Water retention challenge

 

A special challenge is to construct (4x4 and larger) magic squares to get maximum retention of water. For example, see the (pan)magic 4x4 square below:

 

 

16

3

10

5

2

13

8

11

7

12

1

14

9

6

15

4

 

  

The digits in the magic square represent the hight of the cells. Higher cells surround lower cells horizontally and vertically (not diagonally), so it is possible (fictively) to fill the surrounded cells with water. In this magic square 2 cells are surrounded. In total there is 10-8 + 10-1 = 11 units retention of water.

 

To see more, visit the website of Craig Knecht:

 

www.knechtmagicsquare.paulscomputing.com