https://www.sudopedia.org/index.php?action=history&feed=atom&title=Franken_SwordfishFranken Swordfish - Revision history2026-04-29T05:34:25ZRevision history for this page on the wikiMediaWiki 1.34.1https://www.sudopedia.org/index.php?title=Franken_Swordfish&diff=608&oldid=prevRooted at 19:05, 22 July 20252025-07-22T19:05:56Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 19:05, 22 July 2025</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In this example, the defining set contains columns 5, 7 & 8. The secondary set contains rows 5 & 8 and box 3. All the [[candidate]]s in the defining set (marked with '''X''') are located inside the secondary set. The remaining candidates from these 3 [[constraint]]s can be eliminated.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In this example, the defining set contains columns 5, 7 & 8. The secondary set contains rows 5 & 8 and box 3. All the [[candidate]]s in the defining set (marked with '''X''') are located inside the secondary set. The remaining candidates from these 3 [[constraint]]s can be eliminated.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''The 5 Patterns for the Franken Swordfish'''</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The previous example is the maximum pattern for the franken swordfish. It contains 12 cells and because of this its occurence is much rarer than the any of the other 4 patterns. Logical analysis of the minimum pattern shows that 4 of the cells in box 3 of the example are redundant. The other 4 patterns occur when 1, 2, 3, 4 of these redundant cells are removed. The only restriction on this is there must be at least 1 cell in each of the box 3 columns in the pattern. The minimum pattern occurs when there is only 1 cell in each of columns 7 and 8 of box 3. Since there are 9 different ways these cells can occur. The probability of occurence is 9 times that of the maximum pattern. There is nothing finnish or sashimish about any of the 5 patterns. In a finned or sashimi row or column swordfish cell eliminations occur only in the box with the fin. In contrast the 5 franken swordfish patterns with 8 through 12 cells all give exactly the same cell eliminations. They are analogous to the 4 patterns of the row or column swordfish with 6, 7, 8 and 9 cells. Because of the 5 patterns of the franken swordfish, the probobility of occurence may be comparable to that of the row or column swordfish. </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The diagram of a minimum franken swordfish pattern is shown below.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{grid|5=--|7=--|8=G|9=*|14=--|16=H|17=--|18=*|23=--|25=--|26=--|27=*|32=--|34=--|35=--|37=*|38=*|39=*|40=*|41=A|42=*|43=C|44=D|45=*|50=--|52=--|53=--|59=--|61=--|62=--|64=*|65=*|66=*|67=*|68=B|69=*|70=E|71=F|72=*|77=--|79=--|80=--}}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''How It Works.'''</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Since A and B are conjugate pairs either A exclusive or B is X. If A is X none of the peer cells in row 5 can be X. This creates 2 conditional conjugate pairs (EG and FH) in columns 7 and 8. Since G and H are peers and E and F are peers, one and only 1 of each of the peer groups must be X. Therefore X can be no additional X's in row 7 are box 3. If B is X none of the peer cells in row 7 can be X. This creates 2 conditional conjugate pairs (CG and DH) in columns 7 and 8. Since G and H are peers and C and D are peers, one and only 1 of each of the peer groups must be X. Therefore X can be no additional X's in row 5 are box 3. QED</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The logic for the other 4 patterns is similar except that one or both of the conditional conjugate pairs become conditional group conjugates. The logic is still valid for this case. </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''A Combined Franken/Column Swordfish'''</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">It is possible to have an 8 cell pattern which is both a franken swordfish and a column(row) swordfish. In this case additional cell eliminations can be made. An example of this is shown in the diagram below.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{grid|1=*|2=*|3=*|4=*|5=--|6=*|7=X|8=X|9=*|14=--|16=--|17=--|18=*|23=--|25=--|26=--|27=*|32=--|34=--|35=--|37=*|38=*|39=*|40=*|41=X|42=*|43=X|44=X|45=*|50=--|52=--|53=--|59=--|61=--|62=--|64=*|65=*|66=*|67=*|68=X|69=*|70=X|71=X|72=*|77=--|79=--|80=--}}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">It is also possible to have a 9 cell pattern which is both a franken swordfish and a finned column(row) swordfish. In this case the finned swordfish pattern does not provide any additional cell eliminations. An example of this is shown in the diagram below.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{grid|5=--|7=X|8=X|9=*|14=--|16=X|17=--|18=*|23=--|25=--|26=--|27=*|32=--|34=--|35=--|37=*|38=*|39=*|40=*|41=X|42=*|43=X|44=X|45=*|50=--|52=--|53=--|59=--|61=--|62=--|64=*|65=*|66=*|67=*|68=X|69=*|70=X|71=X|72=*|77=--|79=--|80=--}}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''A Finned Franken Swordfish Example'''</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Here is example of a finned franken swordfish. The fin in this example occurs in box 5 and the only cell eliminations for this pattern are also in box 5.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{grid|5=--|7=--|8=X|14=--|16=X|17=--|23=--|25=--|26=--|32=X|34=--|35=--|40=*|41=X|42=*|43=X|44=X|50=--|52=--|53=--|59=--|61=--|62=--|68=X|70=X|71=X|77=--|79=--|80=--}}</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== See Also ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== See Also ==</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Solving Techniques]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Solving Techniques]]</div></td></tr>
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</table>Rootedhttps://www.sudopedia.org/index.php?title=Franken_Swordfish&diff=606&oldid=prevRooted: Created page with "The '''Franken Swordfish''' is a fish pattern of the Franken Fish type. This type allows either the defining set or the secondary set to contain boxes, as..."2025-07-22T19:04:27Z<p>Created page with "The '''Franken Swordfish''' is a <a href="/wiki/Fish" title="Fish">fish</a> pattern of the <a href="/wiki/Franken_Fish" title="Franken Fish">Franken Fish</a> type. This type allows either the <a href="/wiki/Defining_set" title="Defining set">defining set</a> or the <a href="/wiki/Secondary_set" title="Secondary set">secondary set</a> to contain <a href="/wiki/Box" title="Box">boxes</a>, as..."</p>
<p><b>New page</b></p><div>The '''Franken Swordfish''' is a [[fish]] pattern of the [[Franken Fish]] type. This type allows either the [[defining set]] or the [[secondary set]] to contain [[box]]es, as well as [[line]]s.<br />
<br />
This is a [[project:fish diagram|fish diagram]] of a Franken Swordfish:<br />
<br />
[[image:franken swordfish.png]]<br />
<br />
In this example, the defining set contains columns 5, 7 & 8. The secondary set contains rows 5 & 8 and box 3. All the [[candidate]]s in the defining set (marked with '''X''') are located inside the secondary set. The remaining candidates from these 3 [[constraint]]s can be eliminated.<br />
<br />
== See Also ==<br />
* [[Fish]]<br />
* [[Swordfish]]<br />
* [[Franken Fish]]<br />
* [[Franken Jellyfish]]<br />
<br />
[[Category:Solving Techniques]]</div>Rooted