The New Sudoku Players' Forum

by **mith** » Thu Jun 30, 2022 12:31 am

Code: Select all: +-------+-------+-------+ | . . . | . . . | . . 1 | | . . . | . 1 2 | . 3 . | | . . 3 | 4 5 . | . 2 6 | +-------+-------+-------+ | . . . | . 3 4 | 2 6 . | | . . . | 2 6 . | 1 . 5 | | 2 6 . | 5 . 1 | . 4 3 | +-------+-------+-------+ | . . 1 | . . . | . 5 4 | | 6 . . | 1 . . | . . . | | 7 8 . | . . . | . 1 2 | +-------+-------+-------+ ........1....12.3...345..26....3426....26.1.526.5.1.43..1....546..1.....78.....12

by **pjb** » Thu Jun 30, 2022 7:00 am

State after type 1 TH => -789 r2c4:

Code: Select all: 45 2 6 | 3789 789 3789 | 45 789 1 4589 4579 45789 | 6 1 2 | 45 3 789 189 179 3 | 4 5 789 | 789 2 6 ------------------------+----------------------+--------------------- 1589 1579 5789 | 789 3 4 | 2 6 789 3489 3479 4789 | 2 6 789 | 1 789 5 2 6 789 | 5 789 1 | 789 4 3 ------------------------+----------------------+--------------------- 39 39 1 | 78 2 678 | 678 5 4 6 45 2 | 1 4789 35789 | 3789 789 789 7 8 45 | 39 49 3569 | 369 1 2

Then replace all instances of 789 with xyz, and assign x to r1c8, y to r5c8 and z to r8c8:

Code: Select all: 45 2 6 | 3xyz xyz 3xyz | 45 x 1 45xyz 45xyz 45xyz | 6 1 2 | 45 3 xyz 1xyz 1xyz 3 | 4 5 xyz | xyz 2 6 -----------------------+------------------------+--------------------- 15xyz 15xyz 5xyz | xyz 3 4 | 2 6 xyz 34xyz 34xyz 4xyz | 2 6 xyz | 1 y 5 2 6 xyz | 5 xyz 1 | xyz 4 3 -----------------------+-----------------------+--------------------- 3xyz 3xyz 1 | xyz 2 6xyz | 6xyz 5 4 6 45 2 | 1 4xyz 35xyz | 3xyz z xyz xyz xyz 45 | 3xyz 4xyz 356xyz | 36xyz 1 2

Then solve using basic moves:

Code: Select all: 4 2 6 | y z 3 | 5 x 1 z x 5 | 6 1 2 | 4 3 y 1 y 3 | 4 5 x | z 2 6 --------------------------+----------------------+--------------------- 5 1 y | x 3 4 | 2 6 z 3 4 x | 2 6 z | 1 y 5 2 6 z | 5 y 1 | x 4 3 --------------------------+----------------------+--------------------- x 3 1 | z 2 6 | y 5 4 6 5 2 | 1 4 y | 3 z x y z 4 | 3 x 5 | 6 1 2

Therefore y = 7 and z = 8; stte

Phil

by **m_b_metcalf** » Thu Jun 30, 2022 7:19 am

Backdoor values 7r1c4, 9r2c2.

Mike

Website · by **denis_berthier** » Thu Jun 30, 2022 9:23 am

.
First solution, more or less like pjb, but with no x, y z.

