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Double Digit

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?

Not a Polite Question

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

Whole Numbers Only

Can you work out how many of each kind of pencil this student bought?

Arrange the Digits

Age 11 to 14
Challenge Level

The solution refers to digital roots of nine. This document gives some explanation of why, whatever the order of the digits $1-9$, the total will always be a digital root of nine.