### Domino Pairs Sudoku

Monday, April 28th, 2008The last cartoon that referred to Dominos and Sudoku occurred on March 30, 2007. At the time, I was more concerned with the number representation shown by the spots or “pips” than the tiles or “bones”.

So with this cartoon, I offer a variant using the tiles of a double nine set of Dominos.

A little analysis shows that a 9 by 9 Sudoku board permits a filled in arrangement of 40 tiles, keeping 1 cell uncovered. In this cartoon, I choose that cell to be the center cell, identified and covered by a circular single pip. For clarity, the starting tiles that are horizontal, have their border tinged in bright blue. Vertical tiles are shown in black.

Unfortunately, a double nine set of dominos contains 55 tiled pieces, of which 19 are inappropriate for Sudoku uniqueness rules (all tiles containing a blank and all the symmetric pairs). That leaves up to 36 unique tiles to place. This means there will be at least 4 tiles that are “cloned” in order to solve the Sudoku puzzle.

Fortunately, the tiles with pips are rotationally symmetric, unlike numbers printed on tiles, so they can fit into whateveer sudoku nook is required.

In keeping with the “solving rules” of this variant, place tiles or adjacent numbers two at a time. This is an unusual way of solving sudoku, especially at the beginning when you may be hard-pressed to find even a single number.

Perhaps you should invest in a double nine domino set as a solving aid and have a paper copy of the puzzle in progress to record your emerging solution, and place tile pairs only as they become available.