Puzzle of the day · No. 11 · 23 October
Worn buttons
Lucky has forgotten the door code, four digits. Only buttons 1, 3 and 7 on the panel are worn, so the code uses them and each appears at least once. How many combinations will Lucky have to try in the worst case?
Answer: 36. One of the three digits appears twice, and it can be chosen in three ways. Then four digits, two of them the same, can be arranged in 4! / 2 = 12 ways. 3 × 12 = 36.
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