I am thinking of a fifty-digit number divisible by 239, of which, each digit is the same, except the ones digit. What is the ones digit?
(In reply to
Puzzle Solution by K Sengupta)
If we were given that each of the digits except the first digit (reading left to right) is a 1: then, denoting the number by N and the first digit by D, we would have observed that:
N=D*10^49 +R(49), where R(x) denotes the xth repunit.
As it has already been proven that 239| R(49), the we would have:
N(mod 239) = D*10^49
Or, D*10^49 =0(mod 239)
Since 239 does not divide 10^49, this is possible when:
D=0
Then, the ones digit would have been zero.
Edited on September 18, 2023, 2:31 am
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