What is the smallest integer greater than 0 that can be written entirely with zeros and ones and is evenly divisible by 225?

The following is a list of positive integers smaller than the given solution of 11111111100, yet satisfy the conditions that each can be written entirely with zeroes and ones and each is evenly divisible by 225. 

1232100 can be written as 100₁₁₁₀  
1947375 can be written as 1110101₁₁  
102212100 can be written as 100₁₀₁₁₀  
121220100 can be written as 100₁₁₀₁₀ 
123210000 can be written as 100₁₁₁₀₀

225 written in binary, 1110001, is written entirely with zeroes and ones and, of course, would also be evenly divisible by 225. But, as stated in earlier posts, as 225 is written without a radix, we must assume all numbers written without a radix to be in the same base, and if not indicated otherwise, that base is the decimal base 10. 

Edited on February 17, 2008, 1:59 am

Posted by Dej Mar on 2008-02-16 06:46:38