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 A similar problem but perhaps a bit trickier by Kirk)

One way is to find that 564387902841 leaves a remainder of 4 when divided by 11, while 10000 leaves a remainder of 1. So we need to add (11-4) = 7 times 10000, by placing a 7 in that x position (the 10,000's position) in which we had tentatively placed a zero.

Posted by Charlie on 2003-11-20 14:59:49