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All sudoku grids with 7 queens, including rotation & reflection but not transposition
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Here are the 24 arrangements of sudoku numbers such that each placed digit behaves like a queen, i.e., no instance of a given digit "sees" a copy of itself along a diagonal. They are in no particular order. In each grid, digits 1-7 are represented, and 8 & 9 would need to be filled in where there are zeros. The 24 grids all 'collapse' to only 4 unique patterns, with 8, 8, 4, and 4 reflection/rotational equivalents each. | |
Most of these arrangements are broken, however, as you cannot place exactly one 8 and one 9 in each box, column, and row without clashes. The exceptions are grids 3, 7, 19 and 20 (which are rotations of one another). Those four are therefore the only possible solutions to sudokus with 7 queens, disregarding transposition (i.e., substituting a different permutation of digits for 1-9). | |
The other 20 arrangements are still useful, however, as they can be used as the basis for puzzles with 6, 5 or fewer queens. | |
Grid 1. (broken) | |
123|450|670 | |
407|613|052 | |
560|072|134 | |
----------- | |
072|534|061 | |
304|126|507 | |
615|007|423 | |
----------- | |
246|705|310 | |
030|261|745 | |
751|340|206 | |
----------- | |
Grid 2. (broken) | |
102|034|567 | |
637|512|040 | |
054|607|132 | |
----------- | |
423|700|651 | |
706|125|304 | |
510|346|270 | |
----------- | |
345|270|016 | |
260|451|703 | |
071|063|425 | |
----------- | |
Grid 3. (valid) | |
102|345|670 | |
034|617|205 | |
765|200|143 | |
----------- | |
527|034|061 | |
340|176|052 | |
610|520|734 | |
----------- | |
256|003|417 | |
403|761|520 | |
071|452|306 | |
----------- | |
Grid 4. (broken) | |
102|340|567 | |
546|701|302 | |
703|562|014 | |
----------- | |
421|075|036 | |
630|024|175 | |
075|136|240 | |
----------- | |
214|650|703 | |
067|203|451 | |
350|417|620 | |
----------- | |
Grid 5. (broken) | |
123|045|607 | |
605|701|243 | |
470|623|501 | |
----------- | |
250|310|764 | |
317|460|052 | |
046|257|310 | |
----------- | |
501|032|476 | |
734|506|120 | |
062|174|035 | |
----------- | |
Grid 6. (broken) | |
120|345|670 | |
065|701|324 | |
743|620|501 | |
----------- | |
052|416|730 | |
610|073|452 | |
374|052|016 | |
----------- | |
501|267|043 | |
236|504|107 | |
407|130|265 | |
----------- | |
Grid 7. (valid) | |
102|345|670 | |
045|671|302 | |
673|200|541 | |
----------- | |
456|013|027 | |
710|426|053 | |
320|750|416 | |
----------- | |
561|002|734 | |
207|534|160 | |
034|167|205 | |
----------- | |
Grid 8. (broken) | |
123|450|607 | |
040|673|152 | |
657|102|430 | |
----------- | |
732|001|564 | |
405|367|201 | |
016|245|073 | |
----------- | |
270|016|345 | |
501|734|026 | |
364|520|710 | |
----------- | |
Grid 9. (broken) | |
123|456|700 | |
706|023|145 | |
450|107|623 | |
----------- | |
270|645|310 | |
631|070|452 | |
045|312|076 | |
----------- | |
562|704|031 | |
314|560|207 | |
007|231|564 | |
----------- | |
Grid 10. (broken) | |
123|405|607 | |
075|620|143 | |
460|173|025 | |
----------- | |
230|540|716 | |
501|736|402 | |
746|012|350 | |
