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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:
 
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?