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Futoshiki Puzzle Book
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Introduction
Futoshiki is a Japanese game of inequality, where greater than and less thansigns are the main clues. Like Sudoku, each digit must appear once in everysingle row and column.
So with a 4x4 puzzle, each row and column will contain the digits 1,2,3 and 4.Whilst the smaller puzzles are easy, larger ones will be a real test of yourdeductive powers.
To get started, let's look at a simple example:
To begin with we can see that row 3 already has one number, 2, and that the topcell is greater than the cell below it.
We know the remaining numbers in the row are 1 and 3, so 3 must be in the top cell
and 1 below it.
It's now straightforward to complete the puzzle by filling in the remaining cells.
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A Full Sized Game
Now let's look at a full sized 5x5 puzzle:
Begin by making pencil marks for each cell, showing all the possible numbers.
If a cell is less than a neighbour, all possible values must be less than thatneighbour, and the cell cannot contain a 5, as the neighbour could not hold a 6.
For the first two cells, we can see they are less than their neighbours to the right.So we can write in the pencil marks 1,2,3 2,3,4 and 3,4,5.
Now let's fill in the pencil marks for the first 2 rows:
Once you've filled in the pencil marks, look through each row and column to seeif any numbers are unique. On the first row, 1 can only be placed in the first cell,so it must be the cell value.
Now fill in the 1, and remove 1 from all the other cells in the first row.
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Having filled in all the pencil marks, we can see a number of cells with onlya single value. Let's fill those in and remove the values from the rows andcolumns they're in:
Now look through to see what else can be deduced. In the first row, cell 3must be greater than the 4 to it's right, so it must contain a 5.
After filling that in, we can see the only place a 5 can go in the rightmostcolumn.
Now update the pencil marks to take account of the new values.The 2 remaining 5s can be written in.
Now the 4s in the second and fourth rows can be written down.
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From here we can write down the remaining values.
Larger puzzles call for more advanced techniques, such as removing pairs ofnumbers
Good luck!
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Puzzle #1
Puzzle #2
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Puzzle #3
2
8
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Puzzle #4
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Puzzle #5
10
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Puzzle #6
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Puzzle #7
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Puzzle #8
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Puzzle #9
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Puzzle #10
15
Solutions
Solution #1 Solution #2 Solution #3
5
24
3
1
1
35
4
2
4
13
2
5
2
41
5
3
3
52
1
4
2 4 3 1 4 3 2 1
1 3 2 4 2 1 4 3
3 1 4 2 1 4 3 2
4 2 1 3 3 2 1 4
Solution #4 Solution #5 Solution #6
2
5
4
3
1
1
4
3
2
5
3
1
5
4
2
5
3
2
1
4
4
2
1
5
3
2
3
4
5
1
3
4
5
1
2
5
1
2
3
4
4
5
1
2
3
1
2
3
4
5
5
1
4
3
2
1
2
5
4
3
4
5
3
2
1
3
4
2
1
5
2
3
1
5
4Solution #7 Solution #8 Solution #9
6
3
4
1
2
5
3
6
1
4
5
2
4
1
2
5
6
3
5
2
3
6
1
4
1
4
5
2
3
6
2
5
6
3
4
1
5
3
4
2
1
6
2
6
1
5
4
3
4
2
3
1
6
5
1
5
6
4
3
2
6
4
5
3
2
1
3
1
2
6
5
4
2
4
1
5
6
3
4
6
3
1
2
5
3
5
2
6
1
4
1
3
6
4
5
2
5
1
4
2
3
6
6
2
5
3
4
1Solution #10
63
1
7
2
45
74
2
1
3
56
26
4
3
5
71
15
3
2
4
67
52
7
6
1
34
37
5
4
6
12
41
6
5
7
23
16
