You may also like

problem icon

Calendar Capers

Choose any three by three square of dates on a calendar page...

problem icon

Card Trick 2

Can you explain how this card trick works?

problem icon

Happy Numbers

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

Differs

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?