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Unequaled inequalities (Posted on 2005-01-13) Difficulty: 5 of 5
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?

See The Solution Submitted by Tristan    
Rating: 3.6000 (5 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answerK Sengupta2008-02-08 06:01:21
re(4): a start + Possible solutionnikki2005-01-14 15:13:22
Solutioncomputer solution (spoiler)Charlie2005-01-14 06:32:56
Hints/Tipsre(3): a start + Possible solutionTristan2005-01-14 01:56:09
re(3): a start + Possible solutionHugo2005-01-13 20:48:36
re(3): a start + Possible solutionHugo2005-01-13 20:47:38
Some Thoughtsre(2): a start + Possible solutionCharlie2005-01-13 20:45:02
Some Thoughtsre(2): a start + Possible solutionnikki2005-01-13 20:40:41
Some Thoughtsre: a start + Possible solutionHugo2005-01-13 20:25:29
Some Thoughtsa startCharlie2005-01-13 20:13:53
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