*In this page are the *NOTES (N)* of the “FOZUDOKU” Excel file*

*If you can translate this tex tinto your language, I will be able to make another Excel file in your language that will be available on this website*

*Please get in touch with me*

*Thank you very much.*

**MENU**

From this MENU you can access diferent pages that have explanation NOTES (NOTAS) (N)

All pages have a link to come back to this MENU

In 1 FOZUDOKU and 104 FOZUDOKUS you will find a deck of 48 cards forming 3 Magic Squares of 4x4 where only 6 cards are shown, (18 in total), to copy and place on a table in order to finish the FOZUDOKU by placing the remaining 30 missing cards. Do not play on the computer

In 1 BARAJA and 104 BARAJAS there are lists of the four suits in each baraja (deck of cards), where the 18 cards shown in the FOZUDOKU are also shown and an empty box is next to the remaining 30 cards. These lists can be used by those who have no spanish deck of 48 cards.

When you press the F9 key all the FOZUDOKUS, the BARAJAS and the SOLUCIONES are changed

If the deck of cards used is a tiny little one, in TABLERO you can photocopy three pages of a gaming board to facilitate the placement of the cards on the table.

In INSTRUCCIONES you can find an explanation how to do a FOZUDOKU

In the Cuadrado Magico de FOZ page there is an explanation of this new Magic Square properties that will help you to understand how to do a FOZUDOKU

From BASE de DATOS (DATABASE), you have access to another MENU where there are pages with formulas and data that helps this Excel file to create thousands of FOZUDOKUS

The blue links (BARAJA SUMA -A, BARAJA SUMA - B, TABLA de SUMAR and CUADRO SUMA) are pages to help children practice addition so they can do FOZUDOKUS and the MAGO de FOZ.

**1 FOZUDOKU**

Using a 48 Spanish deck of cards, place on top of a table the 18 cards shown in the same position, leaving the same blank empty spaces (if the deck of cards used is a tiny little one, you can make three photocopies in TABLERO to make a gaming board to place the cards)

The missing remaining 30 cards are placed, bearing in mind that in the same way as the Cuadrado Magico de FOZ, no colour is repeated, in none of the groups of four cards that add up the same: All horizontal, vertical and diagonal lines, the four corners, the small 2x2 little square in the centre, each of the four small 2x2 little squares that form each quarter of the Cuadrado Magico de FOZ. Also this FOZ Magic Square contains four 3x3 square that its four corners are made with four different colours.

The addition of the above mention groups of four cards is in the Magic Square on the left, 22 - in the centre 26 and the right 30

All these groups of four numbers that add up the same without a colour being repeated can be seen in the page Cuadrado Mágico de FOZ

If you do not have a Spanish deck of 48 cards, you can make a photocopy of this FOZUDOKU and the page 1 BARAJA, where there is a list of the 48 cards, with the same 18 cards shown in this FOZUDOKU and a blank box next to the 30 remaining missing cards

To check the solution go and see 1 SOLUCION

To change the selection of 1 FOZUDOKU, press the F9 key

When the F9 key is pressed also the 1 SOLUCION and the list in 1 BARAJA are changed

The three numbers above to the right are to identify each Magic Square of the FOZUDOKU in case there is a mistake, please notify this so it can be corrected.

**1 BARAJA**

If you do not have a 48 deck of Spanish cards, you can make photocopies of the FOZUDOKU and this list, where the same 18 cards are also shown.

Complete the FOZUDOKU writing the name and number of the cards on the empty spaces, marking at the same time the corresponding box in this list

The three numbers above to the right are to identify each Magic Square of the FOZUDOKU in case there is a mistake, please notify this so it can be corrected.

**1 SOLUCION**

In this page there is the solution (SOLUCIÓN) to 1 FOZUDOKU

This solution changes when pressing the F9 key

The three numbers above to the right are to identify each Magic Square of the FOZUDOKU in case there is a mistake, please notify this so it can be corrected

This solution can also be used to prepare a Wizard of FOZ (Un Mago de FOZ) without having to memorize so many cards.

First place ALL the cards of this solution on the table.

Check that all the cards are in the correct place without any mistakes.

Now place all the cards face down

Now go to 104 POSICIONES (POSITIONS) and select the position of six cards for each Magic Square.

Now show these six cards in each Magic Squares (18 cards in total)

Now you have 48 cards on the table, 18 are shown and 30 are face down to be guessed (by logical deduction and aritmethic), exactly the same way as in the Wizard of FOZ presentation (El Mago de FOZ) .

**TABLERO**

If the 48 Spanish deck of cards used is a tiny little one, from this page you can make three photocopies to make a gaming board to use on the table and facilitate the placing of the cards.

It´s better to use thick paper when making the photocopies.

