If S is a finite set, the minimax of S is defined to be the product of the least and greatest elements of S. How many different subsets of {2, 3, 4, 5, ..., 19, 20} have minimax 28?
+128407 { 2,.....,14} number of possible subsets with these two members = 2^(14 - 2 -1) = 2^11
( 4,....,7} number of possible subsets with these two members = 2^(7 - 4 - 1) = 2^2
Total subsets = 2^11 + 2^2 = 2052
To see this, consider the second set .....either the integers 5 and 6 are in or out of each subset
So 2 states ^( number of integers) = = 2^2 = 4 subsets
And in the first subset the integers 3,4,5,6,7,8,9,10,11,12,13 are either in or out of each subset=
2states ^(number of integers) = 2^11
