What is the smallest positive multiple of 450 whose digits are all zeroes and ones?

I tried guess and check but the numbers grew big fast. Thanks in advance!

**Answer**

Can we agree that it must be an even multiple of 450? Otherwise the last two digits will be 50.

What is the smallest positive multiple of 900 such that all the digits are 0s or 1s?

A rule of multiples of 9: the sum of the digits of a multiple of 9 is a multiple of 9.

This rule goes both ways. If the sum of the digits is a multiple of 9, the number is a multiple of 9.

That makes 11111111100 our winner.

**Attribution***Source : Link , Question Author : Dreamer , Answer Author : Ken Wayne VanderLinde*