**104 FOZUDOKUS**

In this page there are 104 FOZUDOKUS. They are in black and white to facilitate making photocopies

(The Instrucctions, below are the same as for the coloured 1 FOZUDOKU page)

Using a 48 Spanish deck of cards, place on top of a table the 18 cards shown in the same position, leaving the same blank empty spaces (if the deck of cards used is a tiny little one, you can make three photocopies in TABLERO to make a gaming board to place the cards)

The missing remaining 30 cards are placed, bearing in mind that in the same way as the Cuadrado Magico de FOZ, no colour is repeated, in none of the groups of four cards that add up the same: All horizontal, vertical and diagonal lines, the four corners, the small 2x2 little square in the centre, each of the four small 2x2 little squares that form each quarter of the Cuadrado Magico de FOZ. Also this FOZ Magic Square contains four 3x3 square that its four corners are made with four different colours.

The addition of the above mention groups of four cards is in the Magic Square on the left, 22 - in the centre 26 and in the right 30

All these groups of four numbers that add up the same without a colour being repeated can be seen in the page Cuadrado Mágico de FOZ

If you do not have a Spanish deck of 48 cards, you can make a photocopy of this FOZUDOKU and the page 104 BARAJAS, where there is a list of the 48 cards, with the same 18 cards shown in this FOZUDOKU and a blank box next to the 30 remaining missing cards

To check the solution go and see 104 SOLUCIONES

To change the selection of 104 FOZUDOKUS, press the F9 key

When the F9 key is pressed also 104 SOLUCIONES and the lists in 104 BARAJAS are changed

The three numbers above to the right are to identify each Magic Square of the FOZUDOKU in case there is a mistake, please notify this so it can be corrected.

**104 BARAJAS**

If you do not have a 48 deck of Spanish cards, you can make photocopies of the FOZUDOKU and this list, where the same 18 cards are also shown.

Complete the FOZUDOKU writing the name and number of the cards on the empty spaces, marking at the same time the corresponding box in this list

The three numbers above to the right are to identify each Magic Square of the FOZUDOKU in case there is a mistake, please notify this so it can be corrected.

**104 SOLUCIONES**

These solutions change when pressing the F9 key

The three numbers above to the right are to identify each Magic Square of the FOZUDOKU in case there is a mistake, please notify this so it can be corrected

Each of these solutions can also be used to prepare a Wizard of FOZ (Un Mago de FOZ) without having to memorize so many cards.

First place ALL the cards of the solution on the table.

Check that all the cards are in the correct place without any mistakes.

Now place all the cards face down

Now go to 104 POSICIONES (POSITIONS) and select the position of six cards for each Magic Square.

Now show these six cards in each Magic Squares (18 cards in total)

Now you have 48 cards on the table, 18 are shown and 30 are face down to be guessed (by logical deduction and aritmethic), exactly the same way as in the Wizard of FOZ presentation (El Mago de FOZ).

**INSTRUCCIONES**

On this page you can photocopy the Instructions how to do a FOZUDOKU to give with a FOZUDOKU to anyone who has no access to a computer.

**BARAJA SUMA - A**

In this page, are the questions of the adding table and in the BARAJA SUMA - B are the answers.

Photocopy this page on one side and use the other side to photocopy the answers.

Once the photocopies are done in both sides, cut the cards to make a small deck of flash cards so children can practice with.

The final result is much better if thick paper is used.

The cards with the questions using three dots are to be used like this: keep adding the last number continuosly until reaching a total higher than 100.

For example

9 + 8 + 8... is calculated like this: 9 + 8 (= 17) + 8 (= 25) + 8 (= 33) + 8 (= 41) + 8 (= 49) + 8 (= 57) + 8 (= 65) + 8 (= 73) + 8 (= 81) + 8 (= 89) + 8 (= 97) + 8 = 105, so the answer, 105, can be checked on the reverse of the card where the question is:

9 + 8 ...

**BARAJA SUMA - B**

In this page, are the answers of the adding table and in the BARAJA SUMA - B are the questions.

Photocopy this page on one side and use the other side to photocopy the questions.

Once the photocopies are done in both sides, cut the cards to make a small deck of flash cards so children can practice with.

The final result is much better if thick paper is used.

The cards with the questions using three dots are to be used like this: keep adding the last number continuosly until reaching a total higher than 100.

For example

9 + 8 + 8... is calculated like this: 9 + 8 (= 17) + 8 (= 25) + 8 (= 33) + 8 (= 41) + 8 (= 49) + 8 (= 57) + 8 (= 65) + 8 (= 73) + 8 (= 81) + 8 (= 89) + 8 (= 97) + 8 = 105, so the answer, 105, can be checked on the reverse of the card where the question is:

9 + 8 ...

