Question

Find the least positive integer, written only by numbers 0, 1 and 2, which is divisible by 225.

Answer 1

9514 1404 393

Answer:

  1,222,200

Step-by-step explanation:

A search using a computer program found ...

  5432 × 225 = 1,222,200

__

1000 mod 225 = 100

4 × 225 = 900

This suggests that if we have some number of thousands whose digits total 9, that we will have the number of interest. Of course, we can add 200 to some number of thousands with a digit total of 7. The smallest such digit total will be had with the number 1222 using the specified digits {0, 1, 2}. This gives rise to the result above: 1222×1000 +200 = 1,222,200. It also explains why moving the 1 to the right will also give a multiple of 225.