCorrect = result.userAnswer[1] === result.correctAnswer[1];
-
   return (
     <span className="inline-flex flex-wrap items-center gap-x-2 gap-y-1">
-      <span className={firstCorrect ? undefined : "font-bold text-blue-700"}>
+      {result.correctAnswer.map((term, index) => {
-        <KatexRenderer latex={`${result.correctAnswer[0]}`} output="mathml" />
+        const operator = term < 0 ? "-" : "+";
-      </span>
+        const correct = result.userAnswer[index] === term;
-      <span
+        const displayLatex =
-        className={secondCorrect ? undefined : "font-bold text-blue-700"}
+          index === 0 ? `${term}` : `${operator} ${Math.abs(term)}`;
-      >
+
-        <KatexRenderer
+        return (
-          latex={`${secondOperator} ${Math.abs(result.correctAnswer[1])}`}
+          <span
-          output="mathml"
+            key={index}
-        />
+            className={correct ? undefined : "font-bold text-blue-700"}
-      </span>
+          >
+            <KatexRenderer latex={displayLatex} output="mathml" />
+          </span>
+        );
+      })}
     </span>
   );
 }
@@ -102,10 +106,7 @@ export default function ScoreSummary({
 
         <ol className="space-y-3">
           {solvedItems.map(({ problem, result }, index) => {
-            const userAnswerLatex = formatAnswerPairLatex(
+            const userAnswerLatex = formatAnswerLatex(result.userAnswer);
-              result.userAnswer[0],
-              result.userAnswer[1],
-            );
 
             return (
               <AnswerResultLine

components/game/VariableChoiceAnswerForm.tsx

@@ -6,11 +6,11 @@ import KatexRenderer from "@/components/math/KatexRenderer";
 import type { VariableTermChoice } from "@/lib/engine/variable-types";
 
 interface VariableChoiceAnswerFormProps {
-  choices: [VariableTermChoice[], VariableTermChoice[]];
+  choices: VariableTermChoice[][];
-  selectedChoiceIds: [string | null, string | null];
+  selectedChoiceIds: (string | null)[];
-  activeTermIndex: 0 | 1;
+  activeTermIndex: number;
-  pendingChoiceLabels: [string, string];
+  pendingChoiceLabels: string[];
-  onSelectChoice: (termIndex: 0 | 1, choiceId: string) => void;
+  onSelectChoice: (termIndex: number, choiceId: string) => void;
 }
 
 export default function VariableChoiceAnswerForm({
@@ -29,7 +29,7 @@ export default function VariableChoiceAnswerForm({
     firstChoiceRef.current?.focus();
   }, [activeTermIndex]);
 
-  function getSelectedChoice(index: 0 | 1) {
+  function getSelectedChoice(index: number) {
     const selectedChoiceId = selectedChoiceIds[index];
 
     if (!selectedChoiceId) return null;
@@ -42,7 +42,7 @@ export default function VariableChoiceAnswerForm({
       <div className="flex flex-wrap items-center justify-between gap-3">
         <div>
           <p className="text-sm font-semibold text-slate-500">
-            {activeTermIndex === 0 ? "첫째 항" : "둘째 항"}을 고르세요.
+            {activeTermIndex + 1}항을 고르세요.
           </p>
         </div>
         <ol
@@ -51,7 +51,7 @@ export default function VariableChoiceAnswerForm({
         >
           {selectedChoiceIds.map((choiceId, index) => {
             const selected = activeTermIndex === index;
-            const selectedChoice = getSelectedChoice(index as 0 | 1);
+            const selectedChoice = getSelectedChoice(index);
             const completed = choiceId !== null && selectedChoice !== null;
             const statusLabel =
               completed && selectedChoice
@@ -95,7 +95,7 @@ export default function VariableChoiceAnswerForm({
       <div
         className="mt-5 grid gap-3 sm:grid-cols-2"
         role="group"
-        aria-label={`${activeTermIndex === 0 ? "첫째 항" : "둘째 항"} 보기 선택`}
+        aria-label={`${activeTermIndex + 1}항 보기 선택`}
       >
         {activeChoices.map((choice, index) => {
           const selected = selectedChoiceIds[activeTermIndex] === choice.id;

components/game/VariableFeedbackPanel.tsx

@@ -6,7 +6,6 @@ import AnswerResultLine from "@/components/game/AnswerResultLine";
 import type {
   VariableGradeResult,
   VariableParenthesisProblem,
-  VariableParenthesisTerm,
 } from "@/lib/engine/variable-types";
 import { formatVariableTermLatex } from "@/lib/engine/variable-parenthesis";
 
@@ -21,12 +20,6 @@ function formatSignedNumber(value: number) {
   return value < 0 ? `(${value})` : `${value}`;
 }
 
