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Puzzle of the Day

These puzzles are also printed in Eight days a week, a booklet published by the Association of Teachers of Mathematics.

Start with any two-digit number. Multiply each digit by itself then add these answers. Do the same thing to this new number and so on until something happens. For example 32 becomes 9+4 which is 13, 13 becomes 1+9 which is 10, 10 becomes 1+0 =1. This one ends at 1. What else happens when you start with different numbers?

Answer: All end with single digits, 2 is most frequent