If a7! + b8! + c9! + d10! = x, where a, b, c and d are natural numbers that are not multiples of 10, then how many distinct values of unit’s digit of x are possible?

Question

Answer 1

it could be written as 7!(a+8b+72c+720d) so the expression is a multiple of 7!..... since 7!=5040 any multiple of 7! will have 0 as units digit therefore only one value of units digit is possible

Answer 2

it could be written as 7!(a+8b+72c+720d) so the expression is a multiple of 7!..... since 7!=5040 any multiple of 7! will have 0 as units digit therefore only one value of units digit is possible

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If a7! + b8! + c9! + d10! = x, where a, b, c and d are natural numbers that are not multiples of 10, then how many distinct values of unit’s digit of x are possible?

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