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Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Big Powers

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Coordinates of Corners

Age 11 to 16


Move the dots below to make some squares. Can you make a variety of squares whose sides are not parallel to the axes?




If you have a set of four coordinates, is there a quick way to decide (without drawing) whether they form a square?