Solution to Diabolic Str8ts #5 puzzle (http://is.gd/slowthinker_diabolic_str8ts_5)

1. Diabolic Str8ts Puzzle #5 Puzzle & solutionbySlowThinker

2. Start position With the diabolic Str8ts series, I try to push the boundaries a bit. Normal strategies are not enough to solve these puzzles.

3. Setti on 5 After the basic eliminations, we arrive at this position. Because of the 4s at C4 and G6, all numbers larger than 4 are necessary in those columns. Thus 5s appear in all columns  5s are in all rows  we can eliminate 7 from G4 and 1 from F69.

4. A first test: EF6=56 With F6=6 we get F3=7 and H3=29. In addition F2=9 and J2=2. Together with ABC6=789 this leads to J6=1. In turn, H6=2. H1=29, H3=29 and H6=2 contradicts each other  EF6!=56.

5. Second test: HJ3=12 Next we test Hj3=12. Green: H3=2  H1=9  HJ6=56  J9=8s Orange: HJ3=12  C123=56789, together with C56  C8=2  G8=79  G9=8 Because of the contradiction, HJ3 cannot be 12  J3=8, H3=79.

6. Unique rectangle After some further eliminations we arrive at this position, where we find a unique rectangle in AB46. Hence we can set B6=7.

7. Unique solution constraint Next we find a 3x3 unique rectangle in the same area. If we assume that B5!=6, then 89 would be removed in all directions and we could freely exchange 8 and 9 in the green fields, producing two solutions.  B5=6

8. Setti on 6 With the upper area solved, we get a Setti on 6: because all columns contain a 6, so must all rows  D7=6

9. X-Wing on 5 Furthermore, there is an X-Wing on 5 at HJ46 that removes the 5s in the yellow fields. That in turn makes EF7 a hidden pair (45).

10. Settion 5 Because there are 5s in all columns, all rows must contain a 5 too. In row C two compartments have mutually exclusive ranges, which means that C8 cannot be 7, because then there would be no 5 in row C.

11. Jellyfish on 7 With the 7 removed from C8 we get a jellyfish on 7 at GHJ478 that removes the 7s from the yellow fields.

12. Jellyfish on 7 continued Furthermore, because of the jellyfish, 7 is not only a sure candidate in the columns of the jellyfish, but also in its rows. (As there is simply no way to place three 7s in the yellow fields without placing one 7 in row G).  G789 must be 789 and G12=123

13. Solution After this the puzzle can be solved using basic strategies.

14. 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

15. Diabolic Str8ts Puzzle #5 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