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Build one – get two free (Posted on 2011-10-08) Difficulty: 5 of 5

Construct a 4x4 magic square using integer numbers,
fulfilling the following conditions:
-Each number is an average of a twin prime pair.
-The lowest number is 30 - place it in the upper left corner.
- The highest number is 1092 - place it in the lower right corner.

  Rem: Once you’ve created the above magic square you can derive 2 new magic squares, each consisting of prime numbers only, - simply by increasing ( decreasing ) each number by one.

    Hint : The eligible even numbers are a subset of a sequence A014574 of Sloane’s encyclopedia of integer sequences.

It is a tough project - g o o d l u c k !

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
first one ( maybe more) | Comment 1 of 5

after about 5 hours, my mathematica code has produced its first solution, several hours left before i know if there are any more.


30   420  1020 282

312  570  600  270

1062 522  60   108

348  240   72   1092

with common sum 1752

of course a second solution can be made by reflection about the left to right diagonal

will post again once my code completes

**update**

corrected typo in last row, 248 should have been 240
program is still running, will post all solutions found in a seperate post once it completes.

Edited on October 9, 2011, 4:41 pm
  Posted by Daniel on 2011-10-09 04:07:43

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