I've been calculating all the different products from the splitting of pairs or triples or quadruples of numbers that sum to a specific number e.g. For number 12 - the pairs 11 and 1 = product of 11, the pairs 10 and 2 = product 20 with a maximum product in that range of pairs of 6 and 6 = 36. Then for the number 15 - the triples of 13 and 1 and 1 = product 13; then 12, 2, and 1 = 24 with a max product combination of 5,5, and 5 = 125.
Then I made a formula for this pattern of identifying maximum products which for pairs is (n/2) to power of 2; for triples is (n/3) to power of three and so on.
1. Does that make sense?
2. What could be real life applications of being able to determine maximum products in this way - pairs, triples and something more numerically exotic?
Thanks for advice and best wishes.