-function formatSignedTerm(term: VariableParenthesisTerm, sign: 1 | -1) {
-  const coefficient = term.coefficient * sign;
-
-  return formatVariableTermLatex({ ...term, coefficient });
-}
-
 export default function VariableFeedbackPanel({
   result,
   problem,
@@ -34,14 +27,18 @@ export default function VariableFeedbackPanel({
   onNext,
 }: VariableFeedbackPanelProps) {
   const nextButtonRef = useRef<HTMLButtonElement>(null);
-  const signedTerms = [
+  const signedTerms = problem.terms.map((term, index) =>
-    formatSignedTerm(problem.firstTerm, 1),
+    formatVariableTermLatex({
-    formatSignedTerm(problem.secondTerm, problem.operator === "-" ? -1 : 1),
+      ...term,
-  ] as const;
+      coefficient:
+        index > 0 && problem.operators[index - 1] === "-"
+          ? -term.coefficient
+          : term.coefficient,
+    }),
+  );
   const feedbackItems = signedTerms.map((termLatex, index) => {
-    const termIndex = index as 0 | 1;
+    const userAnswer = result.userAnswer[index];
-    const userAnswer = result.userAnswer[termIndex];
+    const correctAnswer = result.correctAnswer[index];
-    const correctAnswer = result.correctAnswer[termIndex];
 
     return {
       formulaLatex: `${formatSignedNumber(problem.multiplier)}\\times ${termLatex}`,

components/game/VariableScoreSummary.tsx

@@ -21,14 +21,10 @@ interface VariableScoreSummaryProps {
 }
 
 function renderTermPair(
-  terms: [DistributedVariableTerm | null, DistributedVariableTerm | null],
+  terms: (DistributedVariableTerm | null)[],
-  comparisonTerms: [DistributedVariableTerm | null, DistributedVariableTerm | null],
+  comparisonTerms: (DistributedVariableTerm | null)[],
   mode: "user" | "correct",
 ) {
-  const secondTerm = terms[1];
-  const secondOperator =
-    secondTerm && secondTerm.coefficient < 0 ? "-" : "+";
-
   return (
     <span className="inline-flex flex-wrap items-center gap-x-2 gap-y-1">
       {terms.map((term, index) => {
@@ -49,10 +45,9 @@ function renderTermPair(
             : correct
               ? undefined
               : "font-bold text-blue-700";
+        const operator = term.coefficient < 0 ? "-" : "+";
         const displayLatex =
-          index === 1
+          index === 0 ? term.latex : `${operator} ${term.latex.replace(/^-/, "")}`;
-            ? `${secondOperator} ${term.latex.replace(/^-/, "")}`
-            : term.latex;
 
         return (
           <span key={index} className={className}>
@@ -111,8 +106,9 @@ export default function VariableScoreSummary({
               key={problem.key}
               expressionLatex={problem.latexBefore}
               userAnswerLatex={formatVariableExpressionLatex([
-                result.userAnswer[0] ?? result.correctAnswer[0],
+                ...result.correctAnswer.map(
-                result.userAnswer[1] ?? result.correctAnswer[1],
+                  (term, termIndex) => result.userAnswer[termIndex] ?? term,
+                ),
               ])}
               correctAnswerLatex={problem.latexAfter}
               correct={result.correct}

lib/engine/parenthesis-sign.test.ts

@@ -63,8 +63,19 @@ describe("parenthesis sign problem engine", () => {
     expect(keys.size).toBe(10);
   });
 
+  it("generates the selected number of terms inside parentheses", () => {
+    const problem = generateProblem(4);
+
+    expect(problem.terms).toHaveLength(4);
+    expect(problem.operators).toHaveLength(3);
+    expect(problem.distributedTerms).toHaveLength(4);
+    expect(
+      gradeAnswer(problem, { terms: problem.distributedTerms }).correct,
+    ).toBe(true);
+  });
+
   it("rejects impossible session sizes", () => {
     expect(() => generateSession(0)).toThrow();
-    expect(() => generateSession(145)).toThrow();
+    expect(() => generateSession(1297)).toThrow();
   });
 });

lib/engine/parenthesis-sign.ts

@@ -8,61 +8,138 @@ const MIN_MULTIPLIER = -9;
 const MAX_MULTIPLIER = -1;
 const MIN_TERM = 1;
 const MAX_TERM = 9;
-const MAX_PROBLEM_COUNT = 9 * 8 * 2;
+const MAX_TERM_COUNT = 4;
 
-type ProblemSeed = Pick<
+export type ParenthesisTermCount = 2 | 3 | 4;
-  ParenthesisSignProblem,
+
-  "multiplier" | "a" | "operator" | "b"
+interface ProblemSeed {
->;
+  multiplier: number;
+  terms: number[];
+  operators: ("+" | "-")[];
+}
 
 function randomInt(min: number, max: number) {
   return Math.floor(Math.random() * (max - min + 1)) + min;
 }
 
-function formatLatexTermPair(first: number, second: number) {
+function formatLatexTerms(terms: number[]) {
-  const operator = second < 0 ? "-" : "+";
+  return terms
+    .map((term, index) => {
+      if (index === 0) return `${term}`;
 