**TABLA DE SUMAR**

Adding table to help children to add well, specially two digits numbers.

**CUADRO DE SUMA**

This page helps to practice addition.

Begin adding the numbers clockwise drom the number in the corner (in yellow), until all the numbers are added. The total should be the same as the number in the centre of the square.

Do it again anti-clockwise and the result should be the same,

The numbers and the TOTAL changes when pressing the F9 key.

**Cuadrado Mágico de FOZ**

Magic squares are squares where numbers are placed in such a way that all horizontal, vertical and diagonal lines add up the same

For centuries these magic squares have marvelled people for their peculiarity as something curious and in ancient times they even were attributed magic properties.

The innovation to the FOZ Magic Square is that four different colours form each group of four numbers that add up the same (34). These colours are blue, red, green and yellow and are not repeated within any group. Those 24 groups of 4 numbers are shown here in this page to show this unique property.

This is something that I discovered playing with coloured magnets on the fridge door in my house in FOZ, (Lugo, Galicia, Spain), and for this reason I named this magic square with the name that is now known: the FOZ Magic Square

As these four colours are the same as the colours of the four suits of the Spanish deck of cards. (blue = swords, red = goblets or cups, green = clubs, yellow = gold), three FOZ Magic Squares can be formed with the traditional 48 deck of Spanish cards.

The magic presentation "The Wizard of FOZ" and the FOZUDOKUS are based on this, having an educational roll and not only as entertainment, motivating children to use logic and arithmetic.

Nine magic presentations were done in four schools in FOZ in 2013

(first one in the Martinez Otero School, later on in Pilar School and the C.E.I.P. 1 and C.E.I.P. 2 schools).

**BASE de DATOS**

From this BASE DE DATOS different technical pages can be accesed in this EXCEL file, with all the information and formulas necessary to make this file work and generate thousand of FOZUDOKUS

There is no need to see these pages to understand how to do a FOZUDOKU. This information is found in the main MENU and the NOTES in the FOZUDOKU pages

All the pages here are technical pages with formulas and several databases, etc. So if in future there is a need to make some modification or improvement, this information can be found easily.

**3 x 104**

There are 104 different positions to show the six cards in each of the three Magic Squares that a FOZUDOKU has, in this page are the formulas that calculate the thousands of those positions so they are not repeated in any FOZUDOKU.

**104 POSICIONES**

Six is the minimun number of cards shown in the three Magic Squares of a FOZUDOKU.

These six cards are strategically placed so they provide enough clues to calculate the other 10 missing cards, this is done by calculating the fourth cards in a group of cards where three cards are already known

In this page there 104 different ways to show these six cards in the 3 Magic Squares of a FOZUDOKU

Position 1 is used in all Magic Squares of page 1280 FOZUDOKUS

In pages 1 FOZUDOKU and 104 FOZUDOKUS, the position of the six cards shown is different for each Magic Square

**DATA**

In this page takes place the selection of the 3 Magic Squares of a FOZUDOKU (yellow for the Magic Square on the left that add up 22, green for the Magic Square on the centre that add up 26 and blue for the Magic Square on the right that add up 30)

On lines 108, 109, 110 and 111 there are formulas to compare the initial position of the Wizard of FOZ with selected FOZUDOKUS (that change every time that the F9 key is pressed)

When a FOZUDOKU.

When a FOZUDOKU selection is chosen where none of the cards are in the same position as the initial position the word EUREKA appears and this FOZUDOKU selection is suitable to memorize and use in the Wizard of FOZ

**SELECCIÓN - 1**

In this page, the cards of a FOZUDOKU are calculated and given the value 1 (for the six cards shown) and the value 0 (for the 10 cards not shown)

Yellow for the Magic Square on the left, Green for the Magic Square on the centre and Blue for the Magic Square on the right.

**SELECCIÓN - 2**

In this page the FOZUDOKU´s 18 cards shown and the FOZUDOKU´s 30 cards not shown are calculated.

**1280 FOZUDOKUS**

In this page there are 1280 FOZUDOKUS in 10 groups of 128 FOZUDOKUS each.

The next 128 FOZUDOKUS, (the first group), were made with cards in the following order: BASTOS (=clubs), COPAS (=cups), ESPADAS (=swords) and OROS (=gold).

This card order is different for all the other groups.

Each of the three Magic Squares in a FOZUDOKU is independent and interchangable with Magic Squares of other FOZUDOKUS within the same group, as they are made from the same cards in different positions and adding up the same (22 in the Magic Square on the left, 26 on the Magic Square on the centre and 30 on the Magic Square on the right, without a colour or suit repeated), so there are thousands of posibilities to form different three Magic Squares in a FOZUDOKU.

