The New Sudoku Players' Forum

by **ArkieTech** » Fri Dec 01, 2006 11:01 pm

Carcul said

[r2c8]=9=[r2c5]-9-[r3c5]=9=[r3c2]-9-[r1c1]-6-[r5c1]=6=[r5c2]=7=
=[r8c2]-7-[r8c4]=7=[r2c4](-7-[r2c8])-7-[r3c5]-3-[r1c5]=3=[r1c78]-3-
-[r2c8], => r2c8=9 solving the puzzle.

Code: Select all: *--------------------------------------------------------* | 69 1 8 | 4 3679 2 | 39 379 5 | | 5 2 367 | 67 36789 38 | 1 379 4 | | 4 39 37 | 1 379 5 | 6 2 8 | |-------------------+------------------+-----------------| | 1 8 2 | 3 4 6 | 7 5 9 | | 67 67 4 | 2 5 9 | 8 1 3 | | 3 5 9 | 8 1 7 | 2 4 6 | |-------------------+------------------+-----------------| | 678 4 1 | 9 3678 38 | 5 36 2 | | 2679 3679 5 | 67 2367 4 | 39 8 1 | | 28 369 36 | 5 28 1 | 4 369 7 | *--------------------------------------------------------*

What do you call this technique? Can you provide me a link to help me understand how to use it?

by **Del** » Sat Dec 02, 2006 2:18 pm

To ArkieTech,

Carcul uses, perhaps invented, a rather complex system of describing a route around the grid to illustrate that a number may or may not be placed in a particular cell.
[r2c8]=9=[r2c5] means that 9 exists in one or the other cell.
[r2c5]-9-[r3c5] means that if 9 is in one of the cells then it is not in the other but if it is not in one cell then it is not necessarily in the other.
There is a full explanation elsewhere in the forum; search for "Nice Loops and SINS".

If I have followed this one correctly Carcul is saying:

If r2c8<>9, then r2c5=9, r3c5<>9, r3c2=9, r1c1=6, r5c1=7, r5c2=6, r39c2=39, r8c2=7, r8c4=6, r2c4=7, r13c5=39, r2c5=8, r2c6=3 and r2c8=9 which is a contradiction. Therefore the hypothesis that r2c8<>9 is untrue, so r2c8=9.

Regards,
Del.

by **ArkieTech** » Sat Dec 02, 2006 9:48 pm

Del said

If r2c8<>9, then r2c5=9, r3c5<>9, r3c2=9, r1c1=6, r5c1=7, r5c2=6, r39c2=39, r8c2=7, r8c4=6, r2c4=7, r13c5=39, r2c5=8, r2c6=3 and r2c8=9 which is a contradiction. Therefore the hypothesis that r2c8<>9 is untrue, so r2c8=9.

Is this a chain? Is developing it a mental or computer excercise?

Thanks -- that really helped. I am still green on nice loops. You did a good job converting it to English.

by **wapati** » Sat Dec 02, 2006 11:06 pm

daj95376 wrote:
Code: Select all
# all include pattern(s) SSTS can't resolve # some include XY-Wing, XYZ-Wing, and/or UR_1 9..3...5..57...4..3..7....1...53.1...8.....2...3.94...8....3..2..4...61..1...5..9 # e_01 ....49.8.2.91...3...6.....9.759.........8.........769.4.....2...5...67.8.1.52.... # e_02 .81....537394...6...5..8.....65.7.......8.......6.14.....9..5...5...637991....24. # e_03 27.59.68..58..71...6........4...8....3.....1....4...5........7...51..96..97.32.41 # e_04 7.63..9..35....2.1....5..34.....9.1...9.2.4...6.8.....64..8....9.7....82..2..73.6 # e_07 .7..9..3...94.7.6.6........8......92..7.5.8..16......3........5.9.5.86...1..2..7. # e_09 ..3.4..96.97...1..1....7.......15..7.2.8.6.4.5..79.......5....2..5...36.61..8.4.. # e_12 ..9...4.6.7.6138...3...4....6.8....1....5....8....7.2....7...1...2135.8.5.7...2.. # e_17 6.9..3.2..2..4.1...14.6...9..3..26..4.......2..17..4..7...8.91...5.2..3..3.9..2.5 # e_20 8..5..4...92.87.63.6..........37.2...7.....4...5.29..........7.12.74.93...6..8..2 # e_23 9...1.2.37..9...5..62.7....6....5.2...9.3.1...7.8....6....5.96..3...9..85.6.8...2 # e_25

