ABSTRACT
Combinatorics, a branch of mathematics closely related to probability asks how many permutations or combinations there are of a set of objects under certain conditions. The numbers involved are often very big which sometimes causes intuition to fail. For example, there are 3,628,800 ways of arranging ten different books on a shelf.
Combinatorics lends itself very well to lateral thinking, seeking short and ingenious ways of solving complex problems where large numbers of possibilities are involved. Magic and anti-magic squares introduce themselves here, as do picking colored socks in a darkened room, and finding how many subsets a set has.
By hand or using a computer, anyone can list the total number of possibilities in a given situation, but that takes a lot of time and uses a lot of paper. The lateral approach is to find a slick general method that will solve the problem in a few lines – very satisfying!
