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Bethanni from McCabe School sent in a clear solution to the first part of the problem. She says:

If you have 3 on one side, and you have to balance it out, without using three 1s. You have to put on the other side an equal amount. That can only be a 2 and a 1.

Adele and Lottie from Aldermaston C of E Primary School answered the next parts of the question for us:

3 and 4 on one side need three 2s plus a 1 to make it balance.

They then went on to say:

These are the ways to make it balance with 10:
6+4
1+9
3+7
8+1+1
5+5
8+2
3+3+3+1
2+3+1+4
7+1+2
6+1+2+1
3+4+3
5+3+2
4+5+1
And lots more as long as they add up to 10. It doesn't matter how many weights you use, but they must add up to 10.

Well done. I wonder if anyone can think of a system so that you could be sure you found all the different ways of making 10?