>>12252541I agree the question is poorly worded. Based on the example answers given, they could have even meant "such that every integer length in 1,..., N is the total length of some subset of your chosen sticks".. That is, sticks must be joined end-to-end in a straight line, and it is the distance between endpoints of sticks that counts, but you can re-arrange them for each target length. For this question, the answer is ceil( log2 (N+1)).
If the sticks must be in a fixed linear end-to-end arrangement, and distances between any pair of endpoints of sticks counts, I don't see how you can get 7 different lengths from just 3 sticks. With end-to-end construction, you only have 4 different locations of endpoints, and that gives you 4!/(2!2!) = 6 different pairs of locations.
