The hardest sudokus (new thread) : General

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Re: The hardest sudokus (new thread)

by mith » Fri Apr 22, 2022 1:04 am

First 39c with more than one guardian:

Code: Select all: .....1..2.12....3.4.5..3.61...17265....895.1..51634....435..12.1.6...3.552.31..46 ED=11.6/11.6/3.4 .....1..2.12....3.4.5..3.61...17265....895.1..51634....235..14.1.6...3.554.31..26 ED=11.6/11.6/3.4

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Re: The hardest sudokus (new thread)

by denis_berthier » Fri Apr 22, 2022 4:46 am

.
As for the solution, nothing special. First puzzle (the second is identical):
Solving with preferences for Tridagons, they appear first (after Subsets):

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 36789 36789 789 ! 479 4568 1 ! 45789 789 2 ! ! 6789 1 2 ! 479 4568 6789 ! 45789 3 4789 ! ! 4 789 5 ! 279 28 3 ! 789 6 1 ! +-------------------+-------------------+-------------------+ ! 389 389 489 ! 1 7 2 ! 6 5 3489 ! ! 2367 367 47 ! 8 9 5 ! 247 1 347 ! ! 2789 5 1 ! 6 3 4 ! 2789 789 789 ! +-------------------+-------------------+-------------------+ ! 789 4 3 ! 5 68 6789 ! 1 2 789 ! ! 1 789 6 ! 2479 248 789 ! 3 789 5 ! ! 5 2 789 ! 3 1 789 ! 789 4 6 ! +-------------------+-------------------+-------------------+ 142 candidates

hidden-pairs-in-a-row: r8{n2 n4}{c4 c5} ==> r8c5≠8, r8c4≠9, r8c4≠7
whip[1]: b8n7{r9c6 .} ==> r2c6≠7
whip[1]: b8n9{r9c6 .} ==> r2c6≠9

Code: Select all: +-------------------+-------------------+-------------------+ ! 36789 36789 789 ! 479 4568 1 ! 45789 789 2 ! ! 6789 1 2 ! 479 4568 68 ! 45789 3 4789 ! ! 4 789 5 ! 279 28 3 ! 789 6 1 ! +-------------------+-------------------+-------------------+ ! 389 389 489 ! 1 7 2 ! 6 5 3489 ! ! 2367 367 47 ! 8 9 5 ! 247 1 347 ! ! 2789 5 1 ! 6 3 4 ! 2789 789 789 ! +-------------------+-------------------+-------------------+ ! 789 4 3 ! 5 68 6789 ! 1 2 789 ! ! 1 789 6 ! 24 24 789 ! 3 789 5 ! ! 5 2 789 ! 3 1 789 ! 789 4 6 ! +-------------------+-------------------+-------------------+ tridagon-link (horiz, same row) for digits 7, 8 and 9 in blocks: b3, with cells: r2c9 (link cell), r3c7, r1c8 b1, with cells: r2c1 (link cell), r3c2, r1c3 b9, with cells: r7c9, r9c7, r8c8 b7, with cells: r7c1, r9c3, r8c2 ==> tridagon-link[12](n4r2c9, n6r2c1) tridagon-forcing-whip-elim[13] based on tridagon-link(n4r2c9, n6r2c1) ....for n4r2c9: - ....for n6r2c1: partial-whip[1]: r2c6{n6 n8} - ==> r2c9≠8 tridagon-forcing-whip-elim[14] based on tridagon-link(n4r2c9, n6r2c1) ....for n4r2c9: - ....for n6r2c1: partial-whip[2]: r1n6{c2 c5} - c5n5{r1 r2} - ==> r2c5≠4, r1c7≠4 whip[1]: b3n4{r2c9 .} ==> r2c4≠4 tridagon-forcing-whip-elim[14] based on tridagon-link(n6r2c1, n4r2c9) ....for n6r2c1: - ....for n4r2c9: partial-whip[2]: c7n4{r2 r5} - r5n2{c7 c1} - ==> r5c1≠6

hidden-single-in-a-block ==> r5c2=6

Code: Select all: Resolution state RS1: +-------------------+-------------------+-------------------+ ! 36789 3789 789 ! 479 4568 1 ! 5789 789 2 ! ! 6789 1 2 ! 79 568 68 ! 45789 3 479 ! ! 4 789 5 ! 279 28 3 ! 789 6 1 ! +-------------------+-------------------+-------------------+ ! 389 389 489 ! 1 7 2 ! 6 5 3489 ! ! 237 6 47 ! 8 9 5 ! 247 1 347 ! ! 2789 5 1 ! 6 3 4 ! 2789 789 789 ! +-------------------+-------------------+-------------------+ ! 789 4 3 ! 5 68 6789 ! 1 2 789 ! ! 1 789 6 ! 24 24 789 ! 3 789 5 ! ! 5 2 789 ! 3 1 789 ! 789 4 6 ! +-------------------+-------------------+-------------------+

The end is in W11.

