20th Putnam 1959 Problem B4 A is the 5 x 5 array: 11 17 25 19 16 24 10 13 15 3 12 5 14 2 18 23 4 1 8 22 6 20 7 21 9 Pick 5 elements, one from each row and column, whose minimum is as large as possible (and prove it so). Solution
: 25, 23, 20, 18, 15. We can only pick one of 16, 17, 19, 25; only one of 23, 24; only one of 18, 22; and only one of 20, 21. That only gives 4 elements, so the minimum cannot be larger than 15. The answer shows that 15 can be achieved. 20th Putnam 1959 © John Scholes jscholes@kalva.demon.co.uk 15 Feb 2002