Briefly

Smart numbers

Smart numbers

A number is elegant if by adding the squares of its figures and repeating this same operation on the result obtained, and iterating this process enough times we finally get 1.

For example, the number 9,100 is elegant, since, first, 92 + 12 + 02 + 02 = 82. Following the process: 82 + 22 = 68.
Iterating once more: 62 + 82 = 100 and finally, 12 + 02 + 02 = 1.

Are you able to find two consecutive elegant numbers?

Solution

31 and 32 are two consecutive smart numbers, since 31 takes us to 9 + 1 = 10 and 10 takes us to 1 + 0 = 1, which is our goal, while 32 takes us to 9 + 4 = 13 and 13 takes us to 1 + 9 = 10 and 10 again brings us to 1.