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by **eleven** » Wed Mar 19, 2008 3:54 pm

I like this one (# 30038) out of gsf's list of hard 17's:

Code: Select all: +-------+-------+-------+ | 3 5 . | . . 2 | . . . | | . 1 . | . . . | . 8 . | | . . . | . 9 . | 7 . . | +-------+-------+-------+ | 4 . . | . 6 . | . . . | | . . . | 8 . . | . 1 . | | . 3 . | . . . | . . . | +-------+-------+-------+ | 6 . . | . . . | 2 . . | | 7 . . | . . . | . . 4 | | . . . | 1 . . | . . . | +-------+-------+-------+

by **daj95376** » Wed Mar 19, 2008 5:16 pm

Code: Select all: "17" Puzzle #30038: 35...2....1.....8.....9.7..4...6.......8...1..3.......6.....2..7.......4...1..... +-----------------------+ | 3 5 . | . . 2 | . . . | | . 1 . | . . . | . 8 . | | . . . | . 9 . | 7 . . | |-------+-------+-------| | 4 . . | . 6 . | . . . | | . . . | 8 . . | . 1 . | | . 3 . | . . . | . . . | |-------+-------+-------| | 6 . . | . . . | 2 . . | | 7 . . | . . . | . . 4 | | . . . | 1 . . | . . . | +-----------------------+

Code: Select all: r6 b5 Locked Candidate 1 <> 7 [r6c89] b3 Hidden Pair - 35 b7 Hidden Pair - 35 r37 X-Wing Finned <> 3 [r8c4] r37 X-Wing Finned <> 5 [r8c4] r34 X-Wing Finned <> 5 [r6c8]

Code: Select all: +--------------------------------------------------------------------------------+ | 3 5 8 | 7 1 2 | 469 469 69 | | 9 1 7 | 3456 345 3456 | 35 8 2 | | 2 6 4 | 35 9 8 | 7 35 1 | |--------------------------+--------------------------+--------------------------| | 4 8 29 | 2359 6 1 | 359 23579 3579 | | 5 7 269 | 8 234 349 | 3469 1 369 | | 1 3 269 | 2459 2457 4579 | 8 2469 569 | |--------------------------+--------------------------+--------------------------| | 6 49 1 | 3459 3457 34579 | 2 3579 8 | | 7 29 35 | 269 8 3569 | 1 3569 4 | | 8 249 35 | 1 23457 345679 | 3569 35679 35679 | +--------------------------------------------------------------------------------+

Code: Select all: [r1c9]=69 [r4c7]<>9 => Remote Pair w/ [r3c4]=35 => [r4c4]<>35 => [r5c 56]=3 => [r5c9]=69 => [r6c456]=5 => [r5c9]=69

Contradiction!!! Therefore, [r4c7]=9 and the puzzle solves simply afterwards.

by **hobiwan** » Wed Mar 19, 2008 5:33 pm

Starting from after the X-Wings and a bit longer than daj95376's solution:

daj95376 wrote:
Code: Select all
+--------------------------------------------------------------------------------+ | 3 5 8 | 7 1 2 | 469 469 69 | | 9 1 7 | 3456 345 3456 | 35 8 2 | | 2 6 4 | 35 9 8 | 7 35 1 | |--------------------------+--------------------------+--------------------------| | 4 8 29 | 2359 6 1 | 359 23579 3579 | | 5 7 269 | 8 234 349 | 3469 1 369 | | 1 3 269 | 2459 2457 4579 | 8 2469 569 | |--------------------------+--------------------------+--------------------------| | 6 49 1 | 3459 3457 34579 | 2 3579 8 | | 7 29 35 | 269 8 3569 | 1 3569 4 | | 8 249 35 | 1 23457 345679 | 3569 35679 35679 | +--------------------------------------------------------------------------------+

Code: Select all: ALS XY-Wing: A=[r4c3789] - {23579}, B=[r5c56],[r6c456] - {234579}, C=[r156c9] - {3569}, Y,Z=3,5, X=2,9 => [r4c4]<>2, [r4c4]<>9 Naked pair 3/5 c4 => [r27c4]<>3, [r267c4]<>5 Naked Pair 4/9 r7 => [r7c56]<>4, [r7c68]<>9 Remote Pair 3/5 [r2c7]-5-[r3c8]-3-[r3c4]-5-[r4c4] => [r4c7]<>3, [r4c7]<>5 Singles .---------------.---------------.---------------. | 3 5 8 | 7 1 2 | 6 4 9 | | 9 1 7 | 6 35 4 | 35 8 2 | | 2 6 4 | 35 9 8 | 7 35 1 | :---------------+---------------+---------------: | 4 8 2 | 35 6 1 | 9 7 35 | | 5 7 69 | 8 2 39 | 4 1 36 | | 1 3 69 | 4 57 579 | 8 2 56 | :---------------+---------------+---------------: | 6 4 1 | 9 357 357 | 2 35 8 | | 7 9 35 | 2 8 35 | 1 6 4 | | 8 2 35 | 1 4 6 | 35 9 7 | '---------------'---------------'---------------' Remote Pair 3/5 [r4c4]-5-[r3c4]-3-[r2c5]-5-[r2c7]-3-[r9c7]-5-[r9c3]-3-[r8c3]-5-[r8c6] => [r5c6],[r7c5]<>3, [r6c6],[r7c5]<>5

Puzzle solves with singles.

by **eleven** » Wed Mar 19, 2008 6:25 pm

Good programs. You also did it with the 35. This is my solution:

Code: Select all: *------------------------------------------------------------* | 3 5 8 | 7 1 2 | 469 469 69 | | 9 1 7 | 3456 345 3456 | 35 8 2 | | 2 6 4 | 35 9 8 | 7 #35 1 | |--------------+-----------------------+---------------------| | 4 8 29 | 2359 6 1 | 359 23579 3579 | | 5 7 269 | 8 234 349 | 3469 1 369 | | 1 3 269 | 2459 2457 4579 | 8 24569 569 | |--------------+-----------------------+---------------------| | 6 49 1 | 3459 3457 34579 | 2 #3579 8 | | 7 29 35 | 23569 8 3569 | 1 #3569 4 | | 8 249 #35 | 1 23457 345679 |#3569 #35679 #35679 | *------------------------------------------------------------*

The pairs 35 in r3c8 and r9c3 are a remote naked pair by the empty rectangle in box 9.
This kills 35 in r469c8 and r9c56.

Code: Select all: *------------------------------------------------------------* | 3 5 8 | 7 1 2 | 469 469 69 | | 9 1 7 | 3456 345 3456 |#35 8 2 | | 2 6 4 |#35 9 8 | 7 *35 1 | |--------------+-----------------------+---------------------| | 4 8 29 |*2359 6 1 |*359 279 35-79 | | 5 7 269 | 8 234 349 | 3469 1 369 | | 1 3 269 | 2459 2457 4579 | 8 2469 569 | |--------------+-----------------------+---------------------| | 6 49 1 | 3459 3457 34579 | 2 3579 8 | | 7 29 35 | 23569 8 3569 | 1 3569 4 | | 8 249 35 | 1 247 4679 | 3569 679 35679 | *------------------------------------------------------------*

Now in row 4 35 is only in columns 479. Since r2c7 and r3c4 must have the same value 3 or 5, also r4c9 can only be 3 or 5.

A kite 3 finally solves the puzzle.

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