Solution to the weekly extreme Str8ts puzzle #49 from www.str8ts.com

1. Weekly Extreme Str8ts Puzzle #49 May 29 – June 4, 2011www.str8ts.com Solution bySlowThinker

2. Start position Extreme Str8ts #49 cannot be solved without testing/guessing. A possible reason is that there are very few small compartments. Solving A5=8c A7=7c G1=7c

3. Solving… J1=4p H9=7s B4=7s D7=3s Note: after J1=4, A3=26 which is a large gap pair, that removes 26 from A12.

4. Testing GH2=89 Using conventional methods and rules we are stuck at this position. As you can see, there are only a few fields with two candidates. And even if you test one of those fields, you cannot draw easy conclusions. An interesting candidate is 8, due to Setti’s rule. GH2 also intersects with 3 in row H, which in turn influences C8. This is why I tested GH2=89 first.

5. Testing GH2=89 G2=8g, H2=9g  H8=3s, C8=8  B8=9c On the other hand, due to Setti’s rule on 8: D3=8S8  F3=6, A3=2, H3=1  B3=9 Which produces a contradiction. Therefore,GH2 cannot be 89.

6. Testing D3=8 If we test 8 with Setti’s rule, we see that only column 2 and row D are undecided. As row D contains only a single 8, let’s test D3=8, which forces an 8 in column 2.

7. Testing D3=8 D3=8 removes 2 from D56 (yellow). On the other hand: D3=8  CE2=78S8  C3=7s  C2=8  C8=3  H8:-3  H2=3s  G2=2c  2 is removed from G567 (yellow) That only leaves E5 and E6 for the 2s in columns 5 and 6 (red)  an illegal position. Therefore D3 cannot be 8 and column 2 doesn’t contain an 8 either(Setti on 8).

8. Solving… H8=3s C8=8 B8=9c F3=8s G4=8s E7=8s

9. Solving… J7=9 J9=8 H7=5s

10. Optional:checkingrow D Row D must contain a 7. There are two ways to detect this: There’s a 7 in every column, therefore (according to Setti’s rule) there must be a 7 in every row. The swordfish on 7 at CDE236 is “built” using columns, and thus forces a 7 in each of its rows as well. (This step is optional and not necessary, in order to solve the puzzle.)

11. Setti on 9 Checking Setti’s rule on 9 we find that all but row D and F contain a 9. Columns 1 and 2 do not contain a 9 either, so columns 4 and 9 must contain a 9.  H4=9S9

12. Solving… C3=9s D3=7s D6=2 D5=6 J5=5 J4=6 F4=5

13. Solving… C5=1 G8=5p G6=4 E6=7 C6=5

14. Solving… A2=3p A3=2c A1=4c C2=7p H3=1 H2=2 G2=1

15. Solving… B3=6 B2=4 B9=5 E2=6 E8=4 F8=6 F7=4

16. Solving… C7=6 C1=3 C9=4 G7=2 B7=1 B1=2 E1=1

17. Solving… E9=9 E5=2 G5=9 G9=6

18. Done This puzzle shows how important small compartments are for removing candidates. With many large compartments and small compartments at the fringe, it is not easy to solve the puzzle.

19. 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

20. Weekly Extreme Str8ts Puzzle #49www.str8ts.com Solution by SlowThinker Note: there are other (maybe easier) ways to solve this puzzle.