I'm thinking of four positive integers A, B, C, and D. A>B>C>D is true.

I have written down another inequality that is also true, but I'm not showing it to you. This inequality puts the following values in order from greatest to smallest:
A, A+C, B, A+D, C, B+C, D, B+D, A+B, C+D
(this is obviously not the order, as A+C can't be less than A or less than C)

I showed the two inequalities to my friend, and he was able to minimize A, B, C, and D all at once. I told him that he had just guessed correctly which numbers were on my mind.

Based only on this information, what is the highest possible sum of the four numbers on my mind?

(In reply to re(2): a start + Possible solution by nikki)

Wow!  Honestly, I don't know where you got all of that.  I don't know where I went wrong in trying to explain the problem clearly (not that I blame you, I blame myself).

I'm not sure what your interpretation is, but I can still explain what I mean.  "Minimizing A, B, C, and D all at once" only means that the minimum of all four values could be true all at once.  A simple case where two variables can't all be minimized at once is X≠Y (assuming both are positive integers).  The minimum X is 1, and the minimum Y is 1, but they can't both be 1.

I do believe that all four variables can be minimized at once for every single possible inequality.  You don't know which inequality I wrote down, but you know the values of the four variables are equal to the minimums.

Posted by Tristan on 2005-01-14 01:56:09