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Rod Measures

Age 7 to 11
Challenge Level

There are exactly 9 different solutions for N=10 units with no rod longer than 10 units. Can you find them? With one of these solutions you can measure up to N=13. Can you do better if you can choose 3 longer measuring rods?

If you double the lengths of all three rods in one of these solution sets you can measure even lengths from 2 to 2N units. Introducing a one unit rod to make up a set of four measuring rods you can now measure all lengths from 1 to (2N+1) units. Can you do better than 27 units with 4 rods?