The goal of each Sudoku move is to enter a number -- or at least narrow down what numbers are possible -- in each space.
The "Box In A Box" strategy is one way to use existing numbers to zero in on where to enter a new number.
Consider the following position:
We're interested in the 8s here. Ignore everything else. We're going to use two of the 8s to show where another 8 must go.
Look at the box of nine at the middle right:
We want to put an 8 in there. At first, this might seem very hard. There are six open spaces in that box! Where would the 8 go in that box? The two 8s near the box are going to show us.
First, look at the 8 just to the left of the box:
We know one thing for sure: there can't be another 8 in the same row as that 8. This means that there can't be an 8 in the bottom row of three in that box. Pretty good! We've eliminated three of the possible six spaces in that box!
Next, look at the 8 below the box:
Another thing we know for sure: there can't be another 8 in the same column as that 8. This means that there can't be an 8 in the left column of three in that box. Great! We've just eliminated two more possible spaces in that box!
But wait! That leaves only one space where the 8 can go in this box:
The 8 goes in the only space left over when the bottom row and left column of the box are eliminated.
If you look at the pictures, you can see where this strategy gets its name. We originally started with a box of nine spaces. But we used one 8 to eliminate one row and another 8 to eliminate one column. We formed a "box" of only four spaces in the box of nine spaces. It's a box in a box.
Notice that this ONLY works if there are already three numbers in our little box of four spaces. In this case, there already were a 9, a 3, and a 5 in that box of four. There was only one space left over for that 8 to go.
If there aren't already three numbers in the little box of four, this doesn't work. For instance, if you look at the left middle box, two of the 8s also eliminate its bottom row and its left column, also forming a box of four spaces. But the only number in that box of four is that 1, and it's not enough to tell us where the 8 would go.
What to look for:
* Two numbers that eliminate a row and a column in a box.
* Three numbers already in the remaining box of four.
Good luck!
The "Box In A Box" strategy is one way to use existing numbers to zero in on where to enter a new number.
Consider the following position:
We're interested in the 8s here. Ignore everything else. We're going to use two of the 8s to show where another 8 must go.
Look at the box of nine at the middle right:
We want to put an 8 in there. At first, this might seem very hard. There are six open spaces in that box! Where would the 8 go in that box? The two 8s near the box are going to show us.
First, look at the 8 just to the left of the box:
We know one thing for sure: there can't be another 8 in the same row as that 8. This means that there can't be an 8 in the bottom row of three in that box. Pretty good! We've eliminated three of the possible six spaces in that box!
Next, look at the 8 below the box:
Another thing we know for sure: there can't be another 8 in the same column as that 8. This means that there can't be an 8 in the left column of three in that box. Great! We've just eliminated two more possible spaces in that box!
But wait! That leaves only one space where the 8 can go in this box:
The 8 goes in the only space left over when the bottom row and left column of the box are eliminated.
If you look at the pictures, you can see where this strategy gets its name. We originally started with a box of nine spaces. But we used one 8 to eliminate one row and another 8 to eliminate one column. We formed a "box" of only four spaces in the box of nine spaces. It's a box in a box.
Notice that this ONLY works if there are already three numbers in our little box of four spaces. In this case, there already were a 9, a 3, and a 5 in that box of four. There was only one space left over for that 8 to go.
If there aren't already three numbers in the little box of four, this doesn't work. For instance, if you look at the left middle box, two of the 8s also eliminate its bottom row and its left column, also forming a box of four spaces. But the only number in that box of four is that 1, and it's not enough to tell us where the 8 would go.
What to look for:
* Two numbers that eliminate a row and a column in a box.
* Three numbers already in the remaining box of four.
Good luck!
