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)

Since 10 is -1 mod 11, we can calculate the alternating sum of the digits and easily find that x=7. A similar method, employing the values of 10^n mod 13, can be used on the original problem, but it would be laborious due to the large number of digits.

Posted by Richard on 2003-11-20 17:47:15