Make a frequency list
Number | Occurances |
1 | 2 |
2 | 3 |
3 | 4 |
4 | 0 |
5 | 4 |
6 | 5 |
7 | 2 |
8 | 3 |
9 | 3 |
Solve the 6's.
Solve the 3's.
Solve the 5's. It's important to notice the occurances of the "65" (see (3,1) and (3,2)) pair combinations in two places in the puzzle. Those pairs can only be either 6/5 or 5/6 combinations.
Solve the 2's. Notice that we get to put the 2 in cell (3,9) because of the fact that a 2 can't go in either (7,9) or (8,9).
Solve the 8's, (3,3) gets placed first because of the little red 8's in (7,1) and (9,1), the 8 in (1,5) and the 8 in (6,2). Then the 8 in (2,8) get's placed. When one of the 2 little "3" numbers gets covered with an 8 then the other one has to be a 3 as in (2,7). When you discover a number (like 3 here) that's not the current number were solving at the moment then we need to re-solve for the new number (3). This yields 3 in (4,6) and (6,8) as shown here.
Solve the 9's. So far we have just used the "elimination" strategy. Another strategy that I use is: If a column, row, or block has 3 or less empty cells then try to solve each of those empty cells. At this point in the puzzle column 3 has only 3 empty cells so try to see if 1, 4, or 9 can go into one. For this puzzle it doesn't yield any results but for many puzzles it does.
Solve the 1's, 7's, and 4's.
Now we're done with the first pass. Next quickly go through all numbers looking for any more cells or pairs of possibilities.
Ok, now comes a not so easy step. We're going to look for blocked columns or rows. Start with column 1 of blocks (a block is a group of 9 cells) and check for the existence of a particular number (I'm cheating on my rule of only writting down pair possibilities to show you what's happening by putting the little 1's in the top block). If the number exists anywhere in the column, go to the next number.
The number 1 does not exist anywhere in column 1 of blocks. Notice that in the top block, 1 can only occur in column 1 or 2 of cells and also that in the bottom block 1 can only occur in column 1 or 2 of cells. This means that in the middle block a 1 can't occur in (2,5) as shown in the X'd out 1. This means (3,6) has to be a 1.
After we put the 1 in, lots of things happen. Here is the order: 1 in (3,6), 1 in (6,5), 2 in (6,4), 2 in (8,5), 5 in (7,6), 2 in (9,8), 6 in (7,9), 5 in (8,9), 5 in (4,5), 4 in (2,5),
Let's do some more. Here is the order: 1 in (5,1), 5 in (6,1), 6 in (3,1), 5 in (3,2), 6 in (8,2), 1 in (8,3), 7 in (4,2),
Now we're at another impasse. So we look for blocked columns or rows. Notice that there are no 4's in the bottom row of blocks. 4's are in the top two rows only of cells of the left and right blocks, so (4,7) can't be a 4 so has to be a 9.
Let's finish up. Here is the order: 4 in (4,1), 4 in (7,2), 4 in (9,6), 7 in (9,7), 4 in (8,8), 4 in (3,7), 8 in (9,1), 7 in (8,1), 2 in (7,1), 8 in (7,4), 7 in (3,8), 9 in (2,1), 9 in (6,3), 4 in (1,3). 7 in (6,6), 8 in (5,6), 4 in (6,9), 4 in (5,4), 7 in (5,9), 7 in (1,4), 9 in (3,4), 2 in (2,2), 1 in (1,2), 1 in (2,9), 9 in (1,9).
Here is a really strange Sudoku, it looks so easy but try to
solve it without a guess!
Go here and keep pressing "Take Step", it will show you how it's solved.