I came across this puzzle at some online contest(now completed)
Alexander, son of Phillip of Macedon, has ascended the throne of his father following his assassination. In these tumultuous times, he appoints you as head of the architectural division of his mighty army. The general of the army wants all the catapults to be inducted in the artillery which have a n-sided polygon base, and no two or more of them should have the same type of polygon as their base.However, for the structures to be agile and economic, it is required that the n should be an odd number and the polygon of the base should be constructable with help of a compass and straightedge.
Given the above situation, you are required to find out the total number of logs of woods required - each log of wood for each side of the base of structure - for the construction of all such catapults
I thought the result would be equal to the sum of the first 5 Fermat's Prime but unfortunately that wasn't correct.
Do you think the data provided is not sufficient or am I missing something? What could the possible answer to this question?