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## 'Rod Measures' printed from http://nrich.maths.org/

Using 3 rods of integer lengths, none longer than 10 units and
not using any rod more than once, you can measure all the lengths
in whole units from 1 to 10 units. How many ways can you do
this?

For example with rods of lengths $3, 4, $ and $9$ the
measurements are:

$4-3,$ $9-4-3,$ $3,$ $4,$ $9-3,$ $9-4,$ $3+4,$ $9+3-4,$ $9,$
$9+4-3,$

Using 3 rods of ANY integer lengths, what is the greatest length
N for which you can measure all lengths from 1 to N units
inclusive? Can you beat 10 units? Can you beat the highest value of
N submitted to date?