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The rules of Sudoku are surprisingly simple. Just Count to
Nine! ( get step-by-step instructions here )
Every column, row, and 3×3 square must contain the numbers 1
through 9 exactly once.
Every Sudoku puzzle has exactly 1 solution that can be solved
logically without guessing.
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A sudoku puzzle consists of a 9 × 9–square grid
subdivided into nine 3 × 3 boxes. Some of the squares contain
numbers. The object is to fill in the remaining squares so that
every row, every column, and every 3 × 3 box contains each of
the numbers from 1 to 9 exactly once.
Solving a Sudoku puzzle involves pure logic. No
guesswork is needed—or even desirable. Getting started
involves mastering just a few simple techniques.
Take the example on this page (in which
we’ve labeled the nine 3 × 3 boxes A to I as shown). Note
that boxes H and I already have 8’s filled in but G does
not. Can you determine where the 8 goes here?
| A | B | C |
| D | E | F |
| G | H | I |
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The 8 can’t appear in the top row of squares in box G,
because an 8 already appears in the top row of I—and no
number can be repeated in a row. Similarly, it can’t appear
in the middle row of G, because an 8 already appears in the
middle row of H. So, by process of elimination, an 8 must appear
in the bottom row of G. Since only one square in this row is
empty—next to the 3 and 6—you have your first answer.
Fill in an 8 to the right of the 6.
Next, look in the three left-handed boxes of
the grid, A, D, and G. An 8 appears in both A and G (the latter
being the one you just entered). In box A, the 8 appears in the
middle column, while in G the 8 appears on the right. By
elimination, in box D, an 8 must go in the leftmost column. But
which square? The column here has two squares open.
The answer is forced by box E. Here an 8
appears in the middle row. This means an 8 cannot appear in the
middle row of D. Therefore, it must appear in the top row of the
leftmost column of D. You have your second answer.
In solving a sudoku, build on the answers
you’ve filled in as far as possible—left, right, up,
and down—before moving on.
For a different kind of logic, consider the
sixth row of numbers—4, ?, 5, 6, ?, ?, 7, 3, 8. The missing
numbers must be 1, 2, and 9, in some order. The sixth square
can’t be a 1, because box E already has a 1. And it
can’t be a 2, because a 2 already appears in the sixth
column in box B. So the sixth square in the sixth row has to be a
9. Fill this in.
Now you’re left with just 1 and 2 for the
empty squares of this row. The fifth square can’t be a 1,
because box E already has a 1. So the fifth square must be a 2.
The second square, by elimination, has a 1. Voilà! Your first
complete row is filled in.
Box E now has only two empty squares, so this
is a good spot to consider next. Only the 4 and 7 remain to be
filled in. The leftmost square of the middle row can’t be a
4, because a 4 already appears in this row in box F. So it must
be 7. The remaining square must be 4. Your first complete box is
done.
One more tip, and then you’re on your own.
Consider 3’s the boxes A, B, and C. Only
one 3 is filled in—in the ninth row, in box C. In box A you
don’t have enough information to fill in a 3 yet. However,
you know the 3 can’t appear in A’s bottom row, because
3 appears in the bottom row of C. And it can’t appear in the
top row, because that row is already done. Therefore, it must
appear in the middle row. Which square you don’t know yet.
But now, by elimination, you do know that in box B a 3 must
appear in the top row. Specifically, it must appear in the fourth
column, because 3’s already appear in the fifth and sixth
columns of E and H. Fill this in.
Following logic, using these and other
techniques left for you to discover, you can work your way around
the grid, filling in the rest of the missing numbers. The
complete solution is shown below.
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| Remember, don’t guess. Be careful not to repeat a number where you shouldn’t, because a wrong answer may force you to start over. And don’t give up. Soon you’ll be a sudoku master! |
^ back to the top of this page ^ From SUDOKU EASY TO HARD PRESENTED BY WILL SHORTZ,
VOLUME 2. |
