All of these puzzles relate to adding together consecutive numbers. Mathematicians do not like doing a lot of, tedious adding up, and so are always on the lookout for cunning shortcuts. It might help ...
Consecutive numbers are ones that follow on from each other in order, like 2, 3, 4 and 5. We can create certain numbers by adding together runs of consecutive numbers, e.g. 1 + 2 + 3 = 6 or 14 + 15 = ...