The New Sudoku Players' Forum

by **wapati** » Tue Nov 07, 2006 9:20 am

I sure don't know the fastest way on this.

It isn't that long, but not short, for me.

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

by **Carcul** » Tue Nov 07, 2006 4:43 pm

Wapati wrote:Three patterns can handle it, used some times.
I am thinking ER, finned sword and xyz. Other patterns work.

Look carefully to the grid:

Code: Select all: *------------------------------------------------------* | 135 26 145 | 34 9 234 | 137 8 367 | | 1389 13 149 | 348 7 6 | 139 5 2 | | 389 26 7 | 1 5 238 | 4 36 369 | |-----------------+-----------------+------------------| | 6 7 3 | 2 4 1 | 8 9 5 | | 2 5 8 | 7 3 9 | 6 4 1 | | 19 4 19 | 6 8 5 | 2 37 37 | |-----------------+-----------------+------------------| | 4 13 6 | 9 2 7 | 5 13 8 | | 7 8 12 | 5 6 34 | 39 12 349 | | 35 9 25 | 348 1 348 | 37 2367 3467 | *------------------------------------------------------*

If r8c7=9 then

{TILA: Turbot Fish (r2c27|r7c28|r9c7), => r9c7<>3; [r9c7]-7-[r12c7]-3-
-[Swordfish: r3c689|r6c89|r8c69]=3=[r6c8]=7=[r9c8]-7-[r9c7], => r9c7<>7}.

So, r8c7<>9 and the puzzle is solved.

Carcul

by **Carcul** » Tue Nov 07, 2006 5:39 pm

Wapati wrote:Somewhat odd, this. You can do it with just ERs.
I did it with a grouped x and some Turbots, (I don't like them much).
I don't normally check colours but I had SS active and yep, colours can do it.

Code: Select all: *------------------------------------------------------------* | 3 459 459 | 6 2 57 | 579 1 8 | | 159 8 6 | 157 3 4 | 579 2 579 | | 15 2 7 | 15 8 9 | 3 46 46 | |-------------------+------------------+---------------------| | 4 59 8 | 57 6 1 | 2 3 579 | | 569 3 1 | 8 57 2 | 45679 469 45679 | | 56 7 2 | 9 4 3 | 56 8 1 | |-------------------+------------------+---------------------| | 8 69 3 | 4 59 56 | 1 7 2 | | 2 1 49 | 3 79 67 | 8 5 469 | | 7 4569 459 | 2 1 8 | 469 469 3 | *------------------------------------------------------------*

Look closely to the grid: if r4c2=5 then the puzzle would have more than one solution. So, r4c2=9 solving the puzzle.

Carcul

by **Carcul** » Tue Nov 07, 2006 5:48 pm

Wapati wrote:sure don't know the fastest way on this. It isn't that long, but not short, for me.

Code: Select all: *----------------------------------------------------* | 17 9 127 | 5 6 27 | 4 3 8 | | 4 2567 8 | 17 129 3 | 2569 169 12 | | 26 3 25 | 4 129 8 | 2569 169 7 | |-----------------+-----------------+----------------| | 9 8 12 | 6 5 4 | 3 7 12 | | 5 27 3 | 178 12 279 | 269 1689 4 | | 17 4 6 | 178 3 279 | 29 189 5 | |-----------------+-----------------+----------------| | 3 1 9 | 2 7 5 | 8 4 6 | | 8 57 57 | 9 4 6 | 1 2 3 | | 26 26 4 | 3 8 1 | 7 5 9 | *----------------------------------------------------*

Put on your glasses and look again carefully to the grid: if r2c9=1 then the puzzle would have more than one solution because of r2c4 and r23c8. So, r2c9<>1 and the puzzle is solved.

Carcul

by **daj95376** » Wed Nov 08, 2006 3:46 am

# Maybe solvable without chains ... no promises. Difficulty varies.
# Send me a pm if too many are unacceptable, and I'll delete the post.

