Add Word Wrangler demos

examples/word-wrangler-gemini-live/client/src/utils/formatTime.ts

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+/**
+ * Formats seconds into MM:SS format
+ */
+export function formatTime(seconds: number): string {
+  const mins = Math.floor(seconds / 60);
+  const secs = seconds % 60;
+  return `${mins}:${secs < 10 ? '0' : ''}${secs}`;
+}

examples/word-wrangler-gemini-live/client/src/utils/timerUtils.ts

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+/**
+ * Safely clears any type of timer
+ * @param timer The timer to clear
+ * @returns null to reassign to the timer reference
+ */
+export function clearTimer(timer: NodeJS.Timeout | null): null {
+  if (timer) {
+    clearTimeout(timer);
+  }
+  return null;
+}
+
+/**
+ * Creates a countdown timer that calls the callback every second
+ * @returns A function to stop the timer
+ */
+export function createCountdownTimer(
+  durationSeconds: number,
+  onTick: (secondsLeft: number) => void,
+  onComplete: () => void
+): () => void {
+  let secondsLeft = durationSeconds;
+
+  const timer = setInterval(() => {
+    secondsLeft--;
+    onTick(secondsLeft);
+
+    if (secondsLeft <= 0) {
+      clearInterval(timer);
+      onComplete();
+    }
+  }, 1000);
+
+  return () => {
+    clearInterval(timer);
+  };
+}

examples/word-wrangler-gemini-live/client/src/utils/wordDetection.ts

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+import { TRANSCRIPT_PATTERNS } from '@/constants/gameConstants';
+
+/**
+ * Checks if a transcript contains a correct guess for the target word
+ */
+export function detectWordGuess(transcript: string, targetWord: string) {
+  const currentWordLower = targetWord.toLowerCase().trim();
+
+  // Primary detection: Look for explicit guesses
+  const guessPattern = TRANSCRIPT_PATTERNS.GUESS_PATTERN;
+  const guessMatch = transcript.match(guessPattern);
+
+  if (guessMatch) {
+    // Extract the guessed word from whichever group matched (group 1 or 2)
+    let guessedWord = (guessMatch[1] || guessMatch[2] || '')
+      .toLowerCase()
+      .trim();
+
+    // Remove articles ("a", "an", "the") from the beginning of the guessed word
+    guessedWord = guessedWord.replace(/^(a|an|the)\s+/i, '');
+
+    return {
+      isCorrect: guessedWord === currentWordLower,
+      isExplicitGuess: true,
+      guessedWord,
+    };
+  }
+
+  // Secondary detection: Check if word appears in transcript
+  const containsWord = transcript.toLowerCase().includes(currentWordLower);
+
+  return {
+    isCorrect: containsWord,
+    isExplicitGuess: false,
+    guessedWord: containsWord ? targetWord : null,
+  };
+}