Square numbers

problem
Square triangle

Age

11 to 14

Challenge level

How many triangles have all three angles perfect squares (in degrees)?
problem
Square subtraction

Age

7 to 11

Challenge level

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
problem
Few and far between?

Age

16 to 18

Challenge level

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

Age

14 to 16

Challenge level

Which numbers can we write as a sum of square numbers?
problem
Generating triples

Age

14 to 16

Challenge level

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
problem
Pythagorean quadruple

Age

14 to 16

Challenge level

The sum of three square numbers equals $121$. What can those numbers be...
problem
No square sums

Age

14 to 16

Challenge level

How many numbers do you need to remove to avoid making a perfect square?
problem
Robert's spreadsheet

Age

14 to 16

Challenge level

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

Age

7 to 11

Challenge level

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you work out the rule for each light?
problem
Four coloured lights

Age

11 to 14

Challenge level

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?