Code: Select all: ...7...1..3.1..2.5...94.8..8.....1...7.653.2...3.....7..5.28...3.8..1.9..1...9... # A 66 ...94.23..5..76..4..4.......2.451..8.........1..237.5.......5..3..59..1..69.28... # A 71 ..1.4..9....3...4......7..23.6....5..14.2.37..2....4.95..6......7...3....4..9.8.. # A 72 ..1.7.....395.8..65.8.2......69...3....2.7....8...34......9.3.49..8.127.....3.8.. # A 76 ..3......45......2.16..73.96.2.74.1.....9.....4.23.9.61.43..27.8......31......6.. # A 90 ..4.8.......2..8757...3..4.876....5...........2....481.5..1...8918..6.......4.7.. # A 103 ..9.4..3.283..1...4.63....17..4..15...........21..5..73....49.8...7..365.9..6.7.. # A 139 .1..8.7.5..76.1.894.8..5...........7..14.68..9...........5..1.424.1.39..1.6.4..7. # A 149 .17..42...3...2..8..875....1.2....4.4...3...6.7....8.2....754..7..4...8...69..72. # A 155 .3..271..1..8......24...8...8.7..2..5.1...7.9..6..3.1...8...95......1..7..756..2. # A 170 .4...79..68..2..1...7.....5...3..24.8...9...6.73..2...1.....5...6..4..82..48...9. # A 183 .681.97..75.....1...15.....1....53..2.3...5.8..62....4.....68...1.....49..49.163. # A 218 .7.12.5....5.7..418....6......8....3.3..4..1.9....2......2....456..8.2....4.69.3. # A 229 .7.62...1.3...5..6..4..1.3.....3654...........2718.....4.2..3..7..3...2.3...69.8. # A 230 .73.6.95...1..7.239......6......2...8...5...9...7......3......269.4..3...58.1.69. # A 232 .768.3..55...1......4..93...5.4..79...8.7.2...29..1.5...57..9......5...48..1.457. # A 236 .9...6..7..5...2.6..2....4....67..3..5.8.2.6..1..93....7....8..8.4...6..6..3...1. # A 255 12..948...4352....7....3..........89.8..6..4.53..........9....8....4695...715..62 # A 294 2..8....5.9..4123......21.....9.87..3.......1..74.3.....65......2918..5.8....7..2 # A 317 214..8...69.4....7.........1....63...82.1.65...93....4.........4....1.93...8..561 # A 324 3.78.124.....7......9.2...76.2........54.28........4.22...4.3......3.....832.59.1 # A 362 35.4...8..6...21.5......94....62....1..759..6....83....92......7.19...6..3...7.59 # A 370 4.165....28..4.......3.8..1..62...14.2.....8.81...32..9..7.5.......3..67....261.5 # A 397 46...1..8...5...4..15..9........6.2.6.42.31.5.5.9........1..25..3...2...1..8...76 # A 414 5.1....3..4.....623..5..7..6..71.4......8......4.92..5..8..6..196.....4..3....6.7 # A 436 7...3..9..4...8..3..67...1...8....6....576....9....3...6...32..9..4...5..8..2...6 # A 497 7..19.2..........38....6.7..8.37.....9..8..5.....19.4..3.5....24..........6.32..8 # A 501 7.6.9..3..5...76....1.3..2.6..4.......59.31.......1..6.4..8.7....76...8..6..2.9.3 # A 510 9...8.3.1..231..8.1....96...6.725.....7...4.....943.6...92....6.2..379..7.5.9...4 # A 560 974...6.3.......2..5....4.1...2.15..51..7..38..95.8...1.7....4..4.......3.8...765 # A 586

