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Topic: Greater Than Sudoku (Read 434 times) |
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towr
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Re: Greater Than Sudoku
« Reply #1 on: May 21st, 2007, 1:06am » |
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Do the regular sudoku rules still apply as well?
step 1: 1 can only be in a square that's not greater than any adjacent square; 9 can only be in a square that's bigger than every adjacent square
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Grimbal
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Re: Greater Than Sudoku
« Reply #2 on: May 21st, 2007, 2:00am » |
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And by following chains of inequalities, you can put an upper and lower limit on some cells.
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rmsgrey
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Re: Greater Than Sudoku
« Reply #3 on: May 21st, 2007, 12:44pm » |
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The host site lets you tackle the puzzles online. This one can be found here.
If I were doing it methodically*, my first step would be to look at each 3*3 nonet in turn. Within each nonet, I'd take each cell in turn and work out how many cells are "above" it and how many "below", using that to work out the range of possible values for that cell:
For example, in the top left nonet of the given puzzle, the top left cell's two neighbours are each below it, and are each below all their neighbours, so it must be in the range 3-9. The top middle cell is below all three neighbours, and two of those neighbours are themselves below the right middle cell, so there are 4 cells above and none below, giving a range of 1-5. Top right is above one neighbour which is below all of its neighbours, and below the other neighbour, which is above all its neighbours, giving a range of 2-8. Working through the entire nonet gives:
3-9, 1-5, 2-8
1-5, 4-8, 7-9
3-9, 1-5, 2-8
Working through the rest of the board this way, you'll find 4 places each with only one possible value - two 9s, an 8 and a 1.
Step 2 is to make use of the sudoku rules to eliminate any potential values in the same column or row as a matching known value - for example, the 9 in the middle right cell of the bottom right nonet rules out the potential 9s in the top and bottom right cells of the middle right nonet. As you do that, you should also tidy up any cells in the same nonet as adjusted cells if their range is reduced as a result - for example, in the middle right nonet, the bottom left and right corner cells both lose their 9, meaning the bottom middle cell which is lower than both cannot be 7 (at best the two corners are 7 and  and the middle middle cell then cannot be 6. Staying in that same nonet, there is now only one cell that could be a 9 - the top left cell, which in turn enables you to locate 9s in the middle middle and top right nonets, etc. You should be able to locate all nine 9s by this process.
From there, it's pretty much more of the same - apply standard sudoku techniques to rows and columns to adjust the list of possibilities in individual cells, and look at individual nonets to follow through on the consequences of those changes.
From where I've left off, you should be able to find the 8 in the second row, which doesn't help you much, or do something with the 5th row, which looks like it will help a lot (the three cells with 1-2, 2-3 and 1-3 must have 1,2,3 between them, meaning that the rest of the row can't have any of those three...)
*Normally, while I tend to start out following a loose method, I'll deviate from it as things catch my eye.
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