Unomino Magic Square

Unomino Magic Square
Armahedi Mahzar (c) 2015

A domino is two connected squares, each containing many dots or none. A unomino  is a single square containing dots like dominos. We can rearrange the little black square places so each column, row and diagonal is containing exactly the same numbers of dots to get


The unonimo magic square is isomorphic to the 3x3 magic square known as Lo Shu was discovered thousand years ago in the back of mythical turtle by Fuh-Shi,  the mythical founder of Chinese civilisation in around 2400 BC.


Before they invented the zero numeral, the Arabs used alphabets as the written symbols of numbers. Here is the 3×3 Magic Square



In fact there are bigger and bigger Magic Squares.

For example, the earliest 4X4 Magic Square is discovered in Khajuraho India dating
from the eleventh or twelfth century.



Later, another 4X4 Magic Square  was found in Albert Dürer’s engraving ” Melencolia”, where the date of its creation, 1514 AD. See it under the bell.



The previous nine monominoes is only part of larger set of monominoes containing dots from 1 up to 16. These are the sixteens monominos arranged is 4x4 square

We can rearrange the unominoes such that each column, row, diagonal and little 2×2 square is containing exactly the same number of dots. For example the following is the unomino magic square of order 4.
 


This magic square  is wonderful. Because all the collumn. rows and diagonals are containing 34 dots. The 2×2 center square is also containing 34 dots. The dots in each corner 2×2 squares are 34.

This is only one solution of the Puzzle. The French mathematician Frenicle de Bessy   in 1693 enumerated the number of all possible 4×4 Magic Square and get the number  880.