Solution to the weekly extreme Str8ts puzzle #47 from www.str8ts.com

1. Weekly Extreme Str8ts Puzzle #47 May 15 – May 21, 2011www.str8ts.com Solution bySlowThinker

2. Start position Extreme Str8ts #47 has several rows and columns that span 9 cells and does only have two compart-ments smaller than 3 cells. This will be beneficial for solving this puzzle using Setti’s rule, as small compartments usually lead to “undecided” rows and columns when applying Setti’s rule.

3. Solving… F6=4c G2=5h J2=6 H2=4 J3=7

4. Solving… J1=9h H1=6s J8=4s A3=2s

5. Solving… D3=3h D4=5 D7=2 J6=2s C5=2s

6. Solving… G6=9s G8=2s H8=3c

7. Optional:Setti’s rule on 3 As you can see there has to be a 3 in every column  There has to be a 3 in row E as well, thus we can remove 89 from row E (Note: This step is not necessary to solve the puzzle.) Border colors:green: number has to be in this row/column,yellow: number may be there, red: number is not there

8. Optional:Setti’s rule on 4 Same is true for number 4 and column 9  we can therefore remove 89 from column 9 (Note: This step is not necessary to solve the puzzle.)  D9=6S4 A7=6s

9. Setti’s rule on 7 There are 8 columns that have a 7 (all except column 2), so there must be 8 rows that contain a 7 as well  F1=7S7 G1=8 G9=3 G5=7 J9=1

10. Solving… J7=3c F7=1 F5=3 E4=3s E3=4s

11. Solving… E5=6s C3=8 B3=6 Note: we could remove 8 remove from H5, because 8 must be in H67, as otherwise we would violate the uniqueness constraint with EH67. But let’s continue without this…

12. Setti’s rule on 1 As we can see there are two columns that do not contain a 1  row A cannot contain a 1 either. Furthermore, column 5 must contain a 1, as seven rows contain a 1  A2=3S1 A4=4S1 A1=5 B1=4 C1=3 C2=1

13. Solving… A9=7 B9=5 C9=4 A6=8 A8=9 C8=7 B8=8

14. Finishing… B5=1 C4=9, B4=7, B7=9 C7=5, E7=7, E6=5 H4=1, H5=5 H6=7 H7=8

15. Done Using Setti’s rule two times(*) (on 7 and 1,) this puzzle was quite easy. If you like, try solving this puzzle without using Setti’s rule. It’s possible, but more difficult. (*) Applying Setti’s rule on 3 and 4 is not necessary to solve this puzzle

16. Glossary Letters appended to steps indicate the last strategy used, just before filling in a field: No letter … number was last candidate in field s … single (last) candidate for that number in compartment c … compartment range check d … stranded (unreachable/impossible) digits removed h … high/low range check across compartments p/t/q … naked pair / naked triple / naked quadruple ph/th/qh … hidden pair / hidden triple / hidden quadruple x … X-wing (2 rows / 2 columns) w … Swordfish (3 rows / 3 columns) j … Jellyfish (4 rows / 4 columns) L … large gap field Sx … Setti’s rule (count the numbers rule) – ‘x’ is the analysed number u … unique rectangle y … Y-Wing or XY-chains

17. Weekly Extreme Str8ts Puzzle #47www.str8ts.com Solution by SlowThinker Note: there are other (maybe easier) ways to solve this puzzle.