Puzzler

Question

My twin lives at the reverse of my house number. The difference between our house numbers ends in two. What are the lowest possible numbers of our houses?

Solution

If the house number is a one digit number then the reverse is the same number and the difference is 0. So, the smallest house number must be a two or more digit number.

Start from smallest pair (11,11). We get 0 as a result.

The next pair (21,12) results in 9.

The third pair is (31,13) results i 18.

The fourth pair (41,14) results in 27.

The fifth pair (51,15) results in 36.

The sixth pair (61,16) results in 45.

The seventh pair (71,17) results in 54.

The eight pair (81,18) results in 63.

The ninth pair (91,19) results in 72.

With this pair (91,19), we finally get a number ending in 2. Therefore, 19 and 91 are the lowest possible numbers of house.