Candy reasoning puzzle
Copy the candy puzzle, then reveal and compare the 21-candy solution and the blind-draw answer of 29.
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A bag contains round candies: 7 apple, 9 peach, 8 watermelon; and star-shaped candies: 7 apple, 6 peach, 4 watermelon. Before each draw, you may choose the shape by touch, but not the flavor. After drawing, you can identify the flavor and use it to choose the next shape. No candies are replaced. You must guarantee a pair of round apple + star peach, or round peach + star apple. What is the smallest draw budget that guarantees success? Give a strategy and explain why a smaller budget cannot suffice. Do not use tools or the web.
With shape selection: 21 candies. Draw rounds until the first apple or peach: at most 9 draws (8 watermelon + 1). If it is apple, draw stars until peach: at most 12 more (7 apple + 4 watermelon + 1 peach), totaling 21. If it is peach, a star apple needs at most 11 more, totaling 20.
Why 20 cannot guarantee success: an adversary can order rounds as 8 watermelon, 9 peach, then apple; and stars as 4 watermelon, 6 peach, then apple. Any interleaving needs at least 9 + 11 = 21 draws for round peach + star apple, or 18 + 5 = 23 for round apple + star peach. This legal ordering defeats every 20-draw strategy.
Count an answer as correct only if it gives 21 and a valid strategy, not just the number.
Why is the blind-draw answer 29?
Blind-draw version: if you cannot select even the shape before drawing, keep the same counts and target; the answer becomes 29. All 12 watermelon plus all 16 round apple/peach candies give 28 without a pair. A pair-free non-watermelon set can contain at most all rounds (16), all stars (13), all apples (14), or all peaches (15). Thus draw 29 guarantees a pair.
What the result means
Performance on this puzzle cannot identify a model or prove account restrictions or a downgrade. Public answers can be memorized or retrieved. This site does not record your result.
Principles and sources
Community puzzle and discussion. We clarified shape selection, flavor observation after drawing, and adaptive choices. Independent exhaustive worst-case verification confirms both optimal values; the bounds are explained above. We have not validated this as a diagnostic using ChatGPT accounts.