Code: Select all: ........953..4.7....72.513.69...3.....5...9.....4...76.215.64....9.3..257........ # B 1 .....3..5.73...82....76.1....562....4.......1....857....7.16....14...23.8..3..... # B 10 ..159...36....2..8......14...6..9.51...2.5...53.8..6...15......3..9....48...219.. # B 58 .34725.1.16..8..7....1.....4......252.3...7.165......3.....8....8..7..56.4.63128. # B 107 .4...6395.153..7..3...........69.2....4...6....9.43...........3..1..594.4637...5. # B 112 1.....284..31.7....9..8...77..2......1.....9......8..26...2..3....4.97..284.....9 # B 155 3....6..9.9...4..1..7....6...3.9...4.1..8..5.9...3.6...3....8..6..8...3.1..5....7 # B 192 4.2..3..8...4...3.7.1.86....1...58..3.76.85.2..53...1....16.4.5.2...4...6..8..3.1 # B 214 4.2.3.6..17.....5.3....6.1.....9.347...564...249.7.....1.2....4.2.....35..4.1.2.6 # B 216 43...6.921.8..9.7.6............6.4..9..7.8..6..4.9............8.4.2..9.389.6...17 # B 221 8..1.5...7.........42.8.7.3..43...12.........35...14..5.6.2.13.........4...7.3..8 # B 278

by **wapati** » Wed Nov 08, 2006 6:33 am

daj95376 wrote:# Maybe solvable without chains ... no promises. Difficulty varies.
# Send me a pm if too many are unacceptable, and I'll delete the post.

Wow, there are some gems in there!

Thanks daj, good puzzles.

by **Carcul** » Wed Nov 08, 2006 1:12 pm

Daj95376 wrote:# Maybe solvable without chains ... no promises. Difficulty varies.

Nice puzzles. For example, for Puzzle A71,

Code: Select all: *----------------------------------------------------* | 678 178 1678 | 9 4 5 | 2 3 17 | | 29 5 123 | 38 7 6 | 189 89 4 | | 79 379 4 | 38 1 2 | 6789 67 5 | |------------------+---------------+-----------------| | 679 2 367 | 4 5 1 | 3679 67 8 | | 47 347 5 | 6 8 9 | 1347 2 137 | | 1 489 68 | 2 3 7 | 469 5 69 | |------------------+---------------+-----------------| | 248 148 128 | 7 6 3 | 5 89 29 | | 3 78 278 | 5 9 4 | 68 1 26 | | 5 6 9 | 1 2 8 | 37 4 37 | *----------------------------------------------------*

Consider the following sets:

A(1,2,3,8)=[r27c3]; B(3,8,9)=[r2c48]; C(8,9)=[r7c8]; D(2,7,8)=[r8c23].

As “2” is restricted common to A and D, “3” to A and B, “9” to B and C, “8” to A and C, and “8” to A and D, then r7c1<>8 which solves the puzzle.

For Puzzle A72:

Code: Select all: *-------------------------------------------------------------* | 28 36 1 | 258 4 258 | 67 9 37 | | 289 5689 7 | 3 168 1289 | 156 4 168 | | 4 35689 389 | 189 168 7 | 156 1368 2 | |--------------------+--------------------+-------------------| | 3 89 6 | 4 7 189 | 2 5 18 | | 89 1 4 | 589 2 5689 | 3 7 68 | | 7 2 5 | 18 3 168 | 4 168 9 | |--------------------+--------------------+-------------------| | 5 389 2389 | 6 18 4 | 179 123 37 | | 16 7 289 | 128 5 3 | 169 126 4 | | 16 4 23 | 7 9 12 | 8 1236 5 | *-------------------------------------------------------------*

If r7c2~3 then:

[r5c1]-8-[r4c2]=8=[r7c2]-8-[r7c5]-1-[r9c6]-2-[r2c6]=2=[r2c1]-2-[r1c1]-8-[r5c1];

{ATILA(9): r2c1|r2c6|r4c6|r5c6|r4c2|r5c1}, => r5c6=9 => r5c1=8.

So, r7c2=3. After that, the same ATILA above solves the puzzle.

