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Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

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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?

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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 square loop is defined exactly as a hexagon one, but with squares instead of hexagons. Some examples are shown in the pictures below:
      

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