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Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?