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Rod Measures

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

There was a great deal in this problem and James has answered part of it:

Using only three rods with each one not exceeding 10 you can add and minus the following numbers which can go from 1-13.

The three numbers are 9, 3 and 1.

1 = 1
2 = 3-1
3 = 3
4 = 3+1
5 = 9-3-1
6 = 9-3
7 = 9-3+1
8 = 9-1
9 = 9
10 = 9+1
11 = 9+3-1
12 = 9+3
13 = 9+3+1!

Well done James. Is 13 the largest number and why?

Can any of you help with some of the rest of the question:

In how many ways can you make 10?

What is the maximum number you can make with 4 rods?

Perhaps you can send in some more ideas.