In this page, all the 1280 FOZUDOKUS, have the six cards shown in each Magic Square in the same position (position 1), but there are 104 different positions to show these six cards, those are used in 1 FOZUDOKU, 104 FOZUDOKUS and 104 POSICIONES.

**1280 SOLUCIONES**

In this page there are the solutions to 1280 FOZUDOKUS.

These 1280 FOZUDOKUS are in 10 groups of 128 FOZUDOKUS each.

The next 128 FOZUDOKUS, (the first group), were made with cards in the following order: BASTOS (=clubs), COPAS (=cups), ESPADAS (=swords) and OROS (=gold).

This card order is different for all the other groups.

Each of the three Magic Squares in a FOZUDOKU is independent and interchangable with Magic Squares of other FOZUDOKUS within the same group, as they are made from the same cards in different positions and adding up the same (22 in the Magic Square on the left, 26 on the Magic Square on the centre and 30 on the Magic Square on the right, without a colour or suit repeated), so there are thousands of posibilities to form different three Magic Squares in a FOZUDOKU.

**SECUENCIAS**

The three dots (...) after the number 6 in the flash card with the question 5 + 6 + 6 ... indicates that the last digit (6) is to be added continuosly until the total is over 100

In this case is like this:

5 + 6 (= 11) + 6 (= 17) + 6 (= 23) + 6 (= 29) + 6 (= 35) + 6 (= 41) + 6 (= 47) + 6 (= 53) + 6 (= 59) + 6 (= 65) + 6 (= 71) + 6 (= 77) + 6 (= 83) + 6 (= 89) + 6 (= 95) + 6 = 101

and 101 is the answer on the reverse of the flash card

with the question 5 + 6 + 6 ...

The sequence is 5, 1, 7, 3 y 9 these are the last digit on the total of each addition until is repeated continuosly again and again...

like this:

5, 11, 17, 23, 29

35, 41, 47, 53, 59

65, 71, 77, 83, 89

95, 101

**MAGO de FOZ**

El Mago de FOZ or Wizard of FOZ is a Mathe-Magic Presentation made with the traditional 48 Spanish cards. It has four parts that needs to be memorized in order to know, every moment, the number, suit and position of each card.

Before beginning the cards need to be in this order (from 1 to 12): OROS (=gold), ESPADAS (=swords), COPAS (=cups) and BASTOS (clubs).

The order to place the cards and change the cards are shown bellow each card (botton right). This order is ALWAYS the same for the Initial Position but it changes for each of the FOZUDOKUS below.

First part - Place all the cards face down in the Initial Position

Second part - Change ALL the cards, face down (without looking) to a new position where the 48 cards have three Magic Squares. Any of the specially selected FOZUDOKUS below is suitable for this as none of the cards positions are the same as the cards in the Initial Position

After the second part, when all the cards are face down, the Magician will guess

18 cards (6 cards in each Magic Square, in any of the 104 Positions) and the

audience are invited to guess the remaining 30 cards.

Part three after all cards are face up, they are put face down again, placing the cards back to the Initial Position

Part four the cards are collected in reverse order: First OROS (=gold), 1 to 12; Second ESPADAS (=swords), 1 to 12; Third COPAS (=cups), 1 to 12; Fourth BASTOS (=clubs), 1 to 12

**FORMULAS**

In this page there are notes that explain how some of the formulas in the pages of Excel work. These notes appear when the mouse is passed over the interrogation mark (?) of each formula.

This information may be useful in the future to understand how all works and to remember in the future how this file is built

The automatic calculation of the formulas has been desactivated and is now a manual calculation, so the formulas are only activated when pressing the key F9, (this avoids accidentally erasing the FOZUDOKUS, the BARAJAS lists and the SOLUCIONES, as they only change when pressing the F9 key)

In case that the formula´s calculations return to automatic mode, to chamge it again back to manual mode, do the following:

Click on "Archivo" and select "Opciones"

In "Opciones" select "Fórmulas",

In "Formulas" select "Calculodel libro - Manual".

**Construcción Cuadrado Mágico**

In this page, there are, step by step, two different ways to make The FOZ Magic Square.

A difficult and complex way, used in the magic presentation "The Wizard of FOZ" (see squares from 1 to 9)

A more simple and easy to remember way, just reversing the diagonals after placing the 16 numbers in numerical order(see squares 10 to 13)

Each 4x4 square, represents each of the steps to memorised and follow as you move and change the cards in order to produce a magic effect when you do The FOZ Magic square.

For this you need 16 cards with the number 1 to 16, in numerical order, with the colours red, blue, green and yellow.

The squares are numbered with an explnatory note to the left (in blue), that appears in a drop down list when you click the note with the mouse.

Base template by WEB MAGIC.@
CopyrighticjEl Cuadrado Mágico de FOZ all rights reserved.