After RS1, one can also use my newly coded functions for eleven's technique and the rules for its automatic start in relation with Tridagons. One finds a solution in Z5 instead of W11:

Code: Select all: ***** STARTING ELEVEN''S REPLACEMENT TECHNIQUE in resolution state: ***** +-------------------+-------------------+-------------------+ ! 36789 3789 789 ! 479 4568 1 ! 5789 789 2 ! ! 6789 1 2 ! 79 568 68 ! 45789 3 479 ! ! 4 789 5 ! 279 28 3 ! 789 6 1 ! +-------------------+-------------------+-------------------+ ! 389 389 489 ! 1 7 2 ! 6 5 3489 ! ! 237 6 47 ! 8 9 5 ! 247 1 34 ! ! 2789 5 1 ! 6 3 4 ! 2789 789 789 ! +-------------------+-------------------+-------------------+ ! 789 4 3 ! 5 68 6789 ! 1 2 789 ! ! 1 789 6 ! 24 24 789 ! 3 789 5 ! ! 5 2 789 ! 3 1 789 ! 789 4 6 ! +-------------------+-------------------+-------------------+ AFTER APPLYING ELEVEN''S REPLACEMENT METHOD to digits 7, 8 and 9 in cells r7c1, r9c3 and r8c2, the resolution state is: +----------------------+----------------------+----------------------+ ! 36789 3789 789 ! 4789 456789 1 ! 5789 789 2 ! ! 6789 1 2 ! 789 56789 6789 ! 45789 3 4789 ! ! 4 789 5 ! 2789 2789 3 ! 789 6 1 ! +----------------------+----------------------+----------------------+ ! 3789 3789 4789 ! 1 789 2 ! 6 5 34789 ! ! 23789 6 4789 ! 789 789 5 ! 24789 1 34 ! ! 2789 5 1 ! 6 3 4 ! 2789 789 789 ! +----------------------+----------------------+----------------------+ ! 7 4 3 ! 5 6789 6789 ! 1 2 789 ! ! 1 9 6 ! 24 24 789 ! 3 789 5 ! ! 5 2 8 ! 3 1 789 ! 789 4 6 ! +----------------------+----------------------+----------------------+ 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]: r6n7{c9 .} ==> r5c7≠7, r4c9≠7 whip[1]: b8n7{r9c6 .} ==> r2c6≠7 finned-x-wing-in-rows: n9{r9 r3}{c7 c6} ==> r2c6≠9 whip[1]: c6n9{r9 .} ==> r7c5≠9 finned-x-wing-in-columns: n9{c8 c3}{r1 r6} ==> r6c1≠9 whip[1]: r6n9{c9 .} ==> r4c9≠9, r5c7≠9 z-chain[4]: r1c3{n7 n9} - r1c8{n9 n8} - r3c7{n8 n9} - r9c7{n9 .} ==> r1c7≠7 z-chain[4]: r1c3{n9 n7} - r1c8{n7 n8} - b9n8{r8c8 r7c9} - b9n9{r7c9 .} ==> r1c7≠9 whip[4]: r2n4{c7 c9} - c9n7{r2 r6} - c9n9{r6 r7} - r9c7{n9 .} ==> r2c7≠7 z-chain[5]: c1n6{r1 r2} - r2c6{n6 n8} - r8n8{c6 c8} - r1c8{n8 n7} - r1c3{n7 .} ==> r1c1≠9 z-chain[5]: r1c3{n9 n7} - r1c8{n7 n8} - b9n8{r8c8 r7c9} - b9n9{r7c9 r9c7} - r3n9{c7 .} ==> r1c4≠9, r1c5≠9 z-chain[5]: r9c7{n9 n7} - r3c7{n7 n8} - r3c2{n8 n7} - r1c3{n7 n9} - c8n9{r1 .} ==> r6c7≠9 biv-chain[3]: r6n9{c8 c9} - r7c9{n9 n8} - r8c8{n8 n7} ==> r6c8≠7 biv-chain[3]: r6n7{c9 c7} - r9c7{n7 n9} - r7c9{n9 n8} ==> r6c9≠8 z-chain[4]: r1c3{n7 n9} - c8n9{r1 r6} - r6c9{n9 n7} - r2n7{c9 .} ==> r1c5≠7, r1c4≠7 biv-chain[3]: r1c4{n8 n4} - c5n4{r1 r8} - c5n2{r8 r3} ==> r3c5≠8 biv-chain[5]: c8n7{r1 r8} - r8c6{n7 n8} - r2c6{n8 n6} - r1n6{c5 c1} - b1n3{r1c1 r1c2} ==> r1c2≠7 hidden-pairs-in-a-row: r1{n7 n9}{c3 c8} ==> r1c8≠8 biv-chain[3]: b6n9{r6c9 r6c8} - c8n8{r6 r8} - r7c9{n8 n9} ==> r2c9≠9 biv-chain[3]: b6n7{r6c7 r6c9} - c9n9{r6 r7} - r9c7{n9 n7} ==> r3c7≠7 biv-chain[3]: r3c2{n7 n8} - r3c7{n8 n9} - r1c8{n9 n7} ==> r1c3≠7 singles ==> r1c3=9, r1c8=7, r8c8=8, r6c8=9, r6c9=7, r7c9=9, r9c7=7, r9c6=9, r8c6=7, r3c2=7 naked-pairs-in-a-row: r2{c1 c6}{n6 n8} ==> r2c9≠8, r2c7≠8, r2c5≠8, r2c5≠6, r2c4≠8 stte 389461572 612758934 475923861 934172658 267895413 851634297 743586129 196247385 528319746

