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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.