http://sudopedia.sudocue.net/index.php?action=history&feed=atom&title=FootprintFootprint - Revision history2026-04-18T22:19:49ZRevision history for this page on the wikiMediaWiki 1.36.2http://sudopedia.sudocue.net/index.php?title=Footprint&diff=314&oldid=prev127.0.0.1: Created page with "== Definitions == The '''footprint''' of a pattern of solved cells is a list of 27 sets, where: * set 1 = values in row 1 of the pattern * set 2 = values in row 2 of the patt..."2021-10-25T14:17:52Z<p>Created page with "== Definitions == The '''footprint''' of a pattern of solved cells is a list of 27 sets, where: * set 1 = values in row 1 of the pattern * set 2 = values in row 2 of the patt..."</p>
<p><b>New page</b></p><div>== Definitions ==<br />
<br />
The '''footprint''' of a pattern of solved cells is a list of 27 sets, where:<br />
* set 1 = values in row 1 of the pattern<br />
* set 2 = values in row 2 of the pattern<br />
* ...<br />
* set 9 = values in row 9 of the pattern<br />
* sets 10-18 = values in columns 1-9 of the pattern<br />
* sets 19-27 = values in boxes 1-9 of the pattern<br />
<br />
A '''solution''' to a given footprint is any assignment of values to cells that has the prescribed row/column/box memberships.<br />
<br />
A pattern whose footprint has more than one solution is '''[[unavoidable set|unavoidable]]''' (and conversely).<br />
<br />
== Example ==<br />
<br />
The unavoidable set ...<br />
1 . . | 2 . . | . . .<br />
2 . . | 3 . . | . . .<br />
3 . . | 1 . . | . . .<br />
---------+-----------+---------<br />
. . . | . . . | . . .<br />
. . . | . . . | . . .<br />
. . . | . . . | . . .<br />
---------+-----------+---------<br />
. . . | . . . | . . .<br />
. . . | . . . | . . .<br />
. . . | . . . | . . .<br />
... has footprint<br />
* {1,2} in row 1<br />
* {2,3} in row 2<br />
* {1,3} in row 3<br />
* {1,2,3} in column 1<br />
* {1,2,3} in column 4<br />
* {1,2,3} in box 1<br />
* {1,2,3} in box 2<br />
* (all other rows, columns and boxes empty)<br />
<br />
This footprint has two solutions: the one given above, and this:<br />
2 . . | 1 . . | . . .<br />
3 . . | 2 . . | . . .<br />
1 . . | 3 . . | . . .<br />
---------+-----------+---------<br />
. . . | . . . | . . .<br />
. . . | . . . | . . .<br />
. . . | . . . | . . .<br />
---------+-----------+---------<br />
. . . | . . . | . . .<br />
. . . | . . . | . . .<br />
. . . | . . . | . . .<br />
<br />
The two solutions are sometimes described as ''dual'' (but the terminology is not standardised).</div>127.0.0.1