-  return `${first} ${operator} ${Math.abs(second)}`;
+      const operator = term < 0 ? "-" : "+";
+      return `${operator} ${Math.abs(term)}`;
+    })
+    .join(" ");
+}
+
+function formatParenthesisTerms(
+  terms: number[],
+  operators: ("+" | "-")[],
+) {
+  return terms
+    .map((term, index) => {
+      if (index === 0) return `${term}`;
+
+      return `${operators[index - 1]} ${term}`;
+    })
+    .join(" ");
 }
 
 function createProblem({
   multiplier,
-  a,
+  terms,
-  operator,
+  operators,
-  b,
 }: ProblemSeed): ParenthesisSignProblem {
-  const distributedA = multiplier * a;
+  const signedTerms = terms.map((term, index) => {
-  const distributedB = operator === "-" ? multiplier * -b : multiplier * b;
+    if (index === 0) return term;
-  const key = `${multiplier}:${a}:${operator}:${b}`;
+
+    return operators[index - 1] === "-" ? -term : term;
+  });
+  const distributedTerms = signedTerms.map((term) => multiplier * term);
+  const [a, b] = terms;
+  const [operator] = operators;
+  const [distributedA, distributedB] = distributedTerms;
+  const key = [
+    multiplier,
+    ...terms.flatMap((term, index) =>
+      index === 0 ? [`${term}`] : [operators[index - 1], `${term}`],
+    ),
+  ].join(":");
 
   return {
     id: `parenthesis-sign:${key}`,
     key,
     multiplier,
+    terms,
+    operators,
     a,
     operator,
     b,
+    distributedTerms,
     distributedA,
     distributedB,
-    latexBefore: `${multiplier}\\left(${a} ${operator} ${b}\\right)`,
+    latexBefore: `${multiplier}\\left(${formatParenthesisTerms(
-    latexAfter: formatLatexTermPair(distributedA, distributedB),
+      terms,
+      operators,
+    )}\\right)`,
+    latexAfter: formatLatexTerms(distributedTerms),
   };
 }
 
-function createAllProblemSeeds() {
+function createTermCombinations(termCount: ParenthesisTermCount) {
+  const combinations: number[][] = [];
+
+  function addTerms(nextTerms: number[]) {
+    if (nextTerms.length === termCount) {
+      combinations.push(nextTerms);
+      return;
+    }
+
+    for (let term = MIN_TERM; term <= MAX_TERM; term += 1) {
+      if (nextTerms.includes(term)) continue;
+
+      addTerms([...nextTerms, term]);
+    }
+  }
+
+  addTerms([]);
+
+  return combinations;
+}
+
+function createOperatorCombinations(termCount: ParenthesisTermCount) {
+  const combinations: ("+" | "-")[][] = [];
+  const operatorCount = termCount - 1;
+
+  function addOperators(nextOperators: ("+" | "-")[]) {
+    if (nextOperators.length === operatorCount) {
+      combinations.push(nextOperators);
+      return;
+    }
+
+    addOperators([...nextOperators, "+"]);
+    addOperators([...nextOperators, "-"]);
+  }
+
+  addOperators([]);
+
+  return combinations;
+}
+
+function createAllProblemSeeds(termCount: ParenthesisTermCount) {
   const seeds: ProblemSeed[] = [];
+  const termCombinations = createTermCombinations(termCount);
+  const operatorCombinations = createOperatorCombinations(termCount);
 
   for (
     let multiplier = MIN_MULTIPLIER;
     multiplier <= MAX_MULTIPLIER;
     multiplier += 1
   ) {
-    for (let a = MIN_TERM; a <= MAX_TERM; a += 1) {
+    for (const terms of termCombinations) {
-      for (let b = MIN_TERM; b <= MAX_TERM; b += 1) {
+      for (const operators of operatorCombinations) {
-        if (a === b) continue;
+        seeds.push({ multiplier, terms, operators });
-
-        seeds.push({ multiplier, a, operator: "+", b });
-        seeds.push({ multiplier, a, operator: "-", b });
       }
     }
   }
@@ -70,7 +147,14 @@ function createAllProblemSeeds() {
   return seeds;
 }
 
-const ALL_PROBLEM_SEEDS = createAllProblemSeeds();
+const ALL_PROBLEM_SEEDS_BY_TERM_COUNT: Record<
+  ParenthesisTermCount,
+  ProblemSeed[]
+> = {
+  2: createAllProblemSeeds(2),
+  3: createAllProblemSeeds(3),
+  4: createAllProblemSeeds(4),
+};
 
 function shuffle<T>(items: T[]) {
   const shuffled = [...items];
@@ -85,42 +169,69 @@ function shuffle<T>(items: T[]) {
   return shuffled;
 }
 
-export function generateProblem(): ParenthesisSignProblem {
+function assertTermCount(termCount: number): asserts termCount is ParenthesisTermCount {
-  const a = randomInt(MIN_TERM, MAX_TERM);
+  if (!Number.isInteger(termCount) || termCount < 2 || termCount > MAX_TERM_COUNT) {
-  let b = randomInt(MIN_TERM, MAX_TERM);
+    throw new Error("termCount must be 2, 3, or 4.");
+  }
+}
 
