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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


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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