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Weekly Extreme Str8ts Puzzle #43 April 17 – April 23, 2011www.str8ts.com Solution bySlowThinker
Start
J8=7c, H8=8c, G2=8c, G1=7
A9=1h, A1=8h, H4=5d Note that J1 must be 1, because the compartment J3..9 needs the number 2 (naked quadruple ;-)
J1=1q Note how the cross in the centre and the three blue compartments influence each other, which enables removing  candidates there. There is also an X-Wing on 3 at HJ67 that removes the 3s from the green fields.
Unique rectangle Because of G89 (orange), E89 (blue) cannot be 23. Why? Because then we would not get a unique solution (the numbers 2 and 3 in EG89 could be swapped at will)  2 is removed from E89  E1=2s
Variation 1: anotheruniquerectangle Variation by John Number 2 must be inside the blue rectangle  H1=46  H6=3, H7=2, … Why? Because if H2=2, then one could always swap rows C-F of column 1 with column 2, which violates the unique solution constraint.
Variation 2: chaining Variation by Walter E12 can only be 23 or 45 (34 is not possible.) Assume that E12=45  E4=68  J1=4, J6=3, H6=4, H5=6 and H1=2. The only 6s remaining in column 1 and 2 would be DF12 (blue). At least one of them would be a stranded digit, as the 7s are gone, and with E12=45 the 5 is gone in DF12 in one of the two columns too  E12 cannot be 45  E12=23
E1=2u, E2=3c, H6=3p, J6=4 Continuingfrom original uniquerectangle on theright, whichremovesthe 2s from E89  E1=2
H7=2, J7=3, J4=6, J8=2
G8=3, G9=2, A4=7, B4=8, E4=4
E5=6c, E6=5c, E8=8, E9=7, F9=6
F8=7, H5=4, H1=6, C9=5, A6=6, B6=7
A5=3, B5=2, C8=6, C7=7c, C2=4
C1=3, C3=2, F2=5, F1=4, D2=6
D1=5, D8=4, D9=3, B9=4, B8=5
B7=6, B3=3, A3=4c, A7=5
F5=8c, D5=7c Done
Glossary Letters 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 #43www.str8ts.com Solution by SlowThinkerwith variations by John and Walter Note: there are other (maybe easier) ways to solve this puzzle.

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Str8ts Weekly Extreme #43 - Solution

  • 1. Weekly Extreme Str8ts Puzzle #43 April 17 – April 23, 2011www.str8ts.com Solution bySlowThinker
  • 4. A9=1h, A1=8h, H4=5d Note that J1 must be 1, because the compartment J3..9 needs the number 2 (naked quadruple ;-)
  • 5. J1=1q Note how the cross in the centre and the three blue compartments influence each other, which enables removing candidates there. There is also an X-Wing on 3 at HJ67 that removes the 3s from the green fields.
  • 6. Unique rectangle Because of G89 (orange), E89 (blue) cannot be 23. Why? Because then we would not get a unique solution (the numbers 2 and 3 in EG89 could be swapped at will)  2 is removed from E89  E1=2s
  • 7. Variation 1: anotheruniquerectangle Variation by John Number 2 must be inside the blue rectangle  H1=46  H6=3, H7=2, … Why? Because if H2=2, then one could always swap rows C-F of column 1 with column 2, which violates the unique solution constraint.
  • 8. Variation 2: chaining Variation by Walter E12 can only be 23 or 45 (34 is not possible.) Assume that E12=45  E4=68  J1=4, J6=3, H6=4, H5=6 and H1=2. The only 6s remaining in column 1 and 2 would be DF12 (blue). At least one of them would be a stranded digit, as the 7s are gone, and with E12=45 the 5 is gone in DF12 in one of the two columns too  E12 cannot be 45  E12=23
  • 9. E1=2u, E2=3c, H6=3p, J6=4 Continuingfrom original uniquerectangle on theright, whichremovesthe 2s from E89  E1=2
  • 11. G8=3, G9=2, A4=7, B4=8, E4=4
  • 12. E5=6c, E6=5c, E8=8, E9=7, F9=6
  • 13. F8=7, H5=4, H1=6, C9=5, A6=6, B6=7
  • 14. A5=3, B5=2, C8=6, C7=7c, C2=4
  • 15. C1=3, C3=2, F2=5, F1=4, D2=6
  • 16. D1=5, D8=4, D9=3, B9=4, B8=5
  • 19. Glossary Letters 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
  • 20. Weekly Extreme Str8ts Puzzle #43www.str8ts.com Solution by SlowThinkerwith variations by John and Walter Note: there are other (maybe easier) ways to solve this puzzle.