The New Sudoku Players' Forum

by **m_b_metcalf** » Sat Jan 08, 2022 5:01 pm

A recent issue of the New Yorker magazine featured on its a cover, among other puzzles, a crossword and a mostly obscured sudoku. A full set of clues to the crossword was provided inside, but not so for the sudoku. Here is a version which you may, or may not, enjoy:

Code: Select all: . . 5 . . . 3 . . . 8 . . . . . 9 . 9 . . . 6 . . . . . . . 4 . 3 . 7 . 5 . 1 . . . 8 . 2 . 4 . 8 . 5 . . . . . . . 9 . . . 5 . 1 . . . . . 6 . . . 3 . . . 7 . . ..5...3...8.....9.9...6.......4.3.7.5.1...8.2.4.8.5.......9...5.1.....6...3...7..

Mike

by **Cenoman** » Sat Jan 08, 2022 10:32 pm

Thank you Mike for the puzzle !
After singles and locked sets, three simple steps:

Code: Select all: +-----------------------+---------------------+------------------+ | 1 6 5 | 279 *48 2479-8 | 3 *28 47-8 | | 3 8 24 | 127 5 1247 | 6 9 147 | | 9 ^27 247 | 3 6 18 | ^24 5 18 | +-----------------------+---------------------+------------------+ | b28 9 28 | 4 1 3 | 5 7 6 | | 5 3 1 | 69 7 69 | 8 4 2 | | 67 4 67 | 8 2 5 | 9 1 3 | +-----------------------+---------------------+------------------+ | 4678-2 ^a27 2678 | 267 9 24678 | 1 3 5 | | b78-2 1 9 | 5 3 278 | ^24 6 48 | | 46-28 5 3 | 126 *48 1246-8 | 7 *28 9 | +-----------------------+---------------------+------------------+

1. X-Wing (8)c58\r19 => -8 r1c79, r9c17
2. ALS-XZ (2=7)r7c2 - (7=82)r48c1 => -2 r79c1
3. Skyscraper (2)r7c2 = r3c2 - r3c7 = r8c7 => -2 r8c1; 2 placements & ls

Then in the resulting resolution state, two more simple steps solve the puzzle:

Code: Select all: +------------------+--------------------+------------------+ | 1 6 5 | 279 Aa48 E279-4 | 3 b28 7-4 | | 3 8 24 | 127 5 1247 | 6 9 147 | | 9 27 247 | 3 6 18 | c24 5 18 | +------------------+--------------------+------------------+ | 2 9 8 | 4 1 3 | 5 7 6 | | 5 3 1 | 69 7 E69 | 8 4 2 | | 67 4 67 | 8 2 5 | 9 1 3 | +------------------+--------------------+------------------+ | 48 27 267 | 67 9 48 | 1 3 5 | | 78 1 9 | 5 3 27 | 24 6 48 | | C46 5 3 | 126 B48 D126 | 7 28 9 | +------------------+--------------------+------------------+

4. Y-Wing (4=8)r1c5 - (8=2)r1c8 - (2=4)r3c7 => -4 r1c9
5. (4)r1c5 = r9c5 - (4=6)r9c1 - r9c6 = (69)r15c6 => -4 r1c6; ste

Website · by **denis_berthier** » Sun Jan 09, 2022 6:22 am

.
SER = 7.2

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 1 6 5 ! 279 48 24789 ! 3 28 478 ! ! 3 8 247 ! 127 5 1247 ! 6 9 147 ! ! 9 27 247 ! 3 6 12478 ! 24 5 1478 ! +-------------------+-------------------+-------------------+ ! 28 9 28 ! 4 1 3 ! 5 7 6 ! ! 5 3 1 ! 69 7 69 ! 8 4 2 ! ! 67 4 67 ! 8 2 5 ! 9 1 3 ! +-------------------+-------------------+-------------------+ ! 24678 27 2678 ! 267 9 24678 ! 1 3 5 ! ! 278 1 9 ! 5 3 278 ! 24 6 48 ! ! 2468 5 3 ! 126 48 12468 ! 7 28 9 ! +-------------------+-------------------+-------------------+ 101 candidates.

Simplest-first solution, in BC4: Show

It is interesting to see how such an easy puzzle (it is in BC4) can become absurdly complicated if one adds artificial requirements on the number of steps.
There's no 1-step solution, even using whips as long as 8.