Now compare this solution to the original puzzle:

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

and observe on block b5 that (by mere chance), no permutation of digits 7, 8, 9 needs to be done.

denis_berthier

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Re: The hardest sudokus (new thread)

by mith » Sat Apr 23, 2022 3:43 am

Yes, SER reduces to 8.3 after replacement.

An alternate path using an extended trivalue oddagon:

Code: Select all: . . * | . . . | . * . a . . | . . b | . . c . * . | . . . | * . . ------+-------+------ . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ------+-------+------ * . . | . . . | . . * . * . | . . * | . * . . . * | . . * | * . .

After basics: If a is not 6, c is not 789 by trivalue oddagon in b1379. If a is 6, b is 8, and the extended pattern b1379+c6 is also not three colorable so c is again not 789. (Pretty simple after 4r2c9.)

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Re: The hardest sudokus (new thread)

by eleven » Sat Apr 23, 2022 9:47 pm

This pattern looks familiar to me (see here). Who has found it ?

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Re: The hardest sudokus (new thread)

by International_DBA » Sun Apr 24, 2022 8:09 am

I produce extreme sudokus from time to time but they take up a lot of computer time as for each one I have to reject 50 or 100 which are not hard enough.
I then post them on my blog, where (if I'm lucky) they get between 100 and 200 views each.
However, a couple of members in my Facebook group keep asking for very difficult puzzles.
Would you mind if I copied and published one of yours, please?
I will add a link to send people back to this thread if they want more.

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Re: The hardest sudokus (new thread)

by mith » Sun Apr 24, 2022 3:54 pm

eleven wrote:This pattern looks familiar to me (see here). Who has found it ?

I actually just found it messing around figuring out what happens if 6r2c1, and realizing it was the 789 that was breaking. It does look like a morph of the first one in your post.

ryokousha posted a few more versions of the idea, which are probably also morphs or at least very similar to the ones you’ve posted. I need to catch up in the chromatic thread.

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Re: The hardest sudokus (new thread)

by mith » Sun Apr 24, 2022 4:30 pm

Finally found some 39c 11.7s:

Code: Select all: .....1.23..2.3.1.4..1.4256....21.64.14..653.262.4.3....731.6...21.....368963.4... ED=11.7/11.7/8.3 .....1.23..2.3.1.4..1.4256....21.64.14..653.262.3.4....731.6...21.....368964.3... ED=11.7/11.7/8.3 .....1.23..2.3.1.4..1.4256....21.64.14..653.262.3.4....761.3...21.....368934.6... ED=11.7/11.7/8.3

(same puzzle other than some rectangle swaps)

Guardians in opposing boxes, but they collapse pretty quickly with the strong link:

5r6c3 = r4c123 - r4c9 =[to789b2356] = r1c5 - r789c5 = r8c4 => -5r8c3 (solvable with turbot fish from here)

Also noticed that occasionally the same puzzle is getting added to the database twice - presumably a timing thing between the scripts. Will have to figure out where that is happening, but fortunately not frequent and quick to find all the instances and remove duplicates.

