Stage: 3 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.
Trial and improvement. Mathematical reasoning & proof. Place value. Properties of numbers. Integers. Working systematically. Factors and multiples. Number bases. Addition & subtraction. Multiplication & division.
Published October 1997.
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