This document summarizes the solution to a weekly sudoku puzzle from April 17-23, 2011. It describes the steps taken to solve the puzzle, including using naked pairs, X-Wings, unique rectangles, and other sudoku solving techniques. Variations on the solution are also provided by two other solvers. The puzzle is solved through a series of logical deductions until all cells are filled.

1. Weekly Extreme Str8ts Puzzle #43 April 17 – April 23, 2011www.str8ts.comSolution bySlowThinker

2. Start

3. J8=7c, H8=8c, G2=8c, G1=7

4. A9=1h, A1=8h, H4=5dNote that J1 must be 1, because the compartment J3..9 needs the number 2 (naked quadruple ;-)

5. J1=1qNote 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 rectangleBecause 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: anotheruniquerectangleVariation by JohnNumber 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: chainingVariation by WalterE12 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=4Continuingfrom original uniquerectangle on theright, whichremovesthe 2s from E89  E1=2

10. H7=2, J7=3, J4=6, J8=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

17. B7=6, B3=3, A3=4c, A7=5

18. F5=8c, D5=7cDone

19. GlossaryLetters appended to steps indicate the last strategy used, just before filling in a field:No letter … number was last candidate in fields … single (last) candidate for that number in compartmentc … compartment range checkd … stranded (unreachable/impossible) digits removedh … high/low range check across compartmentsp/t/q … naked pair / naked triple / naked quadrupleph/th/qh … hidden pair / hidden triple / hidden quadruplex … X-wing (2 rows / 2 columns)w … Swordfish (3 rows / 3 columns)j … Jellyfish (4 rows / 4 columns)L … large gap fieldSx … Setti’s rule (count the numbers rule) – ‘x’ is the analysed numberu … unique rectangley … Y-Wing or XY-chains

20. Weekly Extreme Str8ts Puzzle #43www.str8ts.comSolution by SlowThinkerwith variations by John and WalterNote: there are other (maybe easier) ways to solve this puzzle.