The FIVE cards that we have discovered and placed face up in each of the FOZUDOKU Magic Squares will be our clues to gradually calculate the other cards, bearing in mind that there are 24 groups of four cards (XXXX) in each Magic Square that are formed by the four suits in the deck and add up to the same: 22 in the first Magic Square on the left, 26 in the second Magic Square in the centre and 30 in the third Magic Square on the right.
To solve the FOZUDOKU, you only need to know well and use the first 15 groups of this list:
– The four horizontal lines
– The four vertical lines
– The two diagonal lines
– The four corners of the Magic Square
– The four 2×2 squares that form the fourth part of the Magic square
Where three of the four cards are known in a group that has the constant sum of the Magic Square (22 in the first square on the left, 26 in the second square in the middle and 30 in thethird square on the right), the fourth card can be calculated.
All Magic Squares have three visible cards in three of their corners so you can calculate the card that goes in the fourth corner (since the four corners are one of the groups of four cards that add up the same).
After calculating and placing the card in the fourth corner, we can look at one of the two diagonals with three visible cards and we can calculate the missing fourth card and complete that diagonal.
And so, where in a group of four cards that have the constant sum, there are three visible cards we can calculate and discover the missing fourth card and complete the group, so little by little we will solve the FOZUDOKU.
But, (and this is very important), when we have placed 5 cards, we will see that we CANNOT place the sixth card, because we have no clues, since there is no group of 4 cards that has the constant sum where three cards are visible.
All groups of 4 cards that are still incomplete only have two visible cards and it is impossible to calculate any more cards.
(this always happens when we have six cards left to place)
Then we can place a card without adding anything up.
(I call this operation placing the «joker«)
To find and place the «joker» we use another strategy that is only used once:
How do we place the sixth card when we have six cards left to place?
This is done by first looking for three cards of the same suit, because by knowing three cards of the same suit, you can identify and place the missing fourth card of that suit without adding anything up, because all the suits have in each Magic Square four cards and are from one of these groups of four consecutive numbers:
( 1, 2, 3, and 4 ) ( 5, 6, 7 and 8 ) ( 9, 10, 11 and 12 )
If in a Magic Square, we have placed:
the 5 of OROS, the 7 of OROS and the 8 of OROS, we know that in that square goes the ( 5, 6, 7 and 8 ) of OROS
We can then identify the 6 of OROS as the missing card,(our JOKER).
The place where the 6 of OROS goes will be at the intersection of lines and columns where there is NO OROS card
So, we will be able to place the 6 of OROS (our JOKER) without adding anything.
Apart from having 24 groups of four cards (XXXX) that add up to the same amount and are made up of the four suits in the deck, the FOZUDOKU also has 30 pairs of cards (XX) that add up to the same amount as 30 other pairs of cards (OO) and the suits of some pairs are the same as the suits of the other pair (XX = OO)
Changing the cards of the pairs (XX) by the cards of the pairs (OO) forms a new FOZUDOKU, (there are seven possible changes).
OTHER WAYS TO SOLVE A FOZUDOKU
Another (slightly more difficult) way to solve a FOZUDOKU is by removing the 33 cards that are face down, leaving the spaces blank.
The 33 cards are shuffled.
Cards are then picked one by one, looking to see if it can be placed or not.
This can be done as a solitaire game or by playing with another person, (whoever places the most cards win)
A variation of this game would be that after shuffling the cards, they are placed again face down in the empty spaces.
Naturally, the cards that are face down now are not in the right place (except for some that just happen to be)
Alternatively, a player uncovers one of the cards and looks to see if he can place it or not, in case he cannot, he place it again face down, in the same place, (trying to remember, the card and the place where it is, for when later that card can be placed)
If we can place the card we have picked, when we do so we will move a card that we will try to place, but if we cannot, we will place it where there is an empty space. After placing a card in the right place you can try to place the card that was in that place, trying to remember the place where the card we are looking for is located (if it was uncovered before), like it is played in the MEMORY game