Carcul

by **Carcul** » Wed Nov 08, 2006 2:26 pm

Puzzle A586:

Code: Select all: *------------------------------------------------------------* | 9 7 4 | 18 18 2 | 6 5 3 | | 68 36 1 | 3469 45 34569 | 89 2 7 | | 268 5 236 | 367 69 367 | 4 89 1 | |-------------------+---------------------+------------------| | 47 8 36 | 2 369 1 | 5 79 46 | | 5 1 26 | 469 7 469 | 29 3 8 | | 47 236 9 | 5 36 8 | 12 17 46 | |-------------------+---------------------+------------------| | 1 269 7 | 3689 258 3569 | 38 4 29 | | 26 4 5 | 36789 28 3679 | 138 18 29 | | 3 29 8 | 149 124 49 | 7 6 5 | *------------------------------------------------------------*

Consider the sets A(2,6,8)=[r28c1], B(2,8,9)=[r25c7], C(1,2,4,6,7)=[r6c1789], D(2,3,6)=[r6c25].
The “2” in r9c2 can see the “2s” in both A and D, and so r9c2<>2 solving the puzzle.

Carcul

by **Carcul** » Wed Nov 08, 2006 2:43 pm

Puzzle A560:

Code: Select all: *------------------------------------------------------* | 9 457 46 | 456 8 2 | 3 457 1 | | 456 457 2 | 3 1 46 | 57 8 9 | | 1 38 38 | 45 7 9 | 6 245 25 | |------------------+-----------------+-----------------| | 348 6 1348 | 7 2 5 | 18 9 38 | | 235 9 7 | 18 6 18 | 4 25 235 | | 258 158 18 | 9 4 3 | 1258 6 7 | |------------------+-----------------+-----------------| | 348 1348 9 | 2 5 148 | 78 137 6 | | 468 2 1468 | 148 3 7 | 9 15 58 | | 7 138 5 | 168 9 168 | 28 123 4 | *------------------------------------------------------*

A(3,4,5,6,8)=[r2478c1], B(5,7,8)=[r27c7], C(1,2,3,5,8)=[r46c7|r5c89], => r5c1<>3.
After that, we have r2c2=5 or r6c1=5, and so r6c2<>5, solving the puzzle.

Carcul

by **Carcul** » Wed Nov 08, 2006 2:54 pm

Puzzle A510:

Code: Select all: *------------------------------------------------------* | 7 28 6 | 15 9 28 | 45 3 145 | | 238 5 23 | 128 4 7 | 6 19 189 | | 4 9 1 | 58 3 6 | 58 2 7 | |-----------------+-----------------+------------------| | 6 1 239 | 4 57 28 | 2358 579 2589 | | 28 278 5 | 9 6 3 | 1 47 248 | | 2389 2378 4 | 28 57 1 | 2358 579 6 | |-----------------+-----------------+------------------| | 1259 4 29 | 3 8 59 | 7 6 125 | | 2359 23 7 | 6 1 459 | 245 8 245 | | 15 6 8 | 7 2 45 | 9 145 3 | *------------------------------------------------------*

1. Unique Rectangle in cells [r46c58], => r2c8<>9.
2. {ATILA(2,8): r6c2|r6c4|r4c6|r1c6|r1c2}, => r6c2=7 solving the puzzle.

Carcul

by **Carcul** » Wed Nov 08, 2006 3:13 pm

Puzzle A501:

Code: Select all: *------------------------------------------------------* | 7 6 5 | 1 9 3 | 2 8 4 | | 129 4 129 | 78 25 78 | 156 16 3 | | 8 12 3 | 4 25 6 | 159 7 159 | |------------------+-----------------+-----------------| | 16 8 4 | 3 7 5 | 19 2 169 | | 126 9 127 | 26 8 4 | 3 5 167 | | 3 5 27 | 26 1 9 | 8 4 67 | |------------------+-----------------+-----------------| | 19 3 189 | 5 4 178 | 167 169 2 | | 4 127 1289 | 789 6 178 | 157 3 15 | | 5 17 6 | 79 3 2 | 4 19 8 | *------------------------------------------------------*

We have r5c1=2 or r5c3=1 or r4c9=9, and r5c3=1 or r5c9=1. But if r5c1~2 then r5c3<>1 => r5c9=1 => r4c7=9 => r4c9<>9. So r5c1=2 and the puzzle is solved (using the UR).

