We have athletes in X columns and Y rows, in a setup.
From each column, we select the tallest ones, and among the tallest ones, the shortest athlete. We name him A.
From each row, we select the shortest ones, and among the shortest ones, the tallest athlete. We name him B.
Compare the heights from athlete A and athlete B. Prove your statement.
Ah, I misread the statement. Thought it was saying the shortest ones from each row and picking the tallest from those, then moving onto the next row; and vice versa.
This is the answer I came up with, I figured this out first by trial and error and was able to prove it by assuming that B is taller than A and proving it to be false.
If B is shortest in his row and is taller than A he isn't in the same row as A.
If B is shortest in his row everyone else in his row has to also be taller than A.
One of these people in his row has to be in the same column as A. But A has to be the tallest in his column.
This is a contradiction, therefore B can't be taller than A.
There is no real way to know which is taller. One row could be all the tallest people, meaning that a tall person could be selected for the shortest in his row, then would be selected as the tallest short as B. The same goes for columns, meaning a short person could be A.
Also, the rows and columns could be evenly spaced with tall and short people, putting the shortest tall underneath the tallest short.
They could also end up being the same person.
I don't think that it is possible to give a definite answer on this one, it could go either way. But I usually miss some details on these things so who knows.
deletedover 8 years
You are selecting the tallest athlete from each column. Once you have one athlete from each column, you take the shortest out of them. That's athlete A. Regardless of how many columns or rows there are you will only have one athlete A and one athlete B, in fact they could even be the same person. I know the solution to this but I'll let either the OP post it or others to figure it out.
This doesn't really make sense and falls apart upon reading it. If you are selecting an athelete A from EACH column, that means you are selecting X number of A's. If you are selecting an athlete B from EACH row, that means you are selecting Y athletes called B.
You then ask me to compare the heights of athlete (notice the singular) A and athlete B, not athletes A and athletes B.
The amount of atheletes we select from each row and column is also crucial, given that it can be as little as 2 or as many as X/Y.
And with this, I'm asking you to say how it's done. Prove your statement.