----------- | |
352|064|071 | |
014|357|260 | |
607|201|534 | |
----------- | |
Grid 11. (broken) | |
123|405|607 | |
075|632|140 | |
460|170|532 | |
----------- | |
032|540|716 | |
501|726|403 | |
746|013|025 | |
----------- | |
350|264|071 | |
214|057|360 | |
607|301|254 | |
----------- | |
Grid 12. (broken) | |
123|450|607 | |
075|603|142 | |
460|172|053 | |
----------- | |
302|045|716 | |
051|726|430 | |
746|310|025 | |
----------- | |
230|064|571 | |
514|207|360 | |
607|531|204 | |
----------- | |
Grid 13. (broken) | |
102|345|607 | |
074|602|135 | |
365|170|042 | |
----------- | |
520|034|716 | |
041|726|350 | |
736|510|204 | |
----------- | |
450|263|071 | |
213|407|560 | |
607|051|423 | |
----------- | |
Grid 14. (broken) | |
123|450|670 | |
406|273|510 | |
750|016|432 | |
----------- | |
301|507|264 | |
640|321|057 | |
572|604|301 | |
----------- | |
215|730|046 | |
034|162|705 | |
067|045|123 | |
----------- | |
Grid 15. (broken) | |
102|345|607 | |
357|602|410 | |
640|017|325 | |
----------- | |
271|450|063 | |
035|261|740 | |
406|073|251 | |
----------- | |
710|526|034 | |
023|104|576 | |
564|730|102 | |
----------- | |
Grid 16. (broken) | |
102|304|567 | |
547|062|310 | |
360|517|024 | |
----------- | |
271|043|056 | |
604|251|703 | |
035|670|241 | |
----------- | |
710|420|635 | |
026|135|470 | |
453|706|102 | |
----------- | |
Grid 17. (broken) | |
102|304|567 | |
047|652|310 | |
653|017|024 | |
----------- | |
271|043|650 | |
504|261|703 | |
360|570|241 | |
----------- | |
710|426|035 | |
025|130|476 | |
436|705|102 | |
----------- | |
Grid 18. (broken) | |
102|034|567 | |
647|502|310 | |
530|617|024 | |
----------- | |
271|340|605 | |
054|261|730 | |
360|075|241 | |
----------- | |
713|420|056 | |
025|106|473 | |
406|753|102 | |
----------- | |
Grid 19. (valid) | |
012|345|607 | |
306|172|450 | |
547|006|321 | |
----------- | |
720|450|163 | |
630|217|045 | |
451|063|072 | |
----------- | |
174|500|236 | |
063|721|504 | |
205|634|710 | |
----------- | |
Grid 20. (valid) | |
012|345|607 | |
605|712|340 | |
743|006|512 | |
----------- | |
160|570|234 | |
530|264|071 | |
274|031|065 | |
----------- | |
451|600|723 | |
027|453|106 | |
306|127|450 | |
----------- | |
Grid 21. (broken) | |
012|034|567 | |
073|516|204 | |
654|270|031 | |
----------- | |
426|103|705 | |
130|765|042 | |
705|402|613 | |
----------- | |
240|051|376 | |
301|627|450 | |
567|340|120 | |
----------- | |
Grid 22. (broken) | |
012|345|067 | |
465|701|320 | |
703|062|541 | |
----------- | |
051|274|630 | |
634|510|072 | |
270|630|415 | |
----------- | |
540|126|703 | |
107|403|256 | |
326|057|104 | |
----------- | |
Grid 23. (broken) | |
012|034|567 | |
630|572|104 | |
457|610|023 | |
----------- | |
720|453|610 | |
103|267|405 | |
564|100|372 | |
----------- | |
075|301|246 | |
341|726|050 | |
206|045|731 | |
----------- | |
Grid 24. (broken) | |
001|234|567 | |
347|560|201 | |
562|107|034 | |
----------- | |
075|342|016 | |
634|010|752 | |
210|675|340 | |
----------- | |
750|401|623 | |
106|023|475 | |
423|756|100 | |
----------- | |
compiled by Philipp Blume from a list provided by Ulrich Voigt |
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