The pile that always leaves one
A pile of coins has a stubborn property: split it among 2, 3, 4, 5, or 6 people and there is always exactly one coin left over. But split it among 7 people and it divides evenly, none left over. What is the smallest number of coins (greater than one) in the pile?
Show hints (2)+
- "Remainder 1 for 2,3,4,5,6" means N−1 is a multiple of their LCM (=60), so N = 60k+1.
- Now force 7 | (60k+1): solve 4k+1 ≡ 0 (mod 7) for the smallest k.
Answer
Reveal answer →Final answer
301
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