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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?

 Jul 18, 2022
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{ 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

 

cool cool cool

 Jul 18, 2022

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