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Age 11 to 14
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  • Problem
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Choose any 4 whole numbers, for example (100, 2, 37, 59). Now take the difference between consecutive numbers, always subtracting the smaller from the larger, and ending with the difference between the first and the last numbers. What happens when you repeat this process over and over again? For example, continue the sequence of 4-tuples:

(100, 2, 37, 59), (98, 35, 22, 41), (63, 13, 19, 57), (50, 6, 38, 6) , ...

Investigate starting with different sets of 4 numbers.

What happens when you use 3 numbers, or 5, or 6, or 7 or 8 numbers?


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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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