Square numbers

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

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

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?

Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?

A woman was born in a year that was a square number, lived a square number of years and died in a year that was also a square number. When was she born?

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

How many numbers do you need to remove to avoid making a perfect square?