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Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

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Can you explain the strategy for winning this game with any target?

Counting Factors

Is there an efficient way to work out how many factors a large number has?

Alison's Quilt

Age 11 to 14 Challenge Level:

 


Alison joins together nine squares with side lengths $1, 4, 7, 8, 9, 10, 14, 15$ and $18$ cm with no gaps and no overlaps, to form a rectangular quilt.
 

Can you find the dimensions of the finished quilt, and show how Alison fitted the squares together?

 


Alison wants to make a second quilt from ten squares with side lengths $3, 5, 6, 11, 17, 19, 22, 23, 24$ and $25$ cm.

Can you find the dimensions of this quilt?