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# The "aha!" problems - 6 fascinating factorial

## Question

We denote by factorial n! the product of the first n integers.

23! = 2585201ab38884976640000.

Without performing multiplications, find the digits denoted here by a and b.

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Sum of all digits = 86+a+b. 9|86+a+b, so a+b equals 4 or 13.

Sum of odd position digits - sum of even position digits = 10+b-a. 11|10+b-a, so b-a = 1. Hence b = 7 and a = 6.

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