-  while (a === b) {
+export function generateProblem(
-    b = randomInt(MIN_TERM, MAX_TERM);
+  termCount: ParenthesisTermCount = 2,
+): ParenthesisSignProblem {
+  assertTermCount(termCount);
+
+  const terms: number[] = [];
+
+  while (terms.length < termCount) {
+    const term = randomInt(MIN_TERM, MAX_TERM);
+
+    if (!terms.includes(term)) {
+      terms.push(term);
+    }
   }
 
   return createProblem({
     multiplier: randomInt(MIN_MULTIPLIER, MAX_MULTIPLIER),
-    a,
+    terms,
-    operator: Math.random() < 0.5 ? "+" : "-",
+    operators: Array.from({ length: termCount - 1 }, () =>
-    b,
+      Math.random() < 0.5 ? "+" : "-",
+    ),
   });
 }
 
-export function generateSession(count = 10): ParenthesisSignProblem[] {
+export function generateSession(
+  count = 10,
+  termCount: ParenthesisTermCount = 2,
+): ParenthesisSignProblem[] {
   if (!Number.isInteger(count) || count < 1) {
     throw new Error("count must be a positive integer.");
   }
 
-  if (count > MAX_PROBLEM_COUNT) {
+  assertTermCount(termCount);
-    throw new Error(`count cannot exceed ${MAX_PROBLEM_COUNT}.`);
+
+  const seeds = ALL_PROBLEM_SEEDS_BY_TERM_COUNT[termCount];
+
+  if (count > seeds.length) {
+    throw new Error(`count cannot exceed ${seeds.length}.`);
   }
 
-  return shuffle(ALL_PROBLEM_SEEDS).slice(0, count).map(createProblem);
+  return shuffle(seeds).slice(0, count).map(createProblem);
 }
 
 export function gradeAnswer(
   problem: ParenthesisSignProblem,
   answer: UserAnswer,
 ): GradeResult {
+  const userAnswer =
+    answer.terms ?? (answer.a !== undefined && answer.b !== undefined
+      ? [answer.a, answer.b]
+      : []);
+
   return {
     correct:
-      answer.a === problem.distributedA && answer.b === problem.distributedB,
+      userAnswer.length === problem.distributedTerms.length &&
-    userAnswer: [answer.a, answer.b],
+      userAnswer.every((value, index) => value === problem.distributedTerms[index]),
-    correctAnswer: [problem.distributedA, problem.distributedB],
+    userAnswer,
+    correctAnswer: problem.distributedTerms,
   };
 }

lib/engine/types.ts

@@ -2,9 +2,12 @@ export interface ParenthesisSignProblem {
   id: string;
   key: string;
   multiplier: number;
+  terms: number[];
+  operators: ("+" | "-")[];
   a: number;
   operator: "+" | "-";
   b: number;
+  distributedTerms: number[];
   distributedA: number;
   distributedB: number;
   latexBefore: string;
@@ -12,12 +15,13 @@ export interface ParenthesisSignProblem {
 }
 
 export interface UserAnswer {
-  a: number;
+  terms?: number[];
-  b: number;
+  a?: number;
+  b?: number;
 }
 
 export interface GradeResult {
   correct: boolean;
-  userAnswer: [number, number];
+  userAnswer: number[];
-  correctAnswer: [number, number];
+  correctAnswer: number[];
 }

lib/engine/variable-parenthesis.test.ts

@@ -10,7 +10,7 @@ import type { VariableParenthesisProblem } from "./variable-types";
 
 function findCorrectChoiceIds(problem: VariableParenthesisProblem) {
   return problem.correctTerms.map((term, index) => {
-    const choices = problem.choices[index as 0 | 1];
+    const choices = problem.choices[index];
     const choice = choices.find(
       (item) =>
         item.coefficient === term.coefficient && item.variable === term.variable,
@@ -19,7 +19,7 @@ function findCorrectChoiceIds(problem: VariableParenthesisProblem) {
     if (!choice) throw new Error("correct choice not found.");
 
     return choice.id;
-  }) as [string, string];
+  });
 }
 
 describe("variable parenthesis engine", () => {
@@ -97,6 +97,21 @@ describe("variable parenthesis engine", () => {
     expect(keys.size).toBe(10);
   });
 