Code: Select all
# SSTS + XYZ-Wing(s) 5.62....8.2.7..4.59............8.53.4.......1.39.7............96.5..3.8.8....51.3 # e_10 .1.25...8..8.....9.3..7.4.......7.5.2.7.9.1.6.9.5.......9.3..8.6.....7..3...61.9. # e_14 1...28..339.........83....5.6.8.5.9.93..7..28.4.2.3.5.5....27.........122..48...9 # e_16 5..43..18.1...5...4.98.........82..4.85...32.7..35.........47.1...5...9.94..73..2 # e_18 ..5.6.1...3.2.1..98...........54..3..23...46..7..23...........43..8.6.7...1.7.9.. # e_21 ....7..5..396.....6.2..5..1...8...14..31.28..89...6...4..9..2.6.....814..1..2.... # e_22

# e_01 finned-sword
# e_02 finned sword-f-x-UR
# e_03 2-sky
# e_04 finned-x
# e_07 xyz-xy-f-x-finned-sword
# e_09 chains
# e_12 xy-chain
# e_17 finned-x-x-sky
# e_20 chain
# e_23 chain
# e_25 chains

# e_10 finned-swords-f-x-xyz
# e_14 turbots-xy-sky-x
# e_16 x-xy-xyz-finned-x
# e_18 3-sky
# e_21 x-xy-xyz-finned-x
# e_22 finned-swords-xyz-x

Great puzzles DAJ, I have saved most of them.

by **wapati** » Tue Dec 05, 2006 8:36 am

Just a thought here.

It would seem that an "average" puzzle has about 26 clues.

I do wonder whether harder puzzles have more clues, in the very general sense.

I note that the 17s pretty much are average. Is that because (say) 38s are average also? Does the number of clues have pretty much no impact on difficulty?

Sorry if this is tired, I thought of this because this puzzle has lots of clues but is hard. (Hard for pattern solvers.)

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

by **Carcul** » Tue Dec 05, 2006 10:58 am

Wapati wrote:Sorry if this is tired, I thought of this because this puzzle has lots of clues but is hard. (Hard for pattern solvers.)

Code: Select all: *------------------------------------------------------* | 2 5 14 | 7 148 6 | 148 3 9 | | 3 9 7 | 148 2 148 | 1468 5 1468 | | 14 8 6 | 3 5 9 | 7 2 14 | |-----------------+-----------------+------------------| | 9 14 3 | 5 6 148 | 148 7 2 | | 148 7 2 | 9 148 3 | 5 6 148 | | 5 6 148 | 148 7 2 | 9 18 3 | |-----------------+-----------------+------------------| | 168 2 158 | 1468 148 7 | 3 9 1568 | | 7 3 158 | 168 9 18 | 2 4 1568 | | 1468 14 9 | 2 3 5 | 168 18 7 | *------------------------------------------------------*

[r5c1]=8=[r6c3]-8-[r6c4|r78c3]-{ATILA(1,4)}-8-[r7c5]-{[r1c7]-8-[r1c5]
=8=[r5c5]-8-[r4c6]=8=[r4c7]-8-[r1c7]}-8-[r1c7](-1,4-[r2c9]-8-[r5c9])
=8=[r1c5]-8-[r5c59]-1,4-[r5c1], => r5c1<>1,4 solving the puzzle.

Carcul

by **wapati** » Wed Dec 06, 2006 5:53 am

Several fins. Fun challenge!

