Solution to the weekly extreme Str8ts puzzle #59 from www.str8ts.com

1. Weekly Extreme Str8ts Puzzle #59 August 7 – August 13, 2011www.str8ts.com Solution & puzzle bySlowThinker

2. Start position Extreme Str8ts #59 was designed by me, and it has a peculiar feature that is the central focus of this puzzle.

3. Solving… Removing stranded digits eliminates many candidates at this point… A5=4d C5=3c A4=5 C4=2

4. Solving… C7=1s A2=89, because of C..G2, therefore C..G2 cannot contain a 9 as it would leave A2 without candidates. Also, 1 is a stranded digit in D3.

5. Solving… G3=1s G6=2s F7=2s A2=9p … and because of the pair 78 in CF2, we can remove 3 as candidate from DE2.

6. Solving… Because of E2=46 we can remove 2 from E3 (stranded) and 9 from E13 (range check.) D3=2s D2=4c D4=3 D5=5

7. Solving… E2=6 B4=4 B3=3p G1=6s D9=6s

8. Setti’s rule on 6 There are 8 rows that have a 6, so 8 columns must contain a 6 too  GHJ5 contains a 6. Note that E5 cannot be 5 or 8 due to E123 and E789.

9. Unique solution constraint This is the key point of this puzzle: looking at E5 we find that of all fields that influence E5, only E789 affects E5. Thus if E789 would notcontain a 9, E5 could be either 1 or 9 which would violate the unique solution constraint  E789=789u E5=1u

10. Solving… E2=4h E3=5h F8=5s B6=6h B7=5

11. Solving… Due to H1, H3..7 cannot end at 9, as this would leave H1 without candidates  H4=7h G4=9 C1=9p C9=5p

12. Solving… H1=8 F1=7 F2=8 F3=9 C2=7 C6=8

13. Solving… A6=7 H3=6 H7=4 H5=5 H6=3 F6=4

14. Solving… A3=8 A7=6 J3=7 J5=6 J6=5 J7=9

15. Solving… J8=4c G5=7c G8=8 D8=7 D7=8 F9=3

16. Solving… E7=7 E8=9 E9=8 G9=4 B9=7c

17. Solution This puzzle showed that the unique solution constraint not only comes in form of a unique rectangle, but also in terms of compartments influencing each other. For more information see my strategy slides.

18. 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

19. Weekly Extreme Str8ts Puzzle #59www.str8ts.com Solution by SlowThinker Note: there are other (maybe easier) ways to solve this puzzle. View & download my strategy slides from: http://slideshare.net/SlowThinker/str8ts-basic-and-advanced-strategies or from Google Docs: http://is.gd/slowthinker_str8ts_strategy