## Solution Path to the Easter Monster Puzzle

Everything about Sudoku that doesn't fit in one of the other sections

### Solution Path to the Easter Monster Puzzle

Old thread from player's forums of which I have a backup.

Here is the puzzle that you will know as the Easter Monster. Or, rather, this is an isomorph of it. Bob Hanson's isomorph, to be specific. Why am I using his isomorph? Because when I first got to know the puzzle, this was what I first set eyes upon, so I saw it before JPF's version of it. So that's what I'm using.

Code: Select all
1..|...|.89
...|..9|..2
...|...|45.
---+---+---
..7|6..|...
.3.|.4.|...
9..|..2|..5
---+---+---
..4|.7.|...
5..|..8|.1.
.6.|3..|...

With a little help from Sudoku Explainer...

Basically, I tried to find a short and neat solution to this unwieldy puzzle. Before I started I messed around with SE for a bit to see where I could find the chains that would crack the puzzle apart. Such searching resulted in me finding 5 crucial candidates to eliminate, and they could all be eliminated using just nested turbot fish or wings inside chains. So, I decided, that was the way to go. However, I ended up becoming lazy and got Sudoku Explainer to guide me through the chains of singles when I couldn't be bothered to work out those singles. And those X-wings inside the chains as well. And all the other stuff. But ultimately the chains were my own creation by hand.

1. SK Loop That Everybody Knows About.

OK, you've all probably heard about this a bazillion times, so I'll just spare the details.

r4578c1, r4579c6, r6c2345, r8c2345
Eliminations: r4c2=/=4, r5c3=/=6, r4c5=/=3, r5c4=/=7, r23c1=/=28, r13c6=/=15, r6c78=/=18, r8c79=/=29

2. Naked triplet 367c7 => r24579c7=/=367.

3. Naked Single r2c7=1.

4. Naked Triplet 367r3 => r3c2345=/=367.

5. The First Long Chain: r8c9=/=3.

These are kind of like Carcul-style chains. The ones that he used when doing #77 from the top1465. With nested stuff inside too. I must mention that any inference in the chain may be used multiple times in the chain.

3r8c9(=4=r8c4(-2)-4-r12c4)(-67)(-3-r37c9)-3-r8c3=3=r7c1-3-r3c1=3=r3c6(-3-r3c3)(-67)(=4=r1c6(-4-r1c2)(-7)=6=r7c6(-6-r7c9-8-r7c12)(=7=r5c6)-6-r8c5=6=r8c7(-2)=7=r8c2(-29)-7-r12c2)(-3-r4c6)-3-r12c5=3=r6c5-3-r6c78=3=r4c8(-2)-3-r2c8=3=r1c7=7=r1c4(-7-r2c4)(=2=Turbot Fish: 2r8 2r4, r3c3)-7-r6c4=7=r6c7-7-r89c7=7=AHS:r9c89,r9c8=9=X-Wing: 9c4 9c8, r7c2=9=r3c2(-9-r7c2)-9-r3c3(-8-r2c2)(-8-r9c3=8=r9c1-8-r5c1)-8-r6c3=8=Hybrid Wing: r2c4 4c2 8r6, r2c2-4-r6c2(=4=r6c1)=4=r6c8-4-r9c8-7-r2c8=7=r3c9-7-r3c1-6-r5c1(-2-r4c2)-2-r5c8=2=r7c8-2-r7c2(-1-r4c2)-1-r6c2(-8-r4c2)-8-r6c4-1-r4c6-5-r4c2 => r8c9=/=3 (no value for r4c2)

