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Jane Street Trader Intern Interview Question

I interviewed in New York, NY and was asked:
"What is the smallest number divisible by 225 that consists of all 1s and 0s?"
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Part of a Trader Intern Interview Review - one of 402 Jane Street Interview Reviews

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- Interview Candidate on Oct 12, 2010 Flag Response
of 14
Two facts to note are:
1) Multiplies of 225 end in 00 25 50 75
2) A number is divisible by 9 if the digits sum to 9.

Only those multiples ending in 00 could have only 1's and 0's.
So, the smallest digit we can multiply 225 by to get 00 at the end is 4. That is,
225*4=900. Now, we want to find the smallest multiple of 900 that contains only 1's and 0's. Let us first focus on 9 and then tack on the 00 after. The smallest multple of 9 with only 1's and 0's is 111111111. This is a consquence of the fact that the digits must sum to 9. Now, we tack on the 00 at the end and obtain 11111111100.
- Interview on Jan 19, 2011 Flag Response
of 7
Think of 225 as (5)^2(9). So this number must end in a 0 to be divisible by 5. Since every number that 5 divides ends in a 5 or 0, that number is also divisible by 5. Since a number divisible by 9 must have the digits sum to a number divisible by 9, then all we need is 9 1's and a 0 on the end for 1111111110.
- Anonymous on Jul 06, 2012 Flag Response
of 1
1111111110 / 225 = 4938271.6
- Anonymous is wrong on Jul 14, 2012 Flag Response
of 0
I fail to understand the above answers. Shouldn't it be 225 or 2250. 225/225 =1 and 2250/225 =10. Both these numbers contain just 1's and 0's

- Anonymous on Oct 11, 2013 Flag Response

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