Difference Sudoku

5798 /www/nrich/html/content/id/5798/ 1 2011-02-01T00:00:01 <mdoxml version="1.0"> By Henry Kwok <div style="text-align: center;"><mdo:image height="498" width="498" src="OctoberSudoku.gif" alt="Sudoku puzzle"></mdo:image></div> <h4>Rules of Difference Sudoku</h4> Like the standard sudoku, the object of the puzzle is to fill in the whole $9 \times 9$ grid with numbers $1$ through $9$ so that each row, each column, and each of the nine $3 \times 3$ squares must contain all the nine different numbers. There are special clue-numbers placed on the border lines between selected pairs of adjacent squares of the grid. Each clue-number is the difference between the two numbers that should be in the adjacent squares just next to left & right from that clue-number. For example, a clue-number $7$ on the border line between two adjacent squares means that possible pairs of numbers for these squares must be from the following combinations: $1$ and $8$; $2$ and $9$; $8$ and $1$; or $9$ and $2$. The inequality sign, which is placed on the border line between r5c7 (row 5 column 7) and r5c8, indicates that the number in r5c7 is smaller than the number in r5c8. As this variant has only one inequality sign on the border line, it is called Minimal Difference Sudoku. A word document containing the problem can be found <a href="/content/id/5798/difference%20sudoku.doc">here</a>, for use in the classroom. </mdoxml> <mdoxml version="1.0"><div style="text-align: center;"><mdo:image width="498" height="498" src="OctSudokuSoln.gif" alt="Solution"></mdo:image></div> </mdoxml> <mdoxml version="1.0">If you can manage to reduce the possibilities of one cell to 2 or 3 numbers, you could try solving the puzzle with each of those values in turn. If you reach a contradiction (for example a number is repeated in a row, column or square) then you can rule out that value and try one of the others instead. Here's an example of a way to start this puzzle. Let's look at this section of the grid: <mdo:image alt="" src="start0.png" style="text-align: center; width: 132px; height: 72px;"></mdo:image> We need two numbers that differ by 8, they can only be 1 and 9. But which way round should they go? Let's try both possibilities, writing one pair at the top of the cells and the other at the bottom: <mdo:image alt="" src="start1.png" style="width: 132px; height: 82px;"></mdo:image> Then we can use the '7' to determine the value of the next cell for each of our possibilities: <mdo:image alt="" src="start2.png" style="width: 184px; height: 68px;"></mdo:image> We can keep going in this way with two possible solutions emerging until one of them ends in a contradiction. Rosie and Zoe solved this Sudoku. They kept a record of the order in which they filled the Sudoku and wrote it in the boxes. Their journey can be found <a href="/content/id/5798/Difference%20Sudoku%20-%20Journey.pdf">here</a>. This is just one possible route through the problem. </mdoxml> 2 5 0 0 1 1 0 Difference Sudoku Use the differences to find the solution to this Sudoku. Using, Applying and Reasoning about Mathematics Selecting and using information Using, Applying and Reasoning about Mathematics Working systematically Calculations and Numerical Methods Mental addition & subtraction Information and Communications Technology smartphone