문제 수 선택 기능 추가 - 5문제 / 10문제

app/(game)/play/page.tsx

@@ -1,5 +1,16 @@
 import PlayClient from "./PlayClient";
+import type { ProblemCount } from "@/store/gameStore";
 
-export default function PlayPage() {
-  return <PlayClient />;
+interface PlayPageProps {
+  searchParams?: {
+    count?: string;
+  };
+}
+
+function parseProblemCount(count?: string): ProblemCount {
+  return count === "5" ? 5 : 10;
+}
+
+export default function PlayPage({ searchParams }: PlayPageProps) {
+  return <PlayClient problemCount={parseProblemCount(searchParams?.count)} />;
 }