6. Another Long Chain: r1c6=/=3.

3r1c6(-3-r1c37r4c6)(-467)(-3-r12c5=3=r6c5(-18)(-3-r6c8)-3-r6c7=3=r8c7(-67)-3-r8c3=3=r7c1(-2)=3=r2c3-8)=4=r9c6(-4-r9c8)(-7)-4-r8c4=4=r8c9(-7)(-4-r4c9)=6=r8c5(-29)(=7=r8c2-2)-6-r12c5=6=r3c6(=7=r5c6-7-r6c4)(-6-r3c9)-6-r3c1-7-r3c9-3-r4c9(-3-r2c8)=3=r4c8(=4=r4c1)=4=r4c8(-6)=7=r6c7(-6)-7-r1c7=7=r2c8(-6)(-7-r9c8=6=r6c3(-18)-6-r12c3=6=r2c1)-7-r2c4=7=r1c4(-2)=4=r2c4(-8)-4-r2c12=4=r1c2(=2=Turbot Fish: 2r1 2r8, r3c4)=8=Turbot Fish: 8r2 8r6, r3c4(-1-r567c4)-1-r6c4=1=r6c2(-1-r4c2)-1-r7c2=1=r7c6-1-r45c6=1=r4c5(=9=r9c5-9-r9c8)(-1-r4c9-8-r4c2)-1-r4c6-5-r4c2-2-r45c1=2=r9c1-2-r9c8 => r1c6=/=3 (no value for r9c8)

7. Yet Another Long Chain: r1c6=/=7.

7r1c6(-3)(-7-r1c27r3c6)(=4=r9c6(-1)-4-r8c4=4=r8c39-36)-7-r5c6=7=r6c4(-18)(-7-r6c8)-7-r6c7=7=r8c7(=3=r8c3-29)(-7-r8c2=7=r9c1-7-r3c1(=7=r3c9-36)=7=r2c2-48)=6=r8c5(-2)-6-r12c5=6=r3c6=3=r4c6-3-r4c9=3=r7c9=6=r7c8(-6-r6c8)-6-r2c8(-3-r2c5=3=r1c5-2)(-3-r6c8-4-r6c2=4=r4c1-4-r2c1(=4=r1c2=2=Turbot Fish: 2r1 2r8, r3c2)=4=r2c4-8)=6=r1c7-6-r6c7=6=r6c3(-1)=8=Turbot Fish: 8r2 8r6, r3c2-9-r78c2=9=r9c3=1=r7c2(-1-r7c46)-1-r6c2=1=r6c5-1-r9c5 => r1c6=/=7 (no place for 1 in block 8)

8. And Yet Another Long Chain: r8c9=/=7.

7r8c9(=4=r8c4(-29)-4-r9c6=4=r1c6(-36)-4-r1c2)(-7-r3c9)-7-r8c2=7=r9c1(-2)(-7-r3c1)-7-r2c1=7=r3c6(-6)(=3=r4c6=6=r7c6-6-r7c789=6=r8c7(-3)(-6-r7c8)-6-r6c7-3-r6c8)-7-r5c6=7=r6c4(-18)(-7-r2c4r6c8)-7-r6c78=7=r5c8(-29)-7-r2c8(=7=r1c7-36)=7=r2c2(-8)=4=r6c2(-1)(=8=Finned X-Wing: 8r2 8r6, r3c5)-4-r6c8-6-r2c8(=6=r3c9-6-r3c1)(-3-r7c8=3=r7c9-3-r7c1=3=r8c3-2)-3-r2c5=3=r1c5=6=r1c3(-6-r56c3=6=r5c1-2)=2=Finned X-Wing: 2r12c8, r3c5(-1-r3c4)-1-r6c5=1=r6c3-1-r9c3=1=r7c2-1-r7c4=1=r5c4(=9=r7c4-9-r7c8)=9=r5c7=2=r4c78-2-r4c1=2=r7c1-2-r7c8 => r8c9=/=7 (no value for r7c8)

At this point I think it's best to take some time out to appreciate the symmetry of the puzzle. As you've noticed, the preceding eliminations have all focused on two cells with values 3467 and reduced them both to 46. The chains were almost identical in that three of them required two turbot fish to kill off two candidates in the same cell and the other chain wasn't that different. (I switched to finned X-wings because I was too lazy to eliminate the other candidate, and hey, they're the same anyway. Combine this with the two bilocations in block 8.