Second solution, without using the tridagon rule at all:
Resolution state after Singles and whips[1]:

Code: Select all: +-------------------------+-------------------------+-------------------------+ ! 4589 24579 2456789 ! 36789 789 36789 ! 45789 789 1 ! ! 4589 4579 456789 ! 6789 1 2 ! 45789 3 789 ! ! 189 179 3 ! 4 5 789 ! 789 2 6 ! +-------------------------+-------------------------+-------------------------+ ! 1589 1579 5789 ! 789 3 4 ! 2 6 789 ! ! 3489 3479 4789 ! 2 6 789 ! 1 789 5 ! ! 2 6 789 ! 5 789 1 ! 789 4 3 ! +-------------------------+-------------------------+-------------------------+ ! 39 239 1 ! 36789 2789 36789 ! 36789 5 4 ! ! 6 23459 2459 ! 1 24789 35789 ! 3789 789 789 ! ! 7 8 459 ! 369 49 3569 ! 369 1 2 ! +-------------------------+-------------------------+-------------------------+ 188 candidates.

hidden-pairs-in-a-column: c7{n4 n5}{r1 r2} ==> r2c7≠9, r2c7≠8, r2c7≠7, r1c7≠9, r1c7≠8, r1c7≠7 (not really necessary)

Code: Select all: +-------------------------+-------------------------+-------------------------+ ! 4589 24579 2456789 ! 36789 789 36789 ! 45 789 1 ! ! 4589 4579 456789 ! 6789 1 2 ! 45 3 789 ! ! 189 179 3 ! 4 5 789 ! 789 2 6 ! +-------------------------+-------------------------+-------------------------+ ! 1589 1579 5789 ! 789 3 4 ! 2 6 789 ! ! 3489 3479 4789 ! 2 6 789 ! 1 789 5 ! ! 2 6 789 ! 5 789 1 ! 789 4 3 ! +-------------------------+-------------------------+-------------------------+ ! 39 239 1 ! 36789 2789 36789 ! 36789 5 4 ! ! 6 23459 2459 ! 1 24789 35789 ! 3789 789 789 ! ! 7 8 459 ! 369 49 3569 ! 369 1 2 ! +-------------------------+-------------------------+-------------------------+

Code: Select all: (solve-sukaku-grid-by-eleven-replacement 7 8 9 1 8 2 9 3 7 +-------------------------+-------------------------+-------------------------+ ! 4589 24579 2456789 ! 36789 789 36789 ! 45 789 1 ! ! 4589 4579 456789 ! 6789 1 2 ! 45 3 789 ! ! 189 179 3 ! 4 5 789 ! 789 2 6 ! +-------------------------+-------------------------+-------------------------+ ! 1589 1579 5789 ! 789 3 4 ! 2 6 789 ! ! 3489 3479 4789 ! 2 6 789 ! 1 789 5 ! ! 2 6 789 ! 5 789 1 ! 789 4 3 ! +-------------------------+-------------------------+-------------------------+ ! 39 239 1 ! 36789 2789 36789 ! 36789 5 4 ! ! 6 23459 2459 ! 1 24789 35789 ! 3789 789 789 ! ! 7 8 459 ! 369 49 3569 ! 369 1 2 ! +---------------+-------------------------+-------------------------+ )

AFTER APPLYING ELEVEN''S REPLACEMENT METHOD to digits 7, 8 and 9 in cells r1c8, r2c9 and r3c7,
the resolution state is:

Code: Select all: +-------------------------+-------------------------+-------------------------+ ! 45789 245789 2456789 ! 36789 789 36789 ! 45 7 1 ! ! 45789 45789 456789 ! 6789 1 2 ! 45 3 8 ! ! 1789 1789 3 ! 4 5 789 ! 9 2 6 ! +-------------------------+-------------------------+-------------------------+ ! 15789 15789 5789 ! 789 3 4 ! 2 6 789 ! ! 34789 34789 4789 ! 2 6 789 ! 1 789 5 ! ! 2 6 789 ! 5 789 1 ! 789 4 3 ! +-------------------------+-------------------------+-------------------------+ ! 3789 23789 1 ! 36789 2789 36789 ! 36789 5 4 ! ! 6 2345789 245789 ! 1 24789 35789 ! 3789 789 789 ! ! 789 789 45789 ! 36789 4789 356789 ! 36789 1 2 ! +-------------------------+-------------------------+-------------------------+

THIS IS THE PUZZLE THAT WILL NOW BE SOLVED.
DON''T FORGET TO DO THE RELEVANT DIGIT REPLACEMENTS AT THE END, based on the original givens.