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Re: The hardest sudokus (new thread)

by yzfwsf » Sun Apr 24, 2022 11:23 pm

mith wrote:Guardians in opposing boxes, but they collapse pretty quickly with the strong link:

5r6c3 = r4c123 - r4c9 =[to789b2356] = r1c5 - r789c5 = r8c4 => -5r8c3 (solvable with turbot fish from here)

5r4c9 = r1c5(Triplet Oddagon) - (5 = 27)r9c57 -(7 = 789)UR15r69c89 - (789 = 5)Virtual ALS b6p15789 => r4c9=5, stte

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Re: The hardest sudokus (new thread)

by hendrik_monard » Sun May 15, 2022 3:36 pm

Before taking a leave I gathered my results of the past weeks:

54 new 11.8s:

Code: Select all: 9876.........958.......4...83....27.7.9...6.3.26....896..2..3..29.3.67.8.73...... 11.8/1.2/1.2 9876.........958.......4...83..6.27.7.9...6.3.2.....896..2..3..29.3.67.8.73...... 11.8/1.2/1.2 98.76....7.54.8....4....7..6.9...........532.........54.79.6....6857........84... 11.8/1.2/1.2 98.76.5..7.48..6....5.49...6..97....59.4...8..47.58........7.3........2.........8 11.8/1.2/1.2 987.........9.........65...8.4...93..23...7.8.......4247....38.2...3..9..39...2.4 11.8/1.2/1.2 98.76.5..7.54..8...46..5...6..8.4.9.4.759......8.76....7.....3........2.........9 11.8/1.2/1.2 98.76....7.54.......6.59...57..4.....698.5.....4..76..4....632....98............4 11.8/1.2/1.2 98.76....7.54......46.5.9..57..9..8.4..5.67...6.8...4......73........2..........9 11.8/1.2/1.2 98.76.5..4.7..56....5.48.9.6.48...7.5..4.9....98.76.......9..3........2.........7 11.8/1.2/1.2 98.76.5..7...4.96..4.....8.65....79.4.75..8...98....4....3....9...2..........5... 11.8/1.2/1.2 98.76.5..7.5.4.96..4.....8.6.....79.4.75..8...98....45...3....9...2..........5... 11.8/1.2/1.2 98.76.54.7.54..8....6..5...6..8.4.9.4.759......8.76....7.....3........2.........9 11.8/1.2/1.2 98.76.5..7.5.4..6..4.9...8.6.....79.4.75..8...98....45...3....9...2..........5... 11.8/1.2/1.2 98.76.5..7...4..6..4.9...8.65....79.4.75..8...98....4....3....9...2..........5... 11.8/1.2/1.2 98.76.54.7.5.4...6..69....86.....7.94.75..8...98....54...3...9....2..........5... 11.8/1.2/1.2 98.76.5..4.7..56....5.48.9.6.48...7..98.76....5.4.9.......9..3........2.........7 11.8/1.2/1.2 98.76.5..7.54.98...46..5...6..8.4.9.4.75......98.76....7.....3........2.........9 11.8/1.2/1.2 987.........9.........65...8.....43..4....2.9.23....784.8...7.237..2.9...92....43 11.8/1.2/1.2 987......6..54.........9...8.3...96..26...7.8.......3237....68.2..6...9...9...2.3 11.8/1.2/1.2 98.76.5..4.7..5.6...5.4.9..6......3........2.........8.7..94.8..4685......96.7... 11.8/1.2/1.2 98.76....7.58.4.....6.59...65.9..7..4...85.9...86.7.4..7....3........2..........8 11.8/1.2/1.2 987......6..54.........9...8.....32..63...7.8.2.....6937.6...9.2.8....76.9....2.3 11.8/1.2/1.2 98.76.5..4.7..56....5.48.9.6.48.....57.4.9....98.76.......9..3........2.........7 11.8/1.2/1.2 98.76.54.7...5...6..69....864.....795.74...8..98.....5...3..9.....2..........4... 11.8/1.2/1.2 98.76.5..7.5.4..6..4.9...8.65....79.4.7...8...98....45...3....9...2..........5... 11.8/1.2/1.2 98.76.54.7.54.98....6..5...6..8.4.9.4.75......98.76....7.....3........2.........9 11.8/1.2/1.2 98.76.54.7.5.4...6..69....865....7.94.7...8...98....54...3...9....2..........5... 11.8/1.2/1.2 98.76.5..7.54.98...46..5...6..8.4.9.4.795......8.76....7.....3........2.........9 11.8/1.2/1.2 98.76.5..4.7..56....5.48.9.75.4.9...6.48......98.76.......9..3........2.........7 11.8/1.2/1.2 98.76.5..4.7..56....5.48.9.75.4.9...6.48...7..98..6.......9..3........2.........7 11.8/1.2/1.2 987......6..54.........8...8.3...62.7..3....8.29...3.73.6...97.2.....8.3.9.....62 11.8/1.2/1.2 987......65.43.........9...8.....52..65...7.8.2.....692.8....76.9....2.5.7.6...9. 11.8/1.2/1.2 98.76.5..7.5..4.8..468...9.8.45.6...57.94.....69..7.......5.3........2..........4 11.8/1.2/1.2 98.76.5..7.5..4.8..468...9.8.45.6...57.9......69..74......5.3........2..........4 11.8/1.2/1.2 98.76.5..7.54.8....64.9.7..85..4..9.4.65......9768.........6.3........2.........9 11.8/1.2/1.2 98.76.5..7.5..4.8..468...9.8..5.6...57.94.....69..74......5.3........2..........4 11.8/1.2/1.2 98.76.5..7.54.8....64.9.7..85..4..9.4.65.9.....768.........6.3........2.........9 11.8/1.2/1.2 98.76.5..7.54.98...46..5...6..8.4.9.4.7.5.....98.76....7.....3........2.........9 11.8/1.2/1.2 987.........9.........65...8.9...43.74....2.8.23....794.8...7.23...2.9...92....43 11.8/1.2/1.2 987.........9.........65...8.9...43..4....2.8.23....794.8...7.237..2.9...92....43 11.8/1.2/1.2 98.76.5..7.5.4.8...648...9.69..78....579.4......65...9.4.....3........2.........8 11.8/1.2/1.2 98.76.5..7.5.......64......8.....4.....97........8.32.6..89....5...47..6.795....4 11.8/1.2/1.2 98.76.5..7.5.4..6...48...9.69..78....579.4......65...9.4.....3........2.........8 11.8/1.2/1.2 98.76.5..7.58.4.6..4..9.7..85......66.45.9....9768.......4...3........2.........7 11.8/1.2/1.2 98.76.5..7.5..4.6..4..9..8.85......66.45.9....9768.......4...3........2.........7 11.8/1.2/1.2 98.76.5..7.5.4.8...648...9.69..78....57..4......95...6.4.....3........2.........8 11.8/1.2/1.2 98.76.5..7.5.4..6...48...9.69..78....57..4......95...6.4.....3........2.........8 11.8/1.2/1.2 98.76.5..7.58.4.6..4..9.7..65......8.9768......45.9......4...3........2.........7 11.8/1.2/1.2 98.76.5..7.5..4.6..4..9..8.65......8.9768......45.9......4...3........2.........7 11.8/1.2/1.2 98.76.5..7.5.......64......6..89....5.8.47.6..795...4....97........8.3.2......4.. 11.8/1.2/1.2 98.76.5..7.5..4.6..46.9..8..9768.....5......8..45.9..6...4...3........2.........7 11.8/1.2/1.2 98.76.5..7.5.49.6...48...9.69..78....57..4..9....5...6.4.....3........2.........8 11.8/1.2/1.2 98.76.5..7.58.4.6..46.9.7...9768.....5......8..45.9..6...4...3........2.........7 11.8/1.2/1.2 98.76.5..7.5.498...648...9.69..78....57..4..9....5...6.4.....3........2.........8 11.8/1.2/1.2

