80 Challenging Tatami Puzzles

by Alejandro Erickson.http://tomokupuzzle.com

Copyright c⇥ by Alejandro Erickson, 2011.ISBN 978-0-9868121-0-1

2 Quickstart guide

Quickstart Guide

Tatami mats are traditional Japanese floor mats ( , , ). In tearooms, it is unlucky to have the corners of four mats touching atone point. That is, a “lucky” layout has no “+”-shapes formed bythe lines where mats meet each other.

Unlucky LuckyHas “+”s. Has no “+”s.

Mats are shown in the Tomoku puzzle beside their containing col-umn or below their containing row. Notice that a appears in both

a row and column. You must check both places before placing a .The order of the mats within each row and column does not matter.

Tomoku Puzzle. Lucky Solution.The object of the Tomoku puzzle game is to find a lucky layoutusing the mats shown in the rows and columns of the puzzle.

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A appears in its A stays in A stays inrow and column. its row. its column.

Are you ready for your first challenge? Try some of the smallergrids first. Come back later and read the tutorial for a few extratips.

Tutorial

To fill in a puzzle, use a short line to represent a or and a dotto represent a . Cross off mats you have used in the arrangement.To place a you must use one from both a row and a column.

Adding a uses one in botha row and a column.

A may only be placed onthe dark gray squares.

Your correct solution will almost always be the one shown in thebook. If it is not, just check that you have used the right numberof mats from each row and column and that your arrangement is

4 Quickstart guide

“lucky”.

Adding a verticalmat.

Adding ahorizontal mat. Completed puzzle.

Try to place mats which force the placement of others. For example,if the corners of two mats meet at a grid intersection, then either a

or a must be placed at that intersection to avoid an unlucky“+”. Another strategy is to place the mats first.Visit http://tomokupuzzle.com for even more tips and the Tomokuweb game.

Acknowledgements

I am grateful to Donald Knuth, Frank Ruskey, Martín Matamala,and Cliff Stoll. Their work and their words inspired me to createthis puzzle book and the Tomoku web game. I also thank MichaelLa Croix, a friend and diagrams expert, who gave valuable adviceon early renditions of the puzzles.

Tomoku was conceived in a conversation between Martín Mata-mala and myself over coffee in Plaza Sotomayor in Valparaíso,Chile, when he asked how hard it is to recover a tatami tilingfrom its tomographic projections.

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Puzzle 1

Puzzle 2

6 3 � 6 Puzzles

Puzzle 3

Puzzle 4

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Puzzle 5

Puzzle 6

8 3 � 6 Puzzles

Puzzle 7

Puzzle 8

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Puzzle 9

Puzzle 10

10 3 � 10 Puzzles

Puzzle 11

Puzzle 12

Puzzle 13

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Puzzle 14

Puzzle 15

Puzzle 16

12 3 � 10 Puzzles

Puzzle 17

Puzzle 18

Puzzle 19

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Puzzle 20

Puzzle 21

14 4 � 10 Puzzles

Puzzle 22

Puzzle 23

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Puzzle 24

Puzzle 25

16 4 � 10 Puzzles

Puzzle 26

Puzzle 27

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Puzzle 28

Puzzle 29

18 5 � 12 Puzzles

Puzzle 30

Puzzle 31

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Puzzle 32

Puzzle 33

20 5 � 12 Puzzles

Puzzle 34

Puzzle 35

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Puzzle 36

Puzzle 37

22 5 � 12 Puzzles

Puzzle 38

Puzzle 39

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Puzzle 40

Puzzle 41

24 5 � 12 Puzzles

Puzzle 42

Puzzle 43

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Puzzle 44

Puzzle 45

26 5 � 12 Puzzles

Puzzle 46

Puzzle 47

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Puzzle 48

Puzzle 49

28 6 � 12 Puzzles

Puzzle 50

Puzzle 51

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Puzzle 52

Puzzle 53

30 6 � 12 Puzzles

Puzzle 54

Puzzle 55

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Puzzle 56

Puzzle 57

32 6 � 12 Puzzles

Puzzle 58

Puzzle 59

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Puzzle 60

Puzzle 61

34 6 � 12 Puzzles

Puzzle 62

Puzzle 63

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Puzzle 64

Puzzle 65

36 6 � 12 Puzzles

Puzzle 66

Puzzle 67

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Puzzle 68

Puzzle 69

38 9 � 14 Puzzles

Puzzle 70

Puzzle 71

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Puzzle 72

Puzzle 73

40 9 � 14 Puzzles

Puzzle 74

Puzzle 75

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Puzzle 76

Puzzle 77

42 9 � 14 Puzzles

Puzzle 78

Puzzle 79

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Puzzle 80

44 Solutions

3 � 6 Solutions.

3 � 10 Solutions.

4 � 10 Solutions.

5 � 12 Solutions.

6 � 12 Solutions.

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9 � 14 Solutions.