Place the numbers 1 to 100 in any order in a 10x10 array.

Create set A = the greatest number in each of the 10 rows.

Create set B = the least number in each of the 10 columns.

1. Demonstrate that the sets may or many not have numbers in common.
2. What is the smallest number that could be in both sets?
3. How many numbers could the two sets have in common?

I was looking at random problems, and ran across this related problem, submitted by levik in 2002.  The Answer to Part 3 of this problem follows directly from the 2002 solution.

Posted by Steve Herman on 2017-09-07 19:03:40