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Quickie XI (Posted on 2017-11-27)

What is the last digit in S=sum(n=1 to 99) n!

See The Solution Submitted by Ady TZIDON

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Puzzle Solution

Comment 3 of 3 |

Let F = sum(n=5 to 99) n!

Since, each of j! is divisible by 10, when j=5(1)99, it follows that:

F = 0 (mod 10)

Then:

S (mod 10) = (1!+2!+3!+4!) (Mod 10)

= 3

Consequently, the required last digit is 3.

Posted by K Sengupta on 2022-01-28 08:08:42

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