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Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

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Relative Powers

Weekly Problem 10 - 2007
The square of a number is 12 more than the number itself. The cube of the number is 9 times the number. What is the number?

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Summing Squares

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?

Robert's Spreadsheet

Age 14 to 16 Challenge Level:

Robert made a spreadsheet with eight columns. He arranged the numbers from 1 to 1000 in his spreadsheet, and then coloured in all the square numbers.
Here is a picture showing the first few rows of Robert's spreadsheet:
Robert noticed some interesting patterns beginning to emerge.
Why not create your own copy of Robert's spreadsheet and see what patterns you notice?
Can you explain the patterns you find?
Will the patterns continue? How can you be sure?