Question

What is the sum of all three digit numbers (abc) such that (ab) * (cc) * (abc)=(abcabc)? (each letter represents one digit of the three digit number)

Answer 1

`1048`

Explanation:

Note that:

`"abcabc" / "abc" = 1001 = 7 * 11 * 13`

`"cc"` must be a multiple of `11` and hence either `"cc" = 11` or `"cc" = 7 * 11 = 77` and we find two solutions:

`"ab" = 7 * 13 = 91 \` and `\ "cc" = 11 \ "` giving `"abc" = 911`

`"ab" = 13 \` and `\ "cc" = 7 * 11 = 77 \ "` giving `"abc" = 137`

So the sum of the three digit numbers `"abc"` is:

`911+137 = 1048`