What is the smallest number divisible by 225 that consists of all 1's and 0's?Despite a heavy workload, I set a mental background processor on the problem. Quickly, I determined that the answer must be a multiple of 4 for there to be only 1's and 0's. 4 times 225 is 900. Consequently, the problem revolves around the smallest number divisible by 9 that consists of all 1's and 0's.
Typically, I really stink at these problems. But my interest was peaked so I created a spreadsheet with multiples of 9 and simply looked for a pattern. After a couple cups of coffee, deep in the recess of this foggy brain I remembered something about multiples of 9 adding up to 9 or adding up to a multiple of 9.
So since multiples of 9 must add up to a multiple of 9 and I know that the last two digits must be "00" I guessed "11111111100". It turns out that 9 * 49382716 = 11111111100.
Needless to say, I would not have gotten the job.
