Weekly Extreme Str8ts Puzzle #70 www.str8ts.com A step by step solution SlowThinker
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.
Only once perline and rowStr8ts rules state thata number may onlyappear once in a rowand column.Hence we can removeall candidates markedyellow here.
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.
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.
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).
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.
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.
And RepeatNext, checkcompartment rangesagain, then again forthose compartmentswhere somethingchanged, thenhigh/low checks: thisleads to G8=2h (asG3456 has 5 as surecandidate).
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.
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!
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
Solving…E8=8E7=9C7=8C6=9(and still doing rangechecks, removingstranded digits, andcross-compartmenthigh/low-checks)
Solving…Still repeatedlyremoving candidateswith range checks,removing strandeddigits, doing high/low-checks, and singles:A7=6sB7=5B8=4B9=7H8=5
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).
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
Weekly Extreme Str8ts Puzzle #70Solution by SlowThinkerNote: there are other (maybe easier) ways to solve this puzzle.View & download my strategy slides from:http://slideshare.net/SlowThinker/str8ts-basic-and-advanced-strategiesor from Google Docs:http://is.gd/slowthinker_str8ts_strategy