Carcul

by **Carcul** » Wed Nov 08, 2006 3:41 pm

Puzzle A436:

Code: Select all: *--------------------------------------------------------------* | 5 2789 1 | 2489 6 4789 | 89 3 489 | | 78 4 79 | 1389 37 13789 | 5 6 2 | | 3 289 6 | 5 24 489 | 7 1 489 | |--------------------+---------------------+-------------------| | 6 589 359 | 7 1 35 | 4 2 89 | | 2 579 3579 | 34 8 345 | 1 79 6 | | 78 1 4 | 6 9 2 | 3 78 5 | |--------------------+---------------------+-------------------| | 4 57 8 | 239 2357 6 | 29 59 1 | | 9 6 257 | 128 257 178 | 28 4 3 | | 1 3 25 | 2489 245 489 | 6 589 7 | *--------------------------------------------------------------*

1. r2c1=8 or r8c7=8, and so r9c8<>8.
2. r2c6=7 or r8c5=7, and so r8c6<>7, solving the puzzle.

Carcul

by **daj95376** » Wed Nov 08, 2006 5:28 pm

wapati and Carcul,

Thanks for the positive response. I'm glad you found some of my puzzles interesting.

by **re'born** » Wed Nov 08, 2006 5:51 pm

Carcul wrote:Puzzle A501:

Code: Select all
*------------------------------------------------------* | 7 6 5 | 1 9 3 | 2 8 4 | | 129 4 129 | 78 25 78 | 156 16 3 | | 8 12 3 | 4 25 6 | 159 7 159 | |------------------+-----------------+-----------------| | 16 8 4 | 3 7 5 | 19 2 169 | | 126 9 127 | 26 8 4 | 3 5 167 | | 3 5 27 | 26 1 9 | 8 4 67 | |------------------+-----------------+-----------------| | 19 3 189 | 5 4 178 | 167 169 2 | | 4 127 1289 | 789 6 178 | 157 3 15 | | 5 17 6 | 79 3 2 | 4 19 8 | *------------------------------------------------------*

We have r5c1=2 or r5c3=1 or r4c9=9, and r5c3=1 or r5c9=1. But if r5c1~2 then r5c3<>1 => r5c9=1 => r4c7=9 => r4c9<>9. So r5c1=2 and the puzzle is solved (using the UR).

Carcul

I hope you don't mind if I restate your solution as it confused me a little at first. You can tell me if I've got the the right idea:

Code: Select all: *------------------------------------------------------* | 7 6 5 | 1 9 3 | 2 8 4 | | 129 4 129 | 78 25 78 | 156 16 3 | | 8 12 3 | 4 25 6 | 159 7 159 | |------------------+-----------------+-----------------| | 16 8 4 | 3 7 5 | 19 2 169 | | 126- 9 127* | 26* 8 4 | 3 5 167*| | 3 5 27* | 26* 1 9 | 8 4 67* | |------------------+-----------------+-----------------| | 19 3 189 | 5 4 178 | 167 169 2 | | 4 127 1289 | 789 6 178 | 157 3 15 | | 5 17 6 | 79 3 2 | 4 19 8 | *------------------------------------------------------*

The starred cells would form a deadly pattern if it weren't for the 1's in r5c39. Therefore, r5c1 <> 1, as it would eliminate those possibilities. Then

