Add hint cooldown and raise player limit to 15

- Lock hint button for 10s per riddle with live countdown display
- Clear hint timer when player finishes their race
- Raise max players from 8 to 15 with 15 distinct player colors

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

public/game.js

@@ -11,6 +11,7 @@ let myRoomId   = null;
 let amHost     = false;
 let myFinished = false;
 let carEmojiMap = {}; // playerId → car emoji
+let hintTimer  = null; // countdown interval for hint button
 
 // ── Screen helpers ─────────────────────
 const screens = {
@@ -225,6 +226,28 @@ function showRiddle(riddle, num, total) {
   hintBox.style.display     = 'none';
   hintText.textContent      = '';
   answerInput.focus();
+  startHintCountdown();
+}
+
+function startHintCountdown() {
+  clearInterval(hintTimer);
+  hintBox.style.display = 'none';
+  hintBtn.disabled = true;
+
+  let remaining = 10;
+  hintBtn.textContent = `💡 Hint (${remaining}s)`;
+
+  hintTimer = setInterval(() => {
+    remaining--;
+    if (remaining <= 0) {
+      clearInterval(hintTimer);
+      hintTimer = null;
+      hintBtn.disabled = false;
+      hintBtn.textContent = '💡 Hint';
+    } else {
+      hintBtn.textContent = `💡 Hint (${remaining}s)`;
+    }
+  }, 1000);
 }
 
 function setFeedback(msg, isCorrect) {
@@ -359,6 +382,8 @@ socket.on('answerResult', ({ correct, finished, finishPosition, riddle, riddleNu
 
   if (finished) {
     myFinished = true;
+    clearInterval(hintTimer);
+    hintTimer = null;
     progressFill.style.width = '100%';
     riddlePanel.style.display   = 'none';
     finishedBanner.style.display = 'flex';