|Main Page - Back|
Sudoku X Strategies
From sudokuwiki.org, the puzzle solver's site
It is a given to expect Naked and Hidden Pairs, Triples and Quads in the diagonals as you would in any row, column or box. Beyond these are the two types of Intersection Removal. Since the diagonals only ever cross one row or one column at a time the only intersections you should look for are with boxes.
This Sudoku X puzzle I have picked specially for being packed with Pointing Pairs and Box/Line Reductions but example Pointing Pair here is aligned on a diagonal.
The two green cells in A9 and B8 are the only two cells in box 3 with the candidate 2. These align on the diagonal and since 2 must occur on one of the two green cells (we just don’t know which one) it can be removed from anywhere else in the diagonal, namely cell H2 and J1.
Pointing Pairs Figure 1: Load Example or : From the Start
There are three simultaneous Box/Line reductions here on numbers 1, 3 and 4. I have highlighted the cells with 1 as a solution or candidate and it is possible to see that the 1s for diagonal 1 (top left to bottom right) exist only in box 1. Therefore A1 or B2 must be a 1 so B1 and A2 cannot be 1. In green is the reduction on Box 5 because of Diagonal 2 (top right to bottom left). Again the 3s only exist in box 5 so the 3s on D4 and F6 can go.
The final reduction is in Box 1 using candidates 4 on Diagonal 1. removing the other 4s in Box 1 gives us a solution of 2 for A2.
Box/Line Reduction Figure 1: Load Example or : From the Start
|Pointing Pairs special to Sudoku X
The diagonals in Sudoku X afford another line of attack because of the angle they cross the board. Any two cells in a diagonal will share neither the same row or column and are therefore form opposite sides of a rectangle. The other two corners can't contain the same candidate as Pair on the diagonal.
Consider D6 and J1 which are a pair on candidate 1. Either D6 or J1 must be a 1 but they can both see D1 and J6. No 1 can be on either of those cells, thus the 1 on D1 can be removed.
Simple Colouring Figure 1: From the Start
|The Pitfalls of Unique Rectangles
All types of Unique Rectangles can be applied to Sudoku X - but there is a catch!
You cannot create the 'deadly pattern' if any of the four cells are on a diagonal.
Remember that the 'deadly pattern' is where you can potentially swap pairs of numbers around and we can make eliminations in order to avoid creating such a pattern. However, if a corner of the pattern is on a diagonal it is not the case that pairs can be swapped around - it would invalidate the diagonal constraint. So we can't use the logic of unique rectangles unless all the cells are away from the diagonals.
This example is rather spectacular - 7 eliminations based on the logic of a Type 2 Rectangle.
Documentation is here.
Unique Rectangle Figure 1: Load Example or : From the Start