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 assume leading zeroes, so that we have 49 zeroes followed by the ones digit(t), then with the usual definition of B as in the last post, the value of B is simply t, which cannot be divisible by 239, unless t=0, since gcd(t, 239) = 1
However, in this situation, we have the same digit, that is 0, repeated 50 times. This is a contradiction.
Consequently, the given number cannot admit of leading zeroes.