+  it("generates the selected number of variable choices", () => {
+    const problem = generateVariableParenthesisProblem(4);
+
+    expect(problem.terms).toHaveLength(4);
+    expect(problem.operators).toHaveLength(3);
+    expect(problem.correctTerms).toHaveLength(4);
+    expect(problem.choices).toHaveLength(4);
+    expect(problem.terms.filter((term) => term.kind === "variable")).toHaveLength(1);
+    expect(
+      gradeVariableParenthesisAnswer(problem, {
+        selectedChoiceIds: findCorrectChoiceIds(problem),
+      }).correct,
+    ).toBe(true);
+  });
+
   it("formats expressions with variable terms", () => {
     expect(
       formatVariableExpressionLatex([

lib/engine/variable-parenthesis.ts

@@ -11,13 +11,14 @@ const MIN_MULTIPLIER = -9;
 const MAX_MULTIPLIER = -1;
 const MIN_COEFFICIENT = 1;
 const MAX_COEFFICIENT = 9;
-const MAX_PROBLEM_COUNT = 9 * 9 * 9 * 2 * 2;
+const MAX_TERM_COUNT = 4;
+
+export type VariableParenthesisTermCount = 2 | 3 | 4;
 
 interface VariableProblemSeed {
   multiplier: number;
-  operator: "+" | "-";
+  terms: VariableParenthesisTerm[];
-  firstTerm: VariableParenthesisTerm;
+  operators: ("+" | "-")[];
-  secondTerm: VariableParenthesisTerm;
 }
 
 function randomInt(min: number, max: number) {
@@ -52,6 +53,26 @@ function createVariableTerm(coefficient: number): VariableParenthesisTerm {
   };
 }
 
+function createUniqueConstantTerms(
+  baseCoefficient: number,
+  count: number,
+): VariableParenthesisTerm[] {
+  const used = new Set<number>();
+  const terms: VariableParenthesisTerm[] = [];
+  let candidate = baseCoefficient;
+
+  while (terms.length < count) {
+    const coef = ((candidate - 1) % MAX_COEFFICIENT) + 1;
+    if (!used.has(coef)) {
+      used.add(coef);
+      terms.push(createConstantTerm(coef));
+    }
+    candidate += 1;
+  }
+
+  return terms;
+}
+
 function termKey(term: VariableParenthesisTerm) {
   return `${term.kind}:${term.coefficient}`;
 }
@@ -79,18 +100,21 @@ function formatParenthesisTermLatex(term: VariableParenthesisTerm) {
 }
 
 export function formatVariableExpressionLatex(
-  terms: [DistributedVariableTerm, DistributedVariableTerm],
+  terms: DistributedVariableTerm[],
 ) {
-  const [firstTerm, secondTerm] = terms;
+  return terms
-  const operator = secondTerm.coefficient < 0 ? "-" : "+";
+    .map((term, index) => {
-  const positiveSecondTerm = {
+      if (index === 0) return term.latex;
-    ...secondTerm,
-    coefficient: Math.abs(secondTerm.coefficient),
-  };
 
-  return `${firstTerm.latex} ${operator} ${formatVariableTermLatex(
+      const operator = term.coefficient < 0 ? "-" : "+";
-    positiveSecondTerm,
+      const positiveTerm = {
-  )}`;
+        ...term,
+        coefficient: Math.abs(term.coefficient),
+      };
+
+      return `${operator} ${formatVariableTermLatex(positiveTerm)}`;
+    })
+    .join(" ");
 }
 
 function distributeTerm(
@@ -110,7 +134,7 @@ function distributeTerm(
 
 function createChoice(
   key: string,
-  termIndex: 0 | 1,
+  termIndex: number,
   term: DistributedVariableTerm,
   coefficient: number,
 ): VariableTermChoice {
@@ -126,7 +150,7 @@ function createChoice(
 
 function createChoices(
   key: string,
-  termIndex: 0 | 1,
+  termIndex: number,
   term: DistributedVariableTerm,
 ) {
   const absoluteCoefficient = Math.abs(term.coefficient);
@@ -139,40 +163,69 @@ function createChoices(
 }
 
 function createProblem(seed: VariableProblemSeed): VariableParenthesisProblem {
-  const { multiplier, operator, firstTerm, secondTerm } = seed;
+  const { multiplier, terms, operators } = seed;
+  const [firstTerm, secondTerm] = terms;
+  const [operator] = operators;
   const key = [
     multiplier,
-    termKey(firstTerm),
+    ...terms.flatMap((term, index) =>
-    operator,
+      index === 0 ? [termKey(term)] : [operators[index - 1], termKey(term)],
-    termKey(secondTerm),
+    ),
   ].join(":");
-  const correctTerms: [DistributedVariableTerm, DistributedVariableTerm] = [
+  const correctTerms = terms.map((term, index) =>
-    distributeTerm(multiplier, firstTerm, 1),
+    distributeTerm(
-    distributeTerm(multiplier, secondTerm, operator === "-" ? -1 : 1),
+      multiplier,
-  ];
+      term,
-  const choices: [VariableTermChoice[], VariableTermChoice[]] = [
+      index === 0 || operators[index - 1] === "+" ? 1 : -1,
-    createChoices(key, 0, correctTerms[0]),
+    ),
-    createChoices(key, 1, correctTerms[1]),
+  );
-  ];
+  const choices = correctTerms.map((term, index) =>
+    createChoices(key, index, term),
+  );
 
