Crows on Fence Riddle

If there are fifteen crows on a fence and the farmer shoots a third of them, how many crows are left?




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A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
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When I divide it by 6, the remainder is 5.
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When I divide it by 10, the remainder is 9.

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When I looked for a smaller number with this property I couldn't find one.

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I have a hole in my back and legs I lack.
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Amazing Facts

Gamers

In 2011, people playing Foldit, an online puzzle game about protein folding, resolved the structure of an enzyme that causes an Aids-like disease in monkeys. Researchers had been working on the problem for 13 years. The gamers solved it in three weeks.