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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: ( Back to comment list | You must be logged in to post comments.)
answer Comment 10 of 10 |

The highest possible sum of the four numbers is 27, which occurs for (A, B, C. D) = (10, 8, 6, 3) 

Edited on February 8, 2008, 6:13 am
  Posted by K Sengupta on 2008-02-08 06:01:21

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