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;

9-4;

9-3, 3+4;

9+3-4;

9 and 9+4-3

(as illustrated).

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?

What is the greatest length that can be measured using 4 rods in this way? Can you beat the best solution submitted so far? Is your answer best possible?