18. An integer is said to be chunky if it consists only of non-zero digits by which it is divisible when written in base 10 .
For example, the number 936 is Chunky since it is divisible by 9,3 and 6 .
How many chunky integers are there between 13 and 113 ?
Solution
014

For a two-digit number $N=$ " $a b$ " we may write $N=10 a+b$.
If $N$ is Chunky, then $N$ will be divisible by $a$ and therefore $b=N-10 a$ will also be divisible by $a$.
It is therefore sufficient to check only those two-digit numbers which have a units digit divisible by their tens digit. Following checking, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88 and 99 are the only two-digit Chunky numbers (excluding 11 and 12, which are not under consideration). Of those three-digit numbers under consideration, only 111 and 112 are Chunky. The answer is 14 .