   return {
     id: `variable-parenthesis:${key}`,
     key,
     multiplier,
+    terms,
+    operators,
     operator,
     firstTerm,
     secondTerm,
     correctTerms,
     choices,
-    latexBefore: `${multiplier}\\left(${formatParenthesisTermLatex(
+    latexBefore: `${multiplier}\\left(${terms
-      firstTerm,
+      .map((term, index) => {
-    )} ${operator} ${formatParenthesisTermLatex(secondTerm)}\\right)`,
+        if (index === 0) return formatParenthesisTermLatex(term);
+
+        return `${operators[index - 1]} ${formatParenthesisTermLatex(term)}`;
+      })
+      .join(" ")}\\right)`,
     latexAfter: formatVariableExpressionLatex(correctTerms),
   };
 }
 
-function createAllProblemSeeds() {
+function createOperatorCombinations(termCount: VariableParenthesisTermCount) {
+  const combinations: ("+" | "-")[][] = [];
+
+  function addOperators(nextOperators: ("+" | "-")[]) {
+    if (nextOperators.length === termCount - 1) {
+      combinations.push(nextOperators);
+      return;
+    }
+
+    addOperators([...nextOperators, "+"]);
+    addOperators([...nextOperators, "-"]);
+  }
+
+  addOperators([]);
+
+  return combinations;
+}
+
+function createAllProblemSeeds(termCount: VariableParenthesisTermCount) {
   const seeds: VariableProblemSeed[] = [];
+  const operatorCombinations = createOperatorCombinations(termCount);
 
   for (
     let multiplier = MIN_MULTIPLIER;
@@ -189,19 +242,22 @@ function createAllProblemSeeds() {
         variableCoefficient <= MAX_COEFFICIENT;
         variableCoefficient += 1
       ) {
-        for (const operator of ["+", "-"] as const) {
+        for (let variableIndex = 0; variableIndex < termCount; variableIndex += 1) {
-          seeds.push({
+          const constantTerms = createUniqueConstantTerms(constant, termCount - 1);
-            multiplier,
+          let constantTermIndex = 0;
-            operator,
+          const terms = Array.from({ length: termCount }, (_, index) =>
-            firstTerm: createVariableTerm(variableCoefficient),
+            index === variableIndex
-            secondTerm: createConstantTerm(constant),
+              ? createVariableTerm(variableCoefficient)
-          });
+              : constantTerms[constantTermIndex++],
-          seeds.push({
+          );
-            multiplier,
+
-            operator,
+          for (const operators of operatorCombinations) {
-            firstTerm: createConstantTerm(constant),
+            seeds.push({
-            secondTerm: createVariableTerm(variableCoefficient),
+              multiplier,
-          });
+              terms,
+              operators,
+            });
+          }
         }
       }
     }
@@ -210,43 +266,70 @@ function createAllProblemSeeds() {
   return seeds;
 }
 
-const ALL_PROBLEM_SEEDS = createAllProblemSeeds();
+const ALL_PROBLEM_SEEDS_BY_TERM_COUNT: Record<
+  VariableParenthesisTermCount,
+  VariableProblemSeed[]
+> = {
+  2: createAllProblemSeeds(2),
+  3: createAllProblemSeeds(3),
+  4: createAllProblemSeeds(4),
+};
+
+function assertTermCount(
+  termCount: number,
+): asserts termCount is VariableParenthesisTermCount {
+  if (!Number.isInteger(termCount) || termCount < 2 || termCount > MAX_TERM_COUNT) {
+    throw new Error("termCount must be 2, 3, or 4.");
+  }
+}
+
+export function generateVariableParenthesisProblem(
+  termCount: VariableParenthesisTermCount = 2,
+): VariableParenthesisProblem {
+  assertTermCount(termCount);
 
-export function generateVariableParenthesisProblem(): VariableParenthesisProblem {
   const constant = randomInt(MIN_COEFFICIENT, MAX_COEFFICIENT);
   const variableCoefficient = randomInt(MIN_COEFFICIENT, MAX_COEFFICIENT);
-  const variableFirst = Math.random() < 0.5;
+  const variableIndex = randomInt(0, termCount - 1);
-  const operator = Math.random() < 0.5 ? "+" : "-";
+
+  const constantTerms = createUniqueConstantTerms(constant, termCount - 1);
+  let constantTermIndex = 0;
 
   return createProblem({
     multiplier: randomInt(MIN_MULTIPLIER, MAX_MULTIPLIER),
-    operator,
+    terms: Array.from({ length: termCount }, (_, index) =>
-    firstTerm: variableFirst
+      index === variableIndex
-      ? createVariableTerm(variableCoefficient)
+        ? createVariableTerm(variableCoefficient)
-      : createConstantTerm(constant),
+        : constantTerms[constantTermIndex++],
-    secondTerm: variableFirst
+    ),
-      ? createConstantTerm(constant)
+    operators: Array.from({ length: termCount - 1 }, () =>
-      : createVariableTerm(variableCoefficient),
+      Math.random() < 0.5 ? "+" : "-",
+    ),
   });
 }
 
 export function generateVariableParenthesisSession(
   count = 10,
+  termCount: VariableParenthesisTermCount = 2,
 ): VariableParenthesisProblem[] {
   if (!Number.isInteger(count) || count < 1) {
     throw new Error("count must be a positive integer.");
   }
 
