모바일 환경에서만 실행되는 가상 키보드 추가

app/(game)/play/PlayClient.tsx

@@ -16,13 +16,14 @@ import KatexRenderer from "@/components/math/KatexRenderer";
 import { useGameStore } from "@/store/gameStore";
 import type { ProblemCount } from "@/store/gameStore";
 
-const MOBILE_BREAKPOINT_QUERY = "(min-width: 640px)";
+const DESKTOP_INPUT_DEVICE_QUERY = "(any-hover: hover) and (any-pointer: fine)";
 const MOBILE_KEYBOARD_SPACER_OFFSET = 480;
+const REAL_NUMBER_PATTERN = /^-?\d+(?:\.\d+)?$/;
 
 function parseAnswer(value: string) {
   const trimmed = value.trim();
 
-  if (!/^-?\d+$/.test(trimmed)) return null;
+  if (!REAL_NUMBER_PATTERN.test(trimmed)) return null;
 
   return Number(trimmed);
 }
@@ -108,7 +109,7 @@ export default function PlayClient({ problemCount }: PlayClientProps) {
     const parsedB = parseAnswer(answerB);
 
     if (parsedA === null || parsedB === null) {
-      setInputError("두 칸 모두 정수로 입력하세요.");
+      setInputError("두 칸 모두 실수로 입력하세요.");
       return;
     }
 
@@ -128,7 +129,7 @@ export default function PlayClient({ problemCount }: PlayClientProps) {
   }, []);
 
   const scrollKatexToViewportTop = useCallback(() => {
-    if (window.matchMedia(MOBILE_BREAKPOINT_QUERY).matches) return;
+    if (window.matchMedia(DESKTOP_INPUT_DEVICE_QUERY).matches) return;
 
     function alignKatex() {
       const katexElement =
@@ -301,7 +302,6 @@ export default function PlayClient({ problemCount }: PlayClientProps) {
         {!submitted && mobileFocusSpacerHeight > 0 ? (
           <div
             aria-hidden="true"
-            className="sm:hidden"
             style={{ height: mobileFocusSpacerHeight }}
           />
         ) : null}