Code: Select all: whip[1]: b9n9{r8c9 .} ==> r8c6≠9, r8c2≠9, r8c3≠9, r8c5≠9 z-chain[4]: r6n9{c3 c5} - r1c5{n9 n8} - r3c6{n8 n7} - r5n7{c6 .} ==> r6c3≠7 biv-chain[2]: c9n7{r8 r4} - r6n7{c7 c5} ==> r8c5≠7 biv-chain[3]: r6c3{n9 n8} - r6c7{n8 n7} - r4c9{n7 n9} ==> r4c1≠9, r4c2≠9, r4c3≠9 z-chain[3]: r4n8{c3 c4} - r4n9{c4 c9} - r5c8{n9 .} ==> r5c3≠8, r5c2≠8, r5c1≠8 biv-chain[4]: r8c9{n7 n9} - b6n9{r4c9 r5c8} - r5n8{c8 c6} - r3c6{n8 n7} ==> r8c6≠7 z-chain[4]: c5n7{r9 r6} - r6c7{n7 n8} - r5n8{c8 c6} - r3c6{n8 .} ==> r9c6≠7, r7c6≠7 z-chain[4]: c8n8{r8 r5} - r6n8{c7 c3} - r6n9{c3 c5} - r1c5{n9 .} ==> r8c5≠8 biv-chain[3]: c3n2{r1 r8} - r8c5{n2 n4} - r9n4{c5 c3} ==> r1c3≠4 biv-chain[4]: c3n6{r2 r1} - c3n2{r1 r8} - r8c5{n2 n4} - r9n4{c5 c3} ==> r2c3≠4 z-chain[5]: r6n7{c5 c7} - r4c9{n7 n9} - b5n9{r4c4 r6c5} - r1c5{n9 n8} - r3c6{n8 .} ==> r5c6≠7 hidden-single-in-a-column ==> r3c6=7 whip[1]: r3n8{c2 .} ==> r1c1≠8, r1c2≠8, r1c3≠8 whip[1]: r5n7{c3 .} ==> r4c1≠7, r4c2≠7, r4c3≠7 naked-pairs-in-a-row: r5{c6 c8}{n8 n9} ==> r5c3≠9, r5c2≠9, r5c1≠9 hidden-single-in-a-block ==> r6c3=9 whip[1]: b4n8{r4c3 .} ==> r4c4≠8 biv-chain[3]: r1c5{n9 n8} - b5n8{r6c5 r5c6} - b5n9{r5c6 r4c4} ==> r1c4≠9, r2c4≠9 stte +-------+-------+-------+ ! 4 2 6 ! 8 9 3 ! 5 7 1 ! ! 9 7 5 ! 6 1 2 ! 4 3 8 ! ! 1 8 3 ! 4 5 7 ! 9 2 6 ! +-------+-------+-------+ ! 5 1 8 ! 7 3 4 ! 2 6 9 ! ! 3 4 7 ! 2 6 9 ! 1 8 5 ! ! 2 6 9 ! 5 8 1 ! 7 4 3 ! +-------+-------+-------+ ! 7 3 1 ! 9 2 6 ! 8 5 4 ! ! 6 5 2 ! 1 4 8 ! 3 9 7 ! ! 8 9 4 ! 3 7 5 ! 6 1 2 ! +-------+-------+-------+

The last part could probably be shortened, but the point is: the solution is in Z5.

Apply 8 -> 7 9 -> 8 and 7 -> 9 in order to have the solution of the original puzzle.

by **mith** » Thu Jun 30, 2022 3:56 pm

Nice

Not a surprise that it can be done with the relabel trick.

