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1, 3, 5, 7, ... (just continue adding 2 at a time).
It sounds like the goal is for each box to have an odd number of pencils. At first it seems impossible, but if one of the boxes can go inside another so that the larger box holds an even # plus the odd number in the smaller box (for a total of an odd number), then you can do it.
Yes. Both are defined on all points other than odd multiples of 90 degrees.
odd. odd=odd odd+odd=even odd+odd+odd=odd it keeps alternating in that fashion