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Maximizing sum (Posted on 2013-07-29) Difficulty: 3 of 5
6*3 & 4*5; 6*4 & 3*5; 5*6 & 4*3 .
The 3 couples above represent six domino tiles chosen in a way such that multiplying the 4 numbers represented by pips of each couple one gets the same product , in our case 360.
If we consider multiplying the digits on both sides of "&" we get 12, 12, and 24, summing up to 48.
Just by changing the order within 1st and 2nd couples this sum can be increased to 84 ( 3*6 & 5*4; 4*6 & 5*3; 5*6 & 4*3).

Problem:
Out of a standard 28-tiles domino set choose 2k tiles selected so that they can be placed in k rows, the product of pips in each row being the same.
For each row choose the highest numbers on each tile and multiply them.
Evaluate the sum of all products.

You are requested to provide the selection with the maximal sum.

No Solution Yet Submitted by Ady TZIDON    
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  Subject Author Date
Solutioncomputer assisted solutionCharlie2013-07-29 17:36:08
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