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# Diabolic Str8ts #5

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

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

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### Diabolic Str8ts #5

1. 1. Diabolic Str8ts Puzzle #5<br />Puzzle & solutionbySlowThinker<br />
2. 2. Start position<br />With the diabolic Str8ts series, I try to push the boundaries a bit. Normal strategies are not enough to solve these puzzles.<br />
3. 3. Setti on 5<br />After the basic eliminations, we arrive at this position.<br />Because of the 4s at C4 and G6, all numbers larger than 4 are necessary in those columns.<br />Thus 5s appear in all columns  5s are in all rows  we can eliminate 7 from G4 and 1 from F69.<br />
4. 4. A first test: EF6=56<br />With F6=6 we get F3=7 and H3=29.<br />In addition F2=9 and J2=2. Together with ABC6=789 this leads to J6=1. In turn, H6=2.<br />H1=29, H3=29 and H6=2 contradicts each other  EF6!=56.<br />
5. 5. Second test: HJ3=12<br />Next we test Hj3=12.<br />Green: H3=2  H1=9  HJ6=56  J9=8s<br />Orange: HJ3=12  C123=56789, together with C56  C8=2  G8=79  G9=8<br />Because of the contradiction, HJ3 cannot be 12  J3=8, H3=79.<br />
6. 6. Unique rectangle<br />After some further eliminations we arrive at this position, where we find a unique rectangle in AB46.<br />Hence we can set B6=7.<br />
7. 7. Unique solution constraint<br />Next we find a 3x3 unique rectangle in the same area.<br />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.<br /> B5=6<br />
8. 8. Setti on 6<br />With the upper area solved, we get a Setti on 6: because all columns contain a 6, so must all rows<br /> D7=6<br />
9. 9. X-Wing on 5<br />Furthermore, there is an X-Wing on 5 at HJ46 that removes the 5s in the yellow fields.<br />That in turn makes EF7 a hidden pair (45).<br />
10. 10. Settion 5<br />Because there are 5s in all columns, all rows must contain a 5 too.<br />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.<br />
11. 11. Jellyfish on 7<br />With the 7 removed from C8 we get a jellyfish on 7 at GHJ478 that removes the 7s from the yellow fields.<br />
12. 12. Jellyfish on 7 continued<br />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).<br /> G789 must be 789 and G12=123<br />
13. 13. Solution<br />After this the puzzle can be solved using basic strategies.<br />
14. 14. Glossary<br />Letters appended to steps indicate the last strategy used, just before filling in a field:<br />No letter … number was last candidate in field<br />s … single (last) candidate for that number in compartment<br />c … compartment range check<br />d … stranded (unreachable/impossible) digits removed<br />h … high/low range check across compartments<br />p/t/q … naked pair / naked triple / naked quadruple<br />ph/th/qh … hidden pair / hidden triple / hidden quadruple<br />x … X-wing (2 rows / 2 columns)<br />w … Swordfish (3 rows / 3 columns)<br />j … Jellyfish (4 rows / 4 columns)<br />L … large gap field<br />Sx … Setti’s rule (count the numbers rule) – ‘x’ is the analysed number<br />u … unique rectangle<br />y … Y-Wing or XY-chains<br />
15. 15. Diabolic Str8ts Puzzle #5<br />Solution by SlowThinker<br />Note: there are other (maybe easier) ways to solve this puzzle.<br />View & download my strategy slides from:<br />http://slideshare.net/SlowThinker/str8ts-basic-and-advanced-strategies<br />or from Google Docs:<br />http://is.gd/slowthinker_str8ts_strategy<br />