By exchanging ALL the cards of a FOZUDOKU you can make another FOZUDOKU.
It is worth doing this, even if it is only once, as we will see and appreciate better the structure and peculiarities of the three Magic Squares of the FOZUDOKU,which will help us to understand it better.
The changes are:
– CHANGES OF PAIRS
– CHANGES OF LINES
– CHANGES OF COLUMNS
– CHANGES OF 2×2 SQUARE
These changes can be made after solving the FOZUDOKU or when the three Magic Squares are already formed with the cards face down.
None of these changes of PAIRS, LINES, COLUMNS and 2×2 SQUARES will alter the properties of the Magic Squares which will continue to have a constant sum and each of the 24 groups of four cards that add up to the same (the constant sum), will continue to be made up of 4 cards of different suits.
– CHANGES OF PAIRS
Magic Squares have two pairs of cards that add up to the same ( XX = OO ) and the suits of one pair are the same as the suits of the other pair.
Exchanging eight of these pairs forms a new FOZUDOKU and there are 7 different ways to do it.
– CHANGES OF LINES
The lines can be changed in three different ways:
1×2 and 3×4
1×3 and 2×4
1×4 and 2×3
– CHANGES OF COLUMNS
The columns can be changed in three different ways
1×2 and 3×4
1×3 and 2×4
1×4 and 2×3
– CROSS CHANGES OF 2×2 SQUARE
Four quarters of the Magic Square is made up of 2×2 squares and we can change them:
the 2×2 square at the top left by the one at the bottom right
and the 2×2 square at the top right by the one at the bottom left.
SUDOKU + FOZ = FOZUDOKU 