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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.

Make a number chain. Write any number (up to 40) and multiply its last digit by 4 then add its other digits to this. Write down the new number and repeat the process until you return to the original. For instance 7, 28, 34, 19, 37, 31, 7. What is the longest chain you can make?

Answer: all except 13, 26 and 39 have 7 in the chain. 40 and above do not behave like this.