Determine the minimum possible value of a
base ten positive integer N, such that:
 N is constituted entirely by 0s and 1s, and:
 N is divisible by 2475.
Extra Challenge: Solve this puzzle without using a computer program.
2475 = 3^2 * 5^2 * 11
Merely two trailing zeros will provide for the 5^2. We need concern ourselves only with mod 99.
100 mod 99 = 1
1000 mod 99 = 10
and in fact the powers of ten mod 99 alternate thereafter.
Then:
1100 mod 99 = 11
110000 mod 99 = 11, etc.
We just need 9 pairs of 1's before two zeros to bring that to 99 mod 99 = 0 mod 99; that is, 18 1's followed by two zeros: 11111111111111111100.

Posted by Charlie
on 20131220 17:32:31 