Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Diabolic Str8ts #1


Published on

Solution to Diabolic Str8ts #1

  • Be the first to comment

  • Be the first to like this

Diabolic Str8ts #1

  1. 1. Diabolic Str8ts Puzzle #1<br />Solution & puzzle bySlowThinker<br />
  2. 2. Start position<br />With the diabolic str8ts series, I try to push the boundaries a bit. Ordinary strategies are not enough to solve these puzzles.<br />
  3. 3. Solving…<br />After applying the basic techniques, we arrive at the position on the right.<br />In D7 and E7 9 is a stranded digit, as D7 contains the only 7 and E7 the only 8 in ABCDE7 <br />E9=9d<br />D5=9s<br />
  4. 4. Split unique UR<br />HJ7 is a split compartment: either it is 234 or it is 789. But in the upper range it would form a unique rectangle with HJ6 <br />to avoid the UR J7 must not be 78 <br />J7=2349<br />H7=348<br />
  5. 5. Setti on 7<br />There’s a 7 in every row, therefore there must be a 7 in every column too:<br />D7=7S7<br />In column 2 we can only deduce that one of B2 and J2 must contain a 7.<br />
  6. 6. Setti on 8<br />Row C does not contain an 8  at least one column must not have an 8 either  column 4 is the only possible column <br />FGHJ4=4567S8<br />D4=2h<br />A4=9h<br />
  7. 7. X-Wing & Setti<br />Again omitting the basic elimination steps, we arrive at this position:<br />There’s an X-wing (marked green) on 3 that removes the 3 from E3 (marked red).<br />Applying Setti’s rule on 4, we find that every row must have a 4  F1 != 9<br />
  8. 8. Setti’s rule on 6& an easy test<br />B1 is the only 6 in row B. If there’s no 6 there, there’s also no 6 in F2 and J2. What if B1=7?<br />B1=7  F2=4S6<br />but also:<br />B1=7  C1=6  F1=4<br />Hence: B1!=7  B2=7<br />Note that we can remove 6 from J2 with very similar logic.<br />
  9. 9. Analysis<br />Due to Setti on 6 we have a link between B1 and F2. There’s also a link between G1 and J7, because of Setti on 2 (marked border).<br />We also have the green cells, which are mostly about 234 and the yellow area mostly about 689.<br />At the intersection: J3<br />
  10. 10. Testing J3=2<br />So let us test J3=2, because it has an impact on J7:<br />J3=2  J7=9  G1=9S2<br />But also:<br />J3=2  E3=4, E2=3  F2=4c  B1=9S6<br />Which is impossible. Hence:<br />J3=6<br />
  11. 11. Solving…<br />With the naked triple in J468 (yellow) we can remove 47 from J1.<br />This gives us anX-wing on 4 at EF12, which removes 4 from F4.<br />
  12. 12. Final test: J7=9<br />Keeping in mind the links we already discovered, we find that J7 cannot be 9:<br />J7=9  G2=9, B1=6  F2=6 and F4=7<br />But also:<br />J7=9  H7=8  H6=7, J6=8, J8=4 and J4=7<br />Thus: J7=2<br />The rest is easy.<br />
  13. 13. Solution<br />There are of course other (maybe easier) ways to solve this puzzle. This solution emphasized links between cells and different areas of the board to test and eliminate candidates.<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 #1<br />Solution by SlowThinker<br />Note: there are other (maybe easier) ways to solve this puzzle.<br />View & download my strategy slides from:<br /><br />or from Google Docs:<br /><br />