I also have lists of 2478 11.7s and 2194 11.6s, so I have to split them.
1st group of 11.7s:

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hendrik_monard: Posts: 96; Joined: 19 April 2021; Location: Leuven (Louvain) Belgium

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Re: The hardest sudokus (new thread)

by hendrik_monard » Sun May 15, 2022 3:38 pm

Second group of 11.7s

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Re: The hardest sudokus (new thread)

by hendrik_monard » Sun May 15, 2022 3:40 pm

Third group of 11.7s

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Re: The hardest sudokus (new thread)

by hendrik_monard » Sun May 15, 2022 3:41 pm

First group of 11.6s

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Re: The hardest sudokus (new thread)

by hendrik_monard » Sun May 15, 2022 3:43 pm

Second group of 11.6s

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Re: The hardest sudokus (new thread)

by hendrik_monard » Sun May 15, 2022 3:45 pm

Last group of 11.6s

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Re: The hardest sudokus (new thread)

by eleven » Mon May 16, 2022 10:22 am

Impressing list.

From the solving point of view there seem to be only 4 different groups in the 11.8's (did not look at all of them). All had a single extra candidate, which
- creates a single (bivalue), and gets trivial
- creates a hidden single and gets easy (ER 5.3 - 3 strong links)
- creates a pair, and gets easy (ER 5.3)
- creates a bivalue single and leaves a ER 9.2 with a [edit:] 14c pattern, which simplifies it to ER 5.4

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