Code: Select all: *------------------------------------------------------* | 7 6 5 | 1 9 3 | 2 8 4 | | 129 4 129 | 78 25 78 | 156 16 3 | | 8 12 3 | 4 25 6 | 159 7 159 | |------------------+-----------------+-----------------| | 16# 8 4 | 3 7 5 | 19 2 169#| | 26# 9 127 | 26 8 4 | 3 5 167#| | 3 5 27 | 26 1 9 | 8 4 67 | |------------------+-----------------+-----------------| | 19 3 189 | 5 4 178 | 167 169 2 | | 4 127 1289 | 789 6 178 | 157 3 15 | | 5 17 6 | 79 3 2 | 4 19 8 | *------------------------------------------------------*

If r5c1 = 6, then r4c1=1 > r4c9 = 6 > r6c9=7 > r5c9=1. This creates a deadly pattern in the #-cells. Hence, r5c1 <> 6, i.e., r5c1=2.

From here there are many singles, but I think one more step is required at:

Code: Select all: *--------------------------------------------------* | 7 6 5 | 1 9 3 | 2 8 4 | | 19 4 29 | 78 25 78 | 156 16 3 | | 8 12 3 | 4 25- 6 | 159% 7 159% | |----------------+----------------+----------------| | 6 8 4 | 3 7 5 | 19% 2 19% | | 2 9 1 | 6 8 4 | 3 5 7 | | 3 5 7 | 2 1 9 | 8 4 6 | |----------------+----------------+----------------| | 19 3 89 | 5 4 178 | 167 169 2 | | 4 127 289 | 789 6 178 | 157 3 15 | | 5 17 6 | 79 3 2 | 4 19 8 | *--------------------------------------------------*

SS suggests a turbot fish to eliminate the '1' from r2c8, but I prefer the UR in r34c79 that eliminates the 5 in r3c5.

Is there a one-step move earlier in the puzzle to avoid this minor complication?

by **Carcul** » Wed Nov 08, 2006 6:19 pm

Rep'nA wrote:I hope you don't mind if I restate your solution as it confused me a little at first. You can tell me if I've got the the right idea:(...) The starred cells would form a deadly pattern if it weren't for the 1's in r5c39. Therefore, r5c1 <> 1, as it would eliminate those possibilities. Then(...) If r5c1 = 6, then r4c1=1 > r4c9 = 6 > r6c9=7 > r5c9=1. This creates a deadly pattern in the #-cells. Hence, r5c1 <> 6, i.e., r5c1=2.

That is not exactly what I had in mind. Let me show you what happens if r5c1~2, r5c3~1, and r4c9~9:

Code: Select all: *------------------------------------------------------* | 7 6 5 | 1 9 3 | 2 8 4 | | 129 4 129 | 78 25 78 | 156 16 3 | | 8 12 3 | 4 25 6 | 159 7 159 | |------------------+-----------------+-----------------| | 16 8 4 | 3 7 5 | 19 2 16 | | 16 9 27 | 26 8 4 | 3 5 167 | | 3 5 27 | 26 1 9 | 8 4 67 | |------------------+-----------------+-----------------| | 19 3 189 | 5 4 178 | 167 169 2 | | 4 127 1289 | 789 6 178 | 157 3 15 | | 5 17 6 | 79 3 2 | 4 19 8 | *------------------------------------------------------*

Here we have Two Incompatible Unique Patterns, one in cells r56c349 and other in cells r45c19. But if r5c1~2 then the naked pair in r45c1 makes r5c3<>1 and so (because of the UP in r56c349) r5c9=1 => r4c7=9 => r4c9<>9. In other words, from the condition "r5c1=2 or r5c3=1 or r4c9=9" we now have showed that if r5c1~2 then also r5c3<>1 and r4c9<>9. So, r5c1=2.

Rep'nA wrote:but I think one more step is required at

The UR is enough as I stated.

Rep'nA wrote:Is there a one-step move earlier in the puzzle to avoid this minor complication?

I see a UR like that as trivial as a naked pair. So I don't count it as a separate step.

Carcul

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