How to retain as much as possible water within magic squares?
A special challenge to produce (4x4 and bigger) magic squares is attempting to retain as much as possible water
(given the size of the magic square). See for example the 4x4 (pan)magic square below.
|
16
|
3
|
10
|
5
|
|
2
|
13
|
8
|
11
|
|
7
|
12
|
1
|
14
|
|
9
|
6
|
15
|
4
|
The value in a cell represents the height of a tower. Heigher cells surround lower cells vertical and horizontal (not
diagonal), which makes it possible to fill the surrounded cells (imaginary) with water. In the above mentioned square
two cells are surrounded. The total of 10-8 + 10-1 = 11 units of water can be retained.
See (the idea of) this funny game on the website of Craig Knecht:
www.knechtmagicsquare.paulscomputing.com | 
