What set of positive integers with sum 2024 has highest possible product?
Same question for 2025.
What is the highest product in this century?
Inspired by: Putnam 1979
(In reply to
Guesses by Larry)
I had some thoughts along the same lines, but then compare {2,2,2} vs {3,3} Both sum to 6, but 2*2*2 < 3*3. Then the optimal partition when restricted to integers is to maximize the number of 3's with at most one or two 2's for mod 3 parity.
Then 2024 = 3*674+2, so the max product of positive integers summing to 2024 would be 2*3^674. Similarly 2025=3*675, so that max would be 3^675.
re: Guesses
