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Summing Consecutive Numbers

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Always the Same

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

Regular Hexagon Loops

Age 11 to 14 Challenge Level:

A hexagon loop is a closed chain of hexagons that meet along a whole edge and in which each hexagon must touch exactly two others.


They do not need to be symmetrical or short:

Can you find any rules connecting the numbers of tiles, the inside perimeter and the outside perimeter?

You might want to start by exploring square loops or growing sequences like these:

If you haven't got a supply of regular hexagons you could work on these regular hexagon sheets

With thanks to Don Steward, whose ideas formed the basis of this problem.