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

by **daj95376** » Wed Dec 06, 2006 11:35 am

wapati wrote:Several fins. Fun challenge!
Code: Select all
. 7 9 | . 8 4 | . . . 8 . 4 | . . . | . . . 5 6 . | 7 . . | . . . --------------------- . . 2 | 1 5 . | . . 9 7 . . | 6 . 3 | . . 1 1 . . | . 7 9 | 3 . . --------------------- . . . | . . 5 | . 2 6 . . . | . . . | 1 . 5 . . . | 9 6 . | 8 7 .

(sans Singles) Only one finned fish is needed.

Code: Select all: # after X-Wing # finned Swordfish *--------------------------------------------------------------------* |*23 7 9 | 5 8 4 | 6 1 *23 | | 8 123 4 | 23 1239 6 | 259 359 7 | | 5 6 13 | 7 239 12 | 249 3489 2348 | |----------------------+----------------------+----------------------| |*346 *34 2 | 1 5 8 | 7 46 9 | | 7 9 58 | 6 24 3 | 245 458 1 | | 1 458 568 | 24 7 9 | 3 4568 248 | |----------------------+----------------------+----------------------| | 49-3 148-3 7 | 348 134 5 | 49 2 6 | | 2469-3 248-3 368 | 2348 234 7 | 1 349 5 | |*234 *2345 #135 | 9 6 12 | 8 7 *34 | *--------------------------------------------------------------------* r7 - 49 Naked Pair b8 - 4 Locked Candidate (1) r7 - 3 Locked Candidate (2) c5 - 24 Naked Pair r8 - 248 Naked Triple b7 - 8 Locked Candidate (1) r2c2 <> 3 XY-Wing on [r3c6] r3c5 <> 3 XY-Wing on [r3c6] r2 - 123 Naked Triple c2 - 128 Naked Triple r3c9 <> 4 XY-Wing on [r1c9] r7c7 <> 4 XY-Wing on [r1c9]

by **wapati** » Thu Dec 07, 2006 7:10 am

Another busy puzzle.

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

by **wapati** » Fri Dec 08, 2006 6:48 am

Too many patterns to list.

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

by **wapati** » Fri Dec 08, 2006 7:15 am

This is not too bad. A lot of a few patterns.

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

by **ArkieTech** » Fri Dec 08, 2006 8:34 am

wapati,

Good puzzle with two brick walls. I wasn't able to find a way to get through without out chains however.

dan

by **daj95376** » Fri Dec 08, 2006 7:21 pm

wapati wrote:This is not too bad. A lot of a few patterns.

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

Code: Select all: # after Singles, Naked Pairs, and Locked Candidate (1) # Colors => [r1c1]<>4, [r6c2]<>4 (not necessary, but helpful) # B G b g # advanced Colors: [r5c3]=3=[r2c3]-3-[r2c45]=3=[r13c6] => [r5c6]<>3 *-----------------------------------------------------------* | 13 14 9 | 8 5 g234 | 23 6 7 | | 2 456 G356 |b34 b36 7 | 8 9 1 | | 367 67 8 | 9 1 g236 | 235 4 235 | |-------------------+-------------------+-------------------| | 467 8 56 | 457 67 1 | 29 3 29 | | 136 9 B136 | 2 8 6-3 | 57 57 4 | | 347 57 2 | 3457 9 345 | 1 8 6 | |-------------------+-------------------+-------------------| | 8 2 4 | 6 37 35 | 3579 1 359 | | 9 16 16 | 357 2 8 | 4 57 35 | | 5 3 7 | 1 4 9 | 6 2 8 | *-----------------------------------------------------------* # Naked Singles, Naked Pairs, and an XY-Wing complete puzzle

by **wapati** » Sat Dec 09, 2006 5:53 am

ArkieTech wrote:wapati,

Good puzzle with two brick walls. I wasn't able to find a way to get through without out chains however.

dan

Which puzzle? I could show, perhaps, the missing pattern.

by **wapati** » Sat Dec 09, 2006 5:55 am

Very many patterns required. Fins, for sure.

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

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CHAINS, not required. Good puzzles.