## Solving using units/jouses

Advanced methods and approaches for solving Sudoku puzzles

### Solving using units/jouses

Recently I posted a new technique here for solving hard puzzles which utilized units/houses. The technique involves creating a
list of all combinations of candidates for a unit, and then determining if any of the combinations caused a contradiction when seeded into a forcing net. Since then I have developed it a bit further, and took the opportunity to test it using champagne's recently published hardest list. The top of his list is:
..34......5...9...7...2...62...7..1..9...5......3....8..1.6...78......21......4..;4024;elev;L406;11.10;11.10;3.40;9;;881

After singles and a naked quad, advanced techniques were required. From this same point, I ran each of the units in turn, and there
were eliminations in all but 6 of them, as detailed below. My program provides full detail of the starting combinations, and the
remaining combinations after those causing contradictions are removed.

units 0-8 = rows 1-9; units 9-17 = columns 1-9; units 18-26 = boxes 1-9.

Unit Eliminations
0 nil
1 r2c7<>2
2 r3c3<>8
3 r4c9<>4
4 r5c3<>4
5 r6c5<>1, r6c6<>1
6 nil
7 r8c2<>4, r8c3<>6, r8c7<>5
8 r9c1<>6, r9c2<>3, r9c3<>9, r9c4<>5,9, r9c5<>9, r9c6<>3, r9c8<>5,9

9 nil
10 r6c2<>4
11 r2c3<>4,8, r3c3<>8, r9c3<>7
12 nil
13 r6c5<>1
14 r6c6<>1, r9c6<>3
15 r8c7<>5
16 r3c8<>8
17 nil

18 r3c3<>8
19 r1c5<>1
20 r1c7<>5,8,9, r2c7<>2, r3c7<>1,9, r3c8<>8,9
21 r6c3<>4
22 r6c5<>1
23 r4c9<>4, r5c7<>3, r5c8<>3,4, r5c9<>2, r6c7<>5,7
24 r8c2<>4, r8c3<>7, r9c3<>7
25 r7c4<>8, r7c6<>8, r8c4<>9, r8c5<>3,5, r8c6<>3,4, r9c4<>2,5,7,9, r9c5<>1,8,9, r9c6<>2,3,7
26 nil

The 9th row and the 8th box in particular yielded many eliminations. When these two were run consecutively, the puzzle was
solved in 2 steps, taking about 15 minutes. Unit 8 (row 9) started with 428 combinations, of which 411 caused contradictions, leaving
only 17 with which to reconstitute the unit.

The technique is as yet unnamed - maybe 'house cleaning' or similar would do.

pjb
pjb
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Joined: 11 September 2011
Location: Sydney, Australia