9. Double W-Wing: 4b8 6b8 46r1c6r8c9: r3c6r8c7=/=6. <= See what I mean?

10. Big Unfinned Mutant Squirmbag 6r3b4c6c7r8\c1r6r1b8c9 => r1c3r2c1r1c5r2c8r5c9r6c8r7c9=/=6 (Yeah, I know that it's useless and it's the same as two swordfish on 6. But this is by far more interesting! My first ever 5-fish!)

11. The Last Long Chain: r8c9=/=6. (Again, symmetry. Or near-symmetry. I know this puzzle is already only SE 9.1, but this is just one step here.)

6r8c9(-6-r357c9)(=4=r8c4-4-r9c6=4=r1c6-37)-6-r8c5=6=r7c6(-1)-6-r3c6(-7)=6=r3c1-6-r5c1=6=r6c3(-1)(-6-r6c78=6=r5c8=7=X-Wing: 7r3 7r5, r9c9)-6-r6c7(-7)=6=r1c7(-6-r1c56=6=r2c5-8)=3=Turbot Fish: 3c6 3b3, r4c8=3=X-Wing: 3r3 3r4, r7c9(-8-r45c9r9c7r7c1)-8-r9c9-4-ALS:r45c9r6c7, r6c8-4-r6c2(=4=r4c1-8)=4=M-Wing: 1c3 8r9 r6c2, r5c1=8=r9c1=7=r2c1(-7-r2c4)-7-r2c8=7=r3c9(-7-r3c6=7=r1c4-7-r6c4)-7-r5c9-1-r5c3=1=r46c2-1-r7c2=1=r7c4(-1-r6c4-8-r23c4)-1-r3c4=1=r3c5-8 => r8c9=/=6 (no place for 8 in block 2) (Oh look, I'm actually surprised this chain is shorter. It's SE 10.7, which I think ties with the record for a chain elimination found manually, although this isn't completely manually.)

And... now it's SE 7.1. Here is the bit where I became lazy and somehow managed to put the puzzle away for a whole week before finishing it off. Oh, and, I did use SE to guide me here again, and I sort of manually picked the stuff I wanted and left the other stuff out. But still, it's only SE 7.1...

12. r9c6=4.

13. All the 6s solve with singles. Do it yourself.

14. Naked triplet 378b9 => r7c7r9c78=/=378.

15. Pointing 8b9c9 => r45c9=/=8.

16. Double W-Wing 37r3c1r8c7 3b7 7b7 => r2c1=/=37 (Again, note the symmetry.)

17. All the 4s solve with singles. Do it yourself.

18. Naked pair 37c8 => r5c8=/=7.

19. Turbot Fish 9c5 9c8 => r5c4=/=9.

20. r5c4=9.

21. Naked pair 28r4 => r4c2=/=28.

22. Swordfish 1c269 => r5c34r7c4=/=1.

23. Hidden pair 17r5 => r5c6=/=5.

24. Hybrid Wing: 7b2 3c6 5b5 => r2c4=/=5.

25. Pointing 5b2c5 => r9c5=/=5.

26. r9c7=5.

27. I-Never-Saw-A-Purple-Cow-I-Hope-I-Never-See-One-But-I-Can-Tell-You-This-Right-Now-I'd-Rather-See-Than-Be-One: 5r2 5r4 3b5 => r2c5=/=3.

28. Singles to end.

And here is the solution:

Code: Select all
123|456|789 <= Yeah, very funny, Bob Hanson. Best joke ever.
456|789|132
789|213|456
---+---+---
217|695|843
635|847|921
948|132|675
---+---+---
394|571|268
572|968|314
861|324|597

DISCLAIMER

I'm rushing this because there's a wasp in the room. So I must say that there are likely to be typos and bits of chains I've missed. Grrr. I hate insects.

Heh, on rereading this I've noticed that my writing style's changed quite a bit in one year.
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Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

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Joined: 27 January 2007
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