Mirrored from Sudopedia, the Free Sudoku Reference Guide


Footprint

Definitions

The footprint of a pattern of solved cells is a list of 27 sets, where:

A solution to a given footprint is any assignment of values to cells that has the prescribed row/column/box memberships.

A pattern whose footprint has more than one solution is unavoidable (and conversely).

Example

The unavoidable set ...

1  .  .  |  2  .  .  |  .  .  .
2  .  .  |  3  .  .  |  .  .  .
3  .  .  |  1  .  .  |  .  .  .
---------+-----------+---------
.  .  .  |  .  .  .  |  .  .  .
.  .  .  |  .  .  .  |  .  .  .
.  .  .  |  .  .  .  |  .  .  .
---------+-----------+---------
.  .  .  |  .  .  .  |  .  .  .
.  .  .  |  .  .  .  |  .  .  .
.  .  .  |  .  .  .  |  .  .  .

... has footprint

This footprint has two solutions: the one given above, and this:

2  .  .  |  1  .  .  |  .  .  .
3  .  .  |  2  .  .  |  .  .  .
1  .  .  |  3  .  .  |  .  .  .
---------+-----------+---------
.  .  .  |  .  .  .  |  .  .  .
.  .  .  |  .  .  .  |  .  .  .
.  .  .  |  .  .  .  |  .  .  .
---------+-----------+---------
.  .  .  |  .  .  .  |  .  .  .
.  .  .  |  .  .  .  |  .  .  .
.  .  .  |  .  .  .  |  .  .  .

The two solutions are sometimes described as dual (but the terminology is not standardised).

This page was last modified 19:07, 29 December 2006.