This one has an interesting solution that avoids the relabel, however. I'll post it in a couple days, if anyone wants to try to find it in the meantime (or you can use the latest YZF_Sudoku to find it!)

by **marek stefanik** » Sun Jul 03, 2022 10:57 am

Code: Select all: .----------------------.---------------------.-----------------. | 4589 24579 2456789 | 36789 #789 36789 | 45 B789 1 | | 4589 4579 456789 |#6–789 1 2 | 45 3 A789 | | 189 179 3 | 4 5 #789 |C789 2 6 | :----------------------+---------------------+-----------------: | 1589 1579 5789 |A789 3 4 | 2 6 A789 | | 3489 3479 4789 | 2 6 B789 | 1 B789 5 | | 2 6 789 | 5 C789 1 |C789 4 3 | :----------------------+---------------------+-----------------: | 39 239 1 | 36789 2789 36789 | 36789 5 4 | | 6 23459 2459 | 1 24789 35789 | 3789 789 789 | | 7 8 459 | 369 49 3569 | 369 1 2 | '----------------------'---------------------'-----------------'

TH with a singular rectangle guardian => -789r2c4, RTs 789A, 789B, 789C

Code: Select all: .-------------------.-------------------.----------------. | 45 2 6 | 3789 789 3789 | 45 789 1 | | 4589 4579 45789 | 6 1 2 | 45 3 789 | | 189 179 3 | 4 5 789 |C789 2 6 | :-------------------+-------------------+----------------: | 1589 1579 5789 | 789 3 4 | 2 6 789 | | 3489 3479 4789 | 2 6 789 | 1 789 5 | | 2 6 789 | 5 C789 1 |C789 4 3 | :-------------------+-------------------+----------------: | 39 39 1 | 78 2 678 |#678 5 4 | | 6 45 2 | 1 4–789 35789 |#3789 #789 #789 | | 7 8 45 | 39 49 3569 |#369 1 2 | '-------------------'-------------------'----------------'

789b9C\r8c57 => –789r8c5

Code: Select all: .-----------------.--------------.---------------. | 45 2 6 | 789 78 3 | 45 789 1 | | 4589 479 5–789| 6 1 2 | 45 3 A789 | | 189 179 3 | 4 5 789 | 789 2 6 | :-----------------+--------------+---------------: |#1589 #179 #5789 |A789 3 4 | 2 6 A789 | | 34 34 #789 | 2 6 789 | 1 789 5 | | 2 6 #789 | 5 78 1 | 789 4 3 | :-----------------+--------------+---------------: | 39 39 1 | 78 2 6 | 78 5 4 | | 6 5 2 | 1 4 78 | 3 789 789 | | 7 8 4 | 3 9 5 | 6 1 2 | '-----------------'--------------'---------------'

789b4A\r24c3 => –789r2c3

Code: Select all: .------------.--------------.---------------. | 4 2 6 | 789 78 3 | 5 789 1 | | 8 79 5 | 6 1 2 | 4 3 79 | | 1 79 3 | 4 5 789 |C789 2 6 | :------------+--------------+---------------: | 5 1 789 | 9–78 3 4 | 2 6 789 | | 3 4 789 | 2 6 789 | 1 789 5 | | 2 6 789 | 5 C78 1 |C789 4 3 | :------------+--------------+---------------: | 9 3 1 |#78 2 6 |#78 5 4 | | 6 5 2 | 1 4 78 | 3 789 789 | | 7 8 4 | 3 9 5 | 6 1 2 | '------------'--------------'---------------'

78r7C\c47b5 => –78r4c4, stte

Marek

The New Sudoku Players' Forum

Stormbreaker (SER 11.7; te3 ID 10401)

Stormbreaker (SER 11.7; te3 ID 10401)

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Re: Stormbreaker (SER 11.7; te3 ID 10401)

Re: Stormbreaker (SER 11.7; te3 ID 10401)

Re: Stormbreaker (SER 11.7; te3 ID 10401)

Re: Stormbreaker (SER 11.7; te3 ID 10401)