-  if (count > MAX_PROBLEM_COUNT) {
+  assertTermCount(termCount);
-    throw new Error(`count cannot exceed ${MAX_PROBLEM_COUNT}.`);
+
+  const seeds = ALL_PROBLEM_SEEDS_BY_TERM_COUNT[termCount];
+
+  if (count > seeds.length) {
+    throw new Error(`count cannot exceed ${seeds.length}.`);
   }
 
-  return shuffle(ALL_PROBLEM_SEEDS).slice(0, count).map(createProblem);
+  return shuffle(seeds).slice(0, count).map(createProblem);
 }
 
 function findSelectedChoice(
   problem: VariableParenthesisProblem,
-  termIndex: 0 | 1,
+  termIndex: number,
   choiceId: string | null,
 ): DistributedVariableTerm | null {
   if (!choiceId) return null;
@@ -267,16 +350,14 @@ export function gradeVariableParenthesisAnswer(
   problem: VariableParenthesisProblem,
   answer: VariableUserAnswer,
 ): VariableGradeResult {
-  const userAnswer: [
+  const userAnswer = problem.correctTerms.map((_, index) =>
-    DistributedVariableTerm | null,
+    findSelectedChoice(problem, index, answer.selectedChoiceIds[index] ?? null),
-    DistributedVariableTerm | null,
+  );
-  ] = [
-    findSelectedChoice(problem, 0, answer.selectedChoiceIds[0]),
-    findSelectedChoice(problem, 1, answer.selectedChoiceIds[1]),
-  ];
   const correct =
-    userAnswer[0]?.coefficient === problem.correctTerms[0].coefficient &&
+    userAnswer.length === problem.correctTerms.length &&
-    userAnswer[1]?.coefficient === problem.correctTerms[1].coefficient;
+    userAnswer.every(
+      (term, index) => term?.coefficient === problem.correctTerms[index].coefficient,
+    );
 
   return {
     correct,

lib/engine/variable-types.ts

@@ -24,21 +24,23 @@ export interface VariableParenthesisProblem {
   id: string;
   key: string;
   multiplier: number;
+  terms: VariableParenthesisTerm[];
+  operators: ("+" | "-")[];
   operator: "+" | "-";
   firstTerm: VariableParenthesisTerm;
   secondTerm: VariableParenthesisTerm;
-  correctTerms: [DistributedVariableTerm, DistributedVariableTerm];
+  correctTerms: DistributedVariableTerm[];
-  choices: [VariableTermChoice[], VariableTermChoice[]];
+  choices: VariableTermChoice[][];
   latexBefore: string;
   latexAfter: string;
 }
 
 export interface VariableUserAnswer {
-  selectedChoiceIds: [string | null, string | null];
+  selectedChoiceIds: (string | null)[];
 }
 
 export interface VariableGradeResult {
   correct: boolean;
-  userAnswer: [DistributedVariableTerm | null, DistributedVariableTerm | null];
+  userAnswer: (DistributedVariableTerm | null)[];
-  correctAnswer: [DistributedVariableTerm, DistributedVariableTerm];
+  correctAnswer: DistributedVariableTerm[];
 }

store/gameStore.ts

@@ -4,6 +4,7 @@ import {
   generateSession,
   gradeAnswer,
 } from "@/lib/engine/parenthesis-sign";
+import type { ParenthesisTermCount } from "@/lib/engine/parenthesis-sign";
 import type {
   GradeResult,
   ParenthesisSignProblem,
@@ -14,42 +15,56 @@ export interface GameSession {
   problems: ParenthesisSignProblem[];
   currentIndex: number;
   results: (GradeResult | null)[];
+  termCount: ParenthesisTermCount;
 }
 
 export type ProblemCount = 5 | 10;
+export type MaxTermCount = ParenthesisTermCount;
 
 interface GameState {
   session: GameSession | null;
   selectedProblemCount: ProblemCount;
+  selectedMaxTermCount: MaxTermCount;
   setProblemCount: (count: ProblemCount) => void;
-  initSession: (count?: ProblemCount) => void;
+  setMaxTermCount: (count: MaxTermCount) => void;
+  initSession: (count?: ProblemCount, maxTermCount?: MaxTermCount) => void;
   submitAnswer: (answer: UserAnswer) => void;
   nextProblem: () => void;
   resetSession: () => void;
 }
 
 const DEFAULT_SESSION_COUNT: ProblemCount = 10;
+const DEFAULT_MAX_TERM_COUNT: MaxTermCount = 2;
 