There are several 2-step solutions, with whip[8], e.g.
whip[5]: r4c3{n8 n2} - b1n2{r3c3 r3c2} - r7c2{n2 n7} - r8c1{n7 n2} - c7n2{r8 .} ==> r4c1≠8
singles ==> r4c1=2, r4c3=8
whip[1]: b7n2{r7c3 .} ==> r7c4≠2, r7c6≠2
whip[8]: r7n8{c1 c6} - b2n8{r1c6 r1c5} - c8n8{r1 r9} - r9c1{n8 n6} - c6n6{r9 r5} - c6n9{r5 r1} - r1n4{c6 c9} - r8c9{n4 .} ==> r7c1≠4
stte
But this is using absurdly long and complicated chains for a puzzle in BC4.

Then, I tried to use only reversible chains (z-chains) of length no more than 6 (not much more than the BC rating) and to apply the fewer steps algorithm. The first try gave a solution in 6 non-W1 steps (not forgetting to count the initial Pair):
1) hidden-pairs-in-a-row: r3{n1 n8}{c6 c9} ==> r3c6≠4, r3c9≠7, r3c9≠4, r3c6≠7, r3c6≠2
whip[1]: r3n7{c3 .} ==> r2c3≠7
2) x-wing-in-columns: n8{c5 c8}{r1 r9} ==> r1c9≠8, r9c6≠8, r9c1≠8, r1c6≠8
3) biv-chain[4]: r1c5{n4 n8} - r1c8{n8 n2} - r3c7{n2 n4} - b1n4{r3c3 r2c3} ==> r2c6≠4
whip[1]: b2n4{r1c6 .} ==> r1c9≠4
naked-single ==> r1c9=7
4) z-chain[6]: c2n2{r7 r3} - b3n2{r3c7 r1c8} - r1c4{n2 n9} - r5c4{n9 n6} - r7c4{n6 n7} - r7c2{n7 .} ==> r7c3≠2, r7c6≠2, r7c1≠2
5) z-chain[6]: r3n7{c2 c3} - r6c3{n7 n6} - r7c3{n6 n8} - r8c1{n8 n2} - c7n2{r8 r3} - r3c2{n2 .} ==> r7c2≠7
singles ==> r7c2=2, r3c2=7, r4c1=2, r4c3=8
6) z-chain[6]: r7n4{c6 c1} - r9c1{n4 n6} - c6n6{r9 r5} - c6n9{r5 r1} - c6n4{r1 r9} - r9c5{n4 .} ==> r7c6≠8
stte

by **RSW** » Sun Jan 09, 2022 9:08 am

Five steps.

Code: Select all: +---------------+---------------+-----------+ | 1 6 5 | 279 #48 2479-8| 3 #28 47-8| | 3 8 24 | 127 5 1247 | 6 9 147 | | 9 27 247 | 3 6 18 | 24 5 18 | +---------------+---------------+-----------+ | 28 9 28 | 4 1 3 | 5 7 6 | | 5 3 1 | 69 7 69 | 8 4 2 | | 67 4 67 | 8 2 5 | 9 1 3 | +---------------+---------------+-----------+ | 24678 27 2678 | 267 9 24678 | 1 3 5 | | 278 1 9 | 5 3 278 | 24 6 48 | | 246-8 5 3 | 126 #48 1246-8| 7 #28 9 | +---------------+---------------+-----------+

X-Wing (8)c58r19 => -8r1c69, -8r9c16

Code: Select all: +---------------+-----------------+-------------+ | 1 6 5 | 29-7 ab48 249-7 | 3 b28 ad7-4 | | 3 8 24 | 127 5 1247 | 6 9 14-7| | 9 27 247 | 3 6 18 |c24 5 18 | +---------------+-----------------+-------------+ | 28 9 28 | 4 1 3 | 5 7 6 | | 5 3 1 | 69 7 69 | 8 4 2 | | 67 4 67 | 8 2 5 | 9 1 3 | +---------------+-----------------+-------------+ | 24678 27 2678 | 267 9 24678 | 1 3 5 | | 278 1 9 | 5 3 278 | 24 6 48 | | 246 5 3 | 126 48 1246 | 7 28 9 | +---------------+-----------------+-------------+

(7=48)r1c59 - (4=82)r1c58 - (2=4)r3c7 - (4=7)r1c9 => -4r1c9 -7r1c46 -7r2c9

Code: Select all: +----------------+--------------+----------+ | 1 6 5 | 29 48 249 | 3 28 7 | | 3 8 24 | 127 5 127 | 6 9 14 | | 9 c27 247 | 3 6 18 |b24 5 18 | +----------------+--------------+----------+ | 28 9 28 | 4 1 3 | 5 7 6 | | 5 3 1 | 69 7 69 | 8 4 2 | | 67 4 67 | 8 2 5 | 9 1 3 | +----------------+--------------+----------+ | 24678 d27 2678 | 267 9 24678 | 1 3 5 | | 78-2 1 9 | 5 3 278 |a24 6 48 | | 246 5 3 | 126 48 1246 | 7 28 9 | +----------------+--------------+----------+

