A number of 50 digits has all its digits equal to 1 except the 26th digit. If the number is divisible by 13, then find the digit in the 26th place.

(In reply to re(3): a little more straightforward by Tristan)

I wrote the number as
111111 111111 111111 111111 x1 111111 111111 111111 111111
and if you call the rightmost (least significant) digit the first digit, then my x is the 26th digit, and x=9 is the answer for this 26th digit. If you call the leftmost digit (most significant) the first digit then the 26th digit moves left one place, giving instead
111111 111111 111111 111111 1x 111111 111111 111111 111111
and x=3 is now the answer. What is important is that 111111 is divisble by 13 and 10^n is not.

Posted by Richard on 2003-11-19 21:21:06