Making Sudoku

Hobbies

Entry posted by Nukora April 24, 2008

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A lot of people (myself included) will get stuck if they just start filling in numbers in a blank 81-square grid. You get...nothing. Just a bunch of numbers in a big square. I found it easier if I started making my own Sudoku puzzles starting with the first row. That made it easier. And this entry takes what I observed while doing so and shares it. You'll notice that the 9 numbers (in this example order 123456789) are divided into three groups by the 3x3 little squares.

Now, we will fill in the second row. Our grounds (A:123, B:456, and C:789) are our main basis for making the grid this way. In Row 2 we can either go (C:789, A:123, and B:456) or (B:456, C:789, and A:123), because of how Sudoku works mathematically. The individual numbers of our group can go in 3! = 6 combinations here. Because of that, we may end with Row 2 being 654879231.

Row three is a little trickier, but by no means hard. You noticed how I pointed out two different ways to order the groups either CAB or BCA in the second row. In Row 3 you use the opposite way. In my example we used BCA in Row 2. Now we use CAB in Row 3. The individual numbers can once again go in any order, so I've used 987312645 in my example.

Row 4 is a lot of fun. The sort of "a lot of fun" your math teacher says and it makes your whole class groan. There are six ways to arrange our groups: (1)ABC, (2)ACB, (3)BCA, (4)BAC, (5)CBA, (6)CAB. Just for simplicity, I'll deal with ABC in this example. As you place the individual numbers of your groups, watch out for the numbers in the previous three rows. They can place some rules about where certain numbers can't go. 231654897

The fifth row...is worse than the fourth. For each of those 6 ways to place our groups we chose from for Row 4, there are two ways to arrange row 5.

ABC: CAB, BCA
ACB: CBA, BAC
BCA: CAB, ABC
BAC: ACB, CAB
CBA: BAC, ACB
CAB: ABC, BCA

This is because we can't have two sets of the same group in the same square. So we have two possibilities. Once you've decided on which of the two to use, place your individual numbers, watching out for the previous numbers in the column. I'll use CAB: 879213564

In the sixth row, use the opposite of the possibilities that you used for the fifth. So, if you used CAB in Row 5 (like I did), use BCA for Row 6. Again, watch those previously filled in numbers in the same column (of course, I would go into how for when you use 123 above you can use either 312 or 231 below, but you've probably got that from the group orders we've discussed). I'll do this: 456987312

The next three rows are very similar to 4-6. In the first row we used 123 order for Group A. In Row 4 we ordered Group A 231. Now in whatever row has Group A in the first 3x3 square we must use the order 312 so that we don't have a repeat in the columns. By now, hopefully you've gotten the idea and can finish the last three rows without step-by-steps.

And I doubt that made sense. Should I have put this in Confusing You category?