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# Str8ts Weekly Extreme #67 - Solution

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Solution to Weekly Extreme #67 str8ts puzzle from str8ts.com

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### Str8ts Weekly Extreme #67 - Solution

1. 1. Weekly Extreme Str8ts Puzzle #67 October 2 – October 8, 2011www.str8ts.com<br />Solution bySlowThinker<br />
2. 2. Start position<br />Extreme Str8ts #67 is one of the toughest Extremes in a long time. In this solution I will only focus on the key points, not on easy removal of candidates.<br />(Links to my strategy slides are on the last page)<br />
3. 3. Mind the gap<br />After the first steps, B2 (marked blue) contains a large gap pair. Thus we can remove 19 from all other fields in column 2. <br />This leads to D2=2 and D1=3.<br />
4. 4. Setti on 6<br />Because all rows contain a 6, all columns must contain a 6 too.<br />Hence J7=6.<br />
5. 5. Setti on 8<br />Column 7 does not contain an 8  at least one row must not contain an 8 either.<br />The only row where an 8 can be missing is row J  remove 89 from row J.<br />
6. 6. Hidden unique rectangle<br />Because of F89 neither G89 nor H89 can contain a 9.<br />If they would, the compartment would contain the candidates 89 and form a UR with F89.<br />Thus 9 can be removed from GH89.<br />
7. 7. Hidden UR continued<br />While it is obvious that GH89 cannot be both 78, the question arises, if the can be both 123.<br />In that case one of GH9 must be 3, which in turn (due to C9) forces the other field to be 1  both GH8 would be 2, which is impossible.<br />
8. 8. Hidden UR continued<br />We now know that GH89 do not have the same range: one is 78, one is 12(3).<br />Together with F89 this forms a (hidden) X-Wing on 8 which removes the 8s from the yellow cells.<br />Also, in one of the pink fields 89 gets removed thus forcing the whole compartment into the range 1234 (due to interlock with ABCD5).<br />
9. 9. Swordfish on 4<br />We now have a swordfish on at FHJ235 (marked blue) that removes the 4s from the red fields.<br />Next we have a naked pair in EJ6 that forces C6=4.<br />
10. 10. Setti on 8 again<br />Due to Setti’s rule an 8 is mandatory in column 3. So the 8 is either in A3 or in EFGHJ3. If it is in EFGHJ3, then A3=23. In the other case A3=8. In both cases, 67 does not appear in A3 and thus can be removed.<br />
11. 11. Setti on 7<br />As GH89 does not contain a 9 anymore, 7 becomes a sure candidate in rows G and H.<br />Due to Setti’s rule, column 3 must contain a 7 too  we can remove 12 from EFGHJ3 (range check).<br />
12. 12. Setti on 2<br />This is one of the rare occasions where we know that a candidate can only appear at the intersection of an undecided row and column.<br />As there are no 2s in EFGHJ3, either A3=2 or not, but there cannot be a 2 anywhere else in row A as this would violate Setti’s rule  remove 2s from the yellow cells.<br />
13. 13. Hidden X-Wing on 7<br />Remember that one of GH89 is 7 which removes 7s in its row and column.<br /> No matter which field you take, we get two X-Wings on 7: one in GHJ34 (pink) and one at AD589 (orange).<br />Both X-Wings remove the 7s in AD4 (yellow).<br />
14. 14. A simple chain:G4 ≠ 3<br />Let’s start with an easy removal: G4 cannot be 3:<br />If G89=12  G5=3<br />If G89=78  G6=6, G2=5, G3=3<br />In both cases, 3 gets removed from G4.<br />
15. 15. Setti on 3<br />Let’s look at Setti on 3 again: either there’s a 3 in row H and column 3 or there is not.<br />Let’s assume no 3: then H89=12  G89=78  G6=6, G2=5  no candidate left in G3!<br />Thus there’s a 3 in row H & column 3  we can remove 2 from A3.<br />
16. 16. H9=3?No, H9 ≠ 3<br />Now that we know that row H has a 3, let’s test H9=3:<br />a) H9=3  G89=78  G6=6, G2=5, G3=3 J5=3s  J6=2<br />b) H9=3  H5=4, H2=6  H3=7 (because G3=3)  J2=4 (because G2=5)  J3=5  J1=2<br />Contradiction! Hence<br />H9!=3  E1=9s!<br />
17. 17. How it would look like<br />Here is how the position would look like, if H9=3:<br />a) H9=3  G89=78  G6=6, G2=5, G3=3 J5=3s  J6=2<br />b) H9=3  H5=4, H2=6  H3=7 (because G3=3)  J2=4 (because G2=5)  J3=5  J1=2<br />78<br />3<br />6<br />5<br />3<br />4<br />6<br />7<br />2<br />5<br />4<br />2<br />3<br />
18. 18. Swordfish on 5<br />After H9!=3 we know that 3 is in H1..6 and thus there’s no 9 there  E1=9s. And with Setti on 5 we get E6789=2345.<br />Furthermore, there’s a swordfish on 5 (marked blue) that removes the 5s from FGJ4 (yellow fields).<br />
19. 19. Hidden triple<br />That leaves us with the hidden triple 459 in ABD4.<br />
20. 20. Jellyfish on 6<br />With the 6s gone in ABD4 we now have a jellyfish on 6 (marked blue) that removes the 6 from G6<br /> G6=8<br />With this we can solve quite a few cells.<br />
21. 21. X-Wing on 9<br />When we arrive at this position, we get an X-Wing on 9 at AD46 that removes the 9s from the yellow fields.<br />
22. 22. XY-Chain: H4 ≠ 6, F1 ≠ 2<br />Starting at F5 (blue) we can form an XY-chain that removes 6 from H4 (red):<br />F5=2  F4=6 (green)<br />F5=4  F3=5, G3=7, G4=6 (yellow)<br />In both cases 6 is removed from H4.<br />Using the same logic and again starting at F5, we can also remove 2 from F1. <br />
23. 23. More XY-Chains: J3 ≠ 4, H5 ≠ 4<br />Starting at G4 we can remove 4 from J3 and 4 from H5.<br />In both cases we just follow the elimination for both possibilities of G4 (6, 7). <br />For example, the removal of 4 from H5:Green arrows for G4=6 (lead to F5=4) and orange arrows for G4=7 (lead to H2=4)<br />
24. 24. More XY-Chains: H4 ≠ 3<br />Again starting at G4 we can remove 3 H4:<br />Orange: G4=6  F4=2, C4=3<br />Green: G4=7  G3=5, F3=4, H3=3<br />With H4=12 we get H3=3s and H1=6p.<br />From there on, the puzzle solves itself.<br />
25. 25. Solution<br />The hardest step in this solution was eliminating 3 from H9.<br />Once the 3 was gone, well known strategies and some XY-chains solved the puzzle.<br />With a puzzle like this, there are of course many other ways to solve it.<br />
26. 26. 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 />
27. 27. Weekly Extreme Str8ts Puzzle #67www.str8ts.com<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 />