Partition an n X n square into multiple non-congruent integer-sided rectangles. a(n) is the least possible difference between the largest and smallest area.
___________| |S|_______|| | | L || |_|_______|| | | || |_____|___||_|_________| (fig. I)The largest rectangle (L) has an area of 2 * 4 = 8, and the smallest rectangle (S) has an area of 1 * 3 = 3. Therefore, the difference is 8 - 3 = 5.
Given an integer n>2, output the least possible difference.
All known values of the sequence at the time of posting:
2, 4, 4, 5, 5, 6, 6, 8, 6, 7, 8, 6, 8, 8, 8, 8, 8, 9, 9, 9, 8, 9, 10, 9, 10, 9, 9, 11, 11, 10, 12, 12, 11, 12, 11, 10, 11, 12, 13, 12, 12, 12So a(3)=2, a(4)=4, ...
Related - this related challenge allows non-optimal solutions, has time constraints, and is not code-golf.
For more information, watch this video by Numberphile