(2)r8c7 = (2)r3c7 - (2)r3c2 = (2)r7c2 => -2r8c1

Code: Select all: +-----------------+--------------+----------+ | 1 6 5 | 29 48 249 | 3 28 7 | | 3 8 c24 | 127 5 127 | 6 9 14 | | 9 27 c247 | 3 6 18 | 24 5 18 | +-----------------+--------------+----------+ |a2-8 9 bc8-2 | 4 1 3 | 5 7 6 | | 5 3 1 | 69 7 69 | 8 4 2 | |d67 4 c67 | 8 2 5 | 9 1 3 | +-----------------+--------------+----------+ | 4678-2 27 267-8| 267 9 24678 | 1 3 5 | |d78 1 9 | 5 3 278 | 24 6 48 | | 46-2 5 3 | 126 48 1246 | 7 28 9 | +-----------------+--------------+----------+

(2)r4c1 = (2)r4c3 - (8=2476)r2346c3 - (6=78)r68c1 - (8=2)r4c1 => -2r79c1 -2r4c3 -8r4c1 -8r7c3

Code: Select all: +--------------+------------+-----------+ | 1 6 5 | 29 48 249 | 3 28 7 | | 3 8 24 | 127 5 127 | 6 9 14 | | 9 #27 b#247 | 3 6 18 |a24 5 18 | +--------------+------------+-----------+ | 2 9 8 | 4 1 3 | 5 7 6 | | 5 3 1 | 69 7 69 | 8 4 2 | | 67 4 67 | 8 2 5 | 9 1 3 | +--------------+------------+-----------+ | 48 #27 c#267 |d67 9 48 | 1 3 5 | | 78 1 9 | 5 3 e27 | 4-2 6 48 | | 46 5 3 | 126 48 126 | 7 28 9 | +--------------+------------+-----------+

UR(27)r37c23
(2=4)r3c7 - (4)r3c3 == (6)r7c3 - (6=7)r7c4 - (7=2)r8c6 => -2r8c7; stte

by **jco** » Sun Jan 09, 2022 3:01 pm

Using bb-plot (simplified) and an extension of medusa coloring,
I found a solution using two long chains. After basics

The first chain was originated from W-wing ideas

Code: Select all: .--------------------------------------------------. | 1 6 5 | 279 48 24789 | 3 28 478 | | 3 8 eD24 | 127 5 1247 | 6 9 147 | | 9 d27 eD247 | 3 6 18 |c24 5 18 | |-------------------+----------------+-------------| | 2-8 9 eD28 | 4 1 3 | 5 7 6 | | 5 3 1 | 69 7 69 | 8 4 2 | | B67 4 C67 | 8 2 5 | 9 1 3 | |-------------------+----------------+-------------| | 24678 27 267-8| 267 9 24678 | 1 3 5 | |aA278 1 9 | 5 3 278 |b24 6 48 | | 2468 5 3 | 126 48 12468 | 7 28 9 | '--------------------------------------------------'

(7*)r8c1 - r6c1 = r6c3 - (7=248)r234c3
||
[(8*=2)r8c1 - r8c7 = r3c7 - (2=7)r3c2 - (7=248)r234c3]
=> -8 r4c1, -8 r7c3 [2 placements & basics]
---
The second chain was derived after noticing a conflict (color) in column 4
that indicated that proving -6 r7c4 would solve the puzzle with singles.

Code: Select all: .-------------------------------------------------. | 1 6 5 |bA29(7) D48 24789 | 3 c28 B478 | | 3 8 24 | 127 5 1247 | 6 9 147 | | 9 27 247 | 3 6 C18 | 24 5 B18 | |--------------+-------------------+--------------| | 2 9 8 | 4 1 3 | 5 7 6 | | 5 3 1 | a69 7 69 | 8 4 2 | | 67 4 67 | 8 2 5 | 9 1 3 | |--------------+-------------------+--------------| | 48 27 267 |gI7-6 9 48 | 1 3 5 | | 78 1 9 | 5 3 fH27 |eG24 6 B48 | | 468 5 3 | 126 E48 126 | 7 dF28 9 | '-------------------------------------------------'

Almost discontinuous loop
(7*)r1c3 - (7=481)r138c9 - (1=8)r3c6 - r1c5 = r9c5 - (8=2)r9c8 - r8c7 = (2-7)r8c6 = (7)r7c4
||
[(6=9)r5c4 - (9*=2)r1c4 - r1c8 = r9c8 - r8c7 = (2-7)r8c6 = (7)r7c4]
=> -6 r7c4; ste

Thanks for the nice puzzle!

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