A                   B                    C                   D
+---+---+---+---+   +---+---+---+---+    +---+---+---+---+   +---+---+---+---+
|61 |   |   |   |   |14 |   |   |62 |    |03 |55 |   |   |   |52 |   |48 |   |
+---+---+---+---+   +---+---+---+---+    +---+---+---+---+   +---+---+---+---+
|   |   |41 |   |   |   |22 |   |   |    |47 |   |   |   |   |   |   |   |56 |
+---+---+---+---+   +---+---+---+---+    +---+---+---+---+   +---+---+---+---+
|   |21 |   |   |   |   |   |42 |   |    |   |   |   |19 |   |12 |   |   |   |
+---+---+---+---+   +---+---+---+---+    +---+---+---+---+   +---+---+---+---+ 
|   |57 |   |01 |   |02 |   |   |   |    |   |   |11 |   |   |   |20 |   |   |
+---+---+---+---+   +---+---+---+---+    +---+---+---+---+   +---+---+---+---+

Using positive integers from 1 to 64 inclusively, complete the grids A to D so that each of the columns, each of the rows and each of the main diagonals in:

1. Grid A totals 124.
2. Grid B totals 128.
3. Grid C totals 132.
4. Grid D totals 136.

When the four grids are placed on top of each other, each of the 16 columns equal 130. For example, 61+14+03+52 = 130. Twenty positive integers have already been displayed in the four grids in terms of the above diagram.

Are you sure there is only one solution. I am seeing whole range of possibilities?

Incase two numbers are remaining to be guessed only if balance is 9,10,115,116,119,121,124 then there is a unique solution.

Incase two numbers are remaining to be guesses only if balance is 11,12,16,18,106,110,111,114,118,122,123 then there are two possibilities. So except for 16 there is no other match hence the solution is only by trial and error with various possibilities.

Edited on September 4, 2013, 8:48 am

Posted by Salil on 2013-09-04 08:40:51