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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?

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Summing Consecutive Numbers

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

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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

Stage: 3 and 4

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?

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