Sudoku 3 - Hard

SUDOKU #3

I'm going to repeat the info at the top of Sudoku #1, just in case you haven't seen that one yet.

I've been doing Sudoku for a while. There are a lot of people like me who have figured out some tricks or techniques that help them complete the puzzles. This page is not really for them. I met a woman recently who was just starting to try to do Sudoku. This page is for people like her. I'm not saying that I know every single trick, but I know enough to complete most puzzles.

The basic rules of Sudoku are that there is only one of each number in each row, column, and 9 square grid. There isn't any mathematics or arithmetic. If you know how to count from 1 to 9, then you can do these puzzles. All of the techniques are based on this rule.

Here is a sample Sudoku puzzle.

This is a Hard difficulty puzzle, and it will allow me to show some examples of a few of the tricks that I've uncovered. I've added the letters below to the rows and columns in order to talk about each of the 81 squares. As a convention, I will talk about squares and boxes. There are 81 squares, but there are 9 boxes of 9 squares.

There are 2s in row A and row B, so the 2 in row C has to be in CJ. That's because sets of 3 boxes are linked when you combine the two rules: (1) one of each number is in each row or column, and (2) there is one of each number in each box.

There is a 3 in column O and in rows D and E, so there has to be a 3 in FM. So there are 3s in columns M and O and in row H, so another 3 is in GN. There is another 3 in IK (because of HR and GN and EL), there is another 3 in AJ (because of BO and IK), and the final 3 is in CP (because of AJ, BO, DQ, and HR).

There is a 1 in BR (because of CK, AN, and IP) and another 1 in EQ, and there is an 8 inn IO (because of GP and HK) and another 8 in BL (because of HK).

Box AJ-CL has two numbers missing -- a 4 and a 6, but there is a 6 in AR, so the 6 is in BK and the 4 is in AK

There is a 6 in IM, which means that there has to be a 6 in column O in box DM-FO, and there is a 6 in BK. All of this put together means that there is a 6 in CN.

There is a 5 in ER (because of DK and FN).

The missing numbers from row I are the 5, 7, and 9, but there is a 7 in columns L and Q. So the 7 has to be in IR. There is an 8 in FR (because DN and GP), and there is an 8 in EJ (because of DN, FR, and HK).

The missing numbers in row E are 2, 6, and 7. There is a 6 in columns K and M, so the 6 has to be in EO. The missing numbers in row I are 5 and 9, but there is a 9 in column L, so the 5 is in IL and the 9 is in IQ.

There is a 9 in CR (because of EP and IQ). The missing numbers in row F are 1, 2, 4, and 6, but there is a 2 in column O and the 4 and 6 in box DM-FO. So there is a 1 in FO. That leaves the 2, 4, and 6. There is a 2 and a 4 in column J, so the 6 is in FJ.