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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.

Exploring Diagonals

Stage: 3 and 4

Move the top right-hand corner of the rectangle.
Can you work out what the purple number represents?

What would be the dimensions of a rectangle with a purple number of 24? Is there more than one?
If I tell you the coordinates, can you find a quick way to work out the purple number?

What other interesting questions might you explore?

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