-function createSession(count: ProblemCount = DEFAULT_SESSION_COUNT): GameSession {
+function createSession(
-  const problems = generateSession(count);
+  count: ProblemCount = DEFAULT_SESSION_COUNT,
+  maxTermCount: MaxTermCount = DEFAULT_MAX_TERM_COUNT,
+): GameSession {
+  const problems = generateSession(count, maxTermCount);
 
   return {
     problems,
     currentIndex: 0,
     results: problems.map(() => null),
+    termCount: maxTermCount,
   };
 }
 
 export const useGameStore = create<GameState>((set, get) => ({
   session: null,
   selectedProblemCount: DEFAULT_SESSION_COUNT,
+  selectedMaxTermCount: DEFAULT_MAX_TERM_COUNT,
   setProblemCount: (count) => {
     set({ selectedProblemCount: count });
   },
-  initSession: (count) => {
+  setMaxTermCount: (count) => {
+    set({ selectedMaxTermCount: count });
+  },
+  initSession: (count, maxTermCount) => {
     const selectedProblemCount = count ?? get().selectedProblemCount;
+    const selectedMaxTermCount = maxTermCount ?? get().selectedMaxTermCount;
 
-    set({ session: createSession(selectedProblemCount) });
+    set({ session: createSession(selectedProblemCount, selectedMaxTermCount) });
   },
   submitAnswer: (answer) => {
     const { session } = get();
@@ -83,6 +98,11 @@ export const useGameStore = create<GameState>((set, get) => ({
     });
   },
   resetSession: () => {
-    set({ session: createSession(get().selectedProblemCount) });
+    set({
+      session: createSession(
+        get().selectedProblemCount,
+        get().selectedMaxTermCount,
+      ),
+    });
   },
 }));

store/variableGameStore.ts

@@ -4,6 +4,7 @@ import {
   generateVariableParenthesisSession,
   gradeVariableParenthesisAnswer,
 } from "@/lib/engine/variable-parenthesis";
+import type { VariableParenthesisTermCount } from "@/lib/engine/variable-parenthesis";
 import type {
   VariableGradeResult,
   VariableParenthesisProblem,
@@ -14,44 +15,59 @@ export interface VariableGameSession {
   problems: VariableParenthesisProblem[];
   currentIndex: number;
   results: (VariableGradeResult | null)[];
+  termCount: VariableParenthesisTermCount;
 }
 
 export type VariableProblemCount = 5 | 10;
+export type VariableMaxTermCount = VariableParenthesisTermCount;
 
 interface VariableGameState {
   session: VariableGameSession | null;
   selectedProblemCount: VariableProblemCount;
+  selectedMaxTermCount: VariableMaxTermCount;
   setProblemCount: (count: VariableProblemCount) => void;
-  initSession: (count?: VariableProblemCount) => void;
+  setMaxTermCount: (count: VariableMaxTermCount) => void;
+  initSession: (
+    count?: VariableProblemCount,
+    maxTermCount?: VariableMaxTermCount,
+  ) => void;
   submitAnswer: (answer: VariableUserAnswer) => void;
   nextProblem: () => void;
   resetSession: () => void;
 }
 
 const DEFAULT_SESSION_COUNT: VariableProblemCount = 10;
+const DEFAULT_MAX_TERM_COUNT: VariableMaxTermCount = 2;
 
 function createSession(
   count: VariableProblemCount = DEFAULT_SESSION_COUNT,
+  maxTermCount: VariableMaxTermCount = DEFAULT_MAX_TERM_COUNT,
 ): VariableGameSession {
-  const problems = generateVariableParenthesisSession(count);
+  const problems = generateVariableParenthesisSession(count, maxTermCount);
 
   return {
     problems,
     currentIndex: 0,
     results: problems.map(() => null),
+    termCount: maxTermCount,
   };
 }
 
 export const useVariableGameStore = create<VariableGameState>((set, get) => ({
   session: null,
   selectedProblemCount: DEFAULT_SESSION_COUNT,
+  selectedMaxTermCount: DEFAULT_MAX_TERM_COUNT,
   setProblemCount: (count) => {
     set({ selectedProblemCount: count });
   },
-  initSession: (count) => {
+  setMaxTermCount: (count) => {
+    set({ selectedMaxTermCount: count });
+  },
+  initSession: (count, maxTermCount) => {
     const selectedProblemCount = count ?? get().selectedProblemCount;
+    const selectedMaxTermCount = maxTermCount ?? get().selectedMaxTermCount;
 
-    set({ session: createSession(selectedProblemCount) });
+    set({ session: createSession(selectedProblemCount, selectedMaxTermCount) });
   },
   submitAnswer: (answer) => {
     const { session } = get();
@@ -85,6 +101,11 @@ export const useVariableGameStore = create<VariableGameState>((set, get) => ({
     });
   },
   resetSession: () => {
-    set({ session: createSession(get().selectedProblemCount) });
+    set({
+      session: createSession(
+        get().selectedProblemCount,
+        get().selectedMaxTermCount,
+      ),
+    });
   },
 }));