47. Magic Pento-square
In a magic square, the sum of the numbers in each row, column and
diagonal row is always the same.
We will start with the most famous magic square, the Lo-Shu.
Lee Sallows had the brilliant idea to replace numbers by shapes. With all shapes in any row, column or diagonal row the same main-shape must be formed.
A magic 2010 !
Matthijs Coster from the Netherlands created a competition for the Dutch magazine Pythagoras.
We changed the question in that competition for our own pentomino-competition.
As shapes we choose the polyominoes.
In the figure below, you can see a magical square with shapes (or a geo-magical square), of which one is a (red) F-pentomino.
Find 11 other geo-magical squares of size 3x3, using each of the other 11 pentominoes as a central piece once.
You have total freedom to decide on the main shape to be formed, as long as each row and column contains a congruent shape.
The sizes of the 9 shapes must be 1 upto 9.