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Str8ts Weekly Extreme #70 - Step-by-step Solution

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Str8ts Weekly Extreme #70 - Step-by-step Solution

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Str8ts Weekly Extreme #70 - Step-by-step Solution

  1. 1. Weekly Extreme Str8ts Puzzle #70 A step by step solution SlowThinker
  2. 2. Start positionI use Extreme #70 asan example to showthe basic steps insolving a Str8ts puzzle.Please make sure toread my strategy slides(link at the end) inorder to understandthe strategies used.
  3. 3. Only once perline and rowStr8ts rules state thata number may onlyappear once in a rowand column.Hence we can removeall candidates markedyellow here.
  4. 4. Range checkAll numbers within acompartment must bein a continues range.Gaps are not allowed.For example, 6 isimpossible in C2,because there’s a 3 inC3 and thus highestvalue reachable in theC234 compartment is5.
  5. 5. Range checkCompartment rangechecks also work ifthere are still two ormore candidates in afield.Look at BCDE4: as thehighest candidate inC4 is 5, we cannotreach a higher numberthan 8 in thecompartment  9 canbe removed.
  6. 6. Stranded digitsSome candidates maybecome detachedfrom others: they arestranded.In G3456 2 and 3 arestranded digits, asthey are detachedfrom the others. Novalid range can beformed with them.Next, check rangesagain (e.g. in F56).
  7. 7. High/low checkNext we do a high/lowcross-compartmentcheck: we see that 4and 5 have to occur inC24, thus we canremove them fromC679 ( C9=6h).Same for 456 in HJ2:we know that thesenumbers must appearin A..F2, as they aresure candidates there.
  8. 8. RepeatWith C9=6, we removethe 6s in row C andcolumn 9, then checkthe compartmentranges again: B9 canonly be 5 or 7, and asC7 is now 89, we canremove 123 fromA..E7.
  9. 9. And RepeatNext, checkcompartment rangesagain, then again forthose compartmentswhere somethingchanged, thenhigh/low checks: thisleads to G8=2h (asG3456 has 5 as surecandidate).
  10. 10. SingleSome compartmentrange checks, removalof stranded digits, andhigh/low checks later,we arrive at thisposition.As the compartmentFGH9 has 3 as surecandidate and 3 onlyappears in G9, we canset G9=3s.
  11. 11. More strandeddigitsHave a look at E78: E7cannot be 6, becauseE8 would be 8, aninvalid range. Same forE7=8  E8=6. Thus wecan remove 68 from E7.Same for 4 in J7: J7=4would leave H7=12,which is impossible.Applying rules again,we solve J7: J7=23d J6=24c  J7=3d!
  12. 12. Solving…So we keep applyingthese strategies andremove candidates andcheck for singles:H9=1s (single in row H)F9=2c F12=4567h DEF1=3567c DEF1=567d, i.e. D1=5dD8=6D7=7
  13. 13. Solving…E8=8E7=9C7=8C6=9(and still doing rangechecks, removingstranded digits, andcross-compartmenthigh/low-checks)
  14. 14. Solving…Still repeatedlyremoving candidateswith range checks,removing strandeddigits, doing high/low-checks, and singles:A7=6sB7=5B8=4B9=7H8=5
  15. 15. Solving…Lather, rinse, repeat:B6=8A6=7B5=9A5=8
  16. 16. Solving…Some range checks andhigh/low checks later,still applying the samestrategies:H7=2sJ2=7sH2=8cH1=9J1=8
  17. 17. Solving…H4=6H5=4F5=5F6=4J6=2G6=5c
  18. 18. Solving…G4=7cG5=6G3=8cF2=6F1=7E1=6
  19. 19. Solving…B3=6sJ3=9After this, we need anew strategy to solvethe last fields of thepuzzle.
  20. 20. Swordfish on 4We can apply theSwordfish strategy on 4:the blue fields make upa row-based swordfishthat removes the 4s inA2 and A3.Next, 5 is a strandeddigit in A123, so we get:A3=2w4D3=4E3=5
  21. 21. Solving…B1=2dC2=5s, C4=4D2=2p (naked pair 13in AB2)E4=4, D4=3, E4=2E5=3cB4=1, B2=3A2=1, A1=3
  22. 22. SolutionThat’s it.When solving a Str8tspuzzle, you just haveto apply the samestrategies over andover again. The hardpart is spottingeverything.For a list of commonstrategies see mystrategy slides (link atthe end).
  23. 23. GlossaryLetters 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
  24. 24. Weekly Extreme Str8ts Puzzle #70Solution by SlowThinkerNote: there are other (maybe easier) ways to solve this puzzle.View & download my strategy slides from: from Google Docs: