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# Diabolic Str8ts #3 and Weekly Extreme #63 - Solution

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Solution to Diabolic Str8ts #3
(http://is.gd/slowthinker_diabolic_str8ts_3)

and solution to Weekly Extreme Str8ts #63.
Watch me solve it on YouTube: http://youtu.be/uE25Kdop9wM

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### Diabolic Str8ts #3 and Weekly Extreme #63 - Solution

1. 1. Weekly Extreme Str8ts Puzzle #63andDiabolic Str8ts Puzzle #3<br />Solutions bySlowThinker<br />
2. 2. Start positionExtreme #63<br />Let’s have a quick look at the key points in Extreme #63 first. I was able to solve it rather quickly.<br />The discussion assumes you are familiar with the strategies discussed. See my strategy slides for more information (link on last slide.)<br />
3. 3. Lockedcompartments<br />Many puzzles have columns with two 4 cell compartments.<br />These are locked compartments, which can be arranged in 6 ways (3 shown + reverse green and orange.)<br />The last line (red) shows the sure candidates. It pays off to remember this, as this pattern occurs often.<br />
4. 4. X-Wing on 5<br />After the basic candidate removal, we encounter an X-Wing on 5 (marked blue) that removes the 5s from the yellow cells.<br />A direct consequence is B9=5s. <br />
5. 5. More lockedcompartments<br />Whenever you see compartments occupying the same range, you should investigate closer.<br />Here E23 cannot be 23, because it would wipe out E7.<br />Thus E3=14 and E2=235.<br />
6. 6. Turbo Setti1/4<br />This puzzle has an interesting property: except for row E, all other rows have a single compartment with 7 or more cells.<br />So in 8 rows 3..7 are surecandidates. And as A8 and J6 are 8, we can actually say that in 8 rows 3..8 are sure candidates.<br />
7. 7. Turbo Setti2/4<br />What about the columns? <br />Columns 2, 3, 5, 7, 8 have at least 8 cells ( 2..8 are sure candidates) and in columns 4 & 6 234678 are sure candidates.<br />Intersect with the sure candidates in the rows and we have the candidates 34678.<br />
8. 8. Turbo Setti3/4<br />We now know that the candidates 34678 appear in at least 8 rows and at least 7 columns.<br />Thus: If one of these numbers does not appear in one of column 1 or 9, it must appear in the other one. If it appears in row E, it must appear in columns 1 and 9.<br />
9. 9. Turbo Setti4/4<br />Let’s look at our candidates 34678:<br />Thus we immediately know that 4 and 8 must appear in column 1 and that 7 must not appear in column 1.<br />
10. 10. Solving…<br />Here’s the result: GHJ1=2345 and CD1=89. Btw, by the same logic we now know that 3 must appear in row E.<br />Following up:<br />J3=9p<br />C8=9s<br />
11. 11. Setti on 2<br />After an X-wing on 3 at GJ12, which sets G9=4, and some more basic removal, we find ourselves at this position.<br />Row E is filled out now, so we can easily conclude that 2 appears in 8 rows 2 must be in GHJ1  H1=24 H2=5s<br />
12. 12. Solution<br />That’s it. The rest is the menial job of basic candidate removal.<br />You can watch me solve the puzzle (in a slightly different way) on YouTube here:<br />http://youtu.be/uE25Kdop9wM<br />
13. 13. Moving on…<br />
14. 14. Start positionDiabolic #3<br />With the diabolic Str8ts series, I try to push the boundaries a bit. Normal strategies are not enough to solve these puzzles.<br />This one has a beautiful hidden unique rectangle.<br />
15. 15. Mind the gap<br />C2 is almost a large gap field, but not quite. But wait: D2 has 3 as its highest candidate.<br />If F1 or G1 would be 7, then we would have a 2 in C1 or D1, which is impossible<br /> No 7 in FG1<br />Following up this leads to G56=89.<br />
16. 16. Hidden unique rectangle<br />Let us analyse HJ34. HJ4 is a split compartment. Hence we can analyse both ranges separately.The upper range (78) is of no interest.<br />But the lower range is a unique rectangle. Let’s have a closer look.<br />
17. 17. Hidden unique rectangle<br />If HJ34 would look like this, we immediately know that one of J34 must be 1. But which one? J3 or J4?<br />The compartment that can influence this decision is A..F4: in this position it must contain a 3, otherwise we could always exchange HJ3 and HJ4.<br />
18. 18. Hidden unique rectangle<br />To sum up, either HJ4=78 or A..F4 contains a 3.<br />But what if A..F4 contains a 9, that is, it has a range of 4 to 9?<br />Then HJ4 would not be 78 and we would not have a 3 in AF..4!!<br /> AF..4 must not contain a 9.<br />
19. 19. Setti on 3<br />Moving on, we arrive at this position.<br />Because of Setti on 3 there’s a 3 in every row.<br />C12 and C45 have mutually exclusive ranges, thus we can remove 1 from both compartments.<br />The same is true for G12 and G89.<br />
20. 20. Setti on 5<br />The same is true for Setti on 5.<br />Again there has to be a 5 in every row and G12 and G89 have mutually exclusive ranges.<br />Thus we can remove 7 from G1 and G9.<br />
21. 21. Applying some logic<br />Seeing so many 2s and 3s next to each other in columns 1&2 should make one curious.<br />Let’s see:<br />G2 cannot be 3, as G2=3  G1=2, C2=2, D2=1  D1=2<br />G2 cannot be 2 either, as G2=2  G1=3, C2=3, D2=1  C1=2  D1=1<br />
22. 22. X-Wing on 2<br />Which brings us to this position and an X-Wing on 2 at CE45 that removes the 2 from H4.<br />And with that the puzzle is solved.<br />Not that hard, no? <br />
23. 23. Solution<br />The unique solution constraint is a very powerful technique for solving Str8ts puzzles. <br />You just have to develop an eye for it.<br />I hope this example has whet your appetite.<br />
24. 24. 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 />
25. 25. Weekly Extreme Str8ts Puzzle #63<br />Diabolic Str8ts Puzzle #3<br />Solution by SlowThinker<br />Note: there are other (maybe easier) ways to solve these puzzles.<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 />