Final shots upon the Easter Monster


The following is the final page of an illustrated campaign to solve the Easter Monster sudoku puzzle. Hopefully, this Easter Monster Solution is at least interesting to some!

If this is your first visit to this blog, WELCOME!!

Previous blog pages may be helpful. Links to these pages are found to the right, under Previous Entries. Specifically, it may be helpful to have visited the following pages:

The illustrations of steps shown in this proof will share the new key style:

  • black line = strong inference performed upon a set (strong link)
  • red line = weak inference performed upon a set (weak link)
  • black containers define a partioning of a strong set(s)
  • candidates crossed out in red = candidates proven false
  • Orange labels mark derived inferences
  • Blue circles indicate proven strong inference set result
  • Green circles indicate intermediate strong inference points
  • Other marks provided prn
Please be aware that, for me, strong and weak need not be mutually exclusive properties.

Step 3d prelude using Kraken cell transport.

Below, two of the three possible values of cell r9c7 are transported out to form a new derived sis. This is very similar to the transportation of 3 of 4 values out of cell r7c9 that was performed as a prelude to step 2j. The entire deduction is so symmetrical, in fact, that it becomes almost easy. Certainly, given step 2j, it was easy to find.

Kraken Cell Transport - again

The sis (359) r9c7 transported into the sis:[(3)r3c48, (35)r7c6, (5)r7c6, (9)r9c7] using:

  • (39=5)r9c7-(5)r9c46=(5)r7c46
  • (59=3)r9c7-(3):[r79c8=r1c8-r1c4=r9c4]=[(3)r3c48,(3)r7c4]
By now, this process should be fairly clear.

Step 3d (2)r5c2=(6)r6c2

Not only is the Kraken transport symmetrical to that used in step 2j, but the conclusion of that step and the conclusion of this step also have a very nice almost symmetrical aspect about them. Furthermore, the entire argument is very similar, as demonstrated below.

Kraken cell chained up

2r5 c2 c8
2r7 c8c6
2r3 c6c4
6r5 c8 c4
1c4 r3 r5r7
1c5 r8r2
1B3 r2r3c8
K3d 5*3* 35*3* 9r9c7
r6c7 2 93
r2c7 1 38
r2c3 83
3B4 r6c3 r5c1
9c1 r9 r5r6
6r6 c2 c6 c1

The conclusion of this step:

  • (2)r5c2=(6)r6c2 => r6c2≠2
  • All the 2's and all the 7's are then solved by hidden singles.
The puzzle is now solvable in myriad manners. To conserve space, I decided to use a step that works quickly, but is more complex than the puzzle now warrants.

Step 4 prelude using guardian 5's and guardian sis transport.

Below, if candidate 5 is limited to the locations circled red, then a number of impossible pentagons exist. Such overlap of impossible oddagons is usually the case if one were to consider using guardians to derive sis. The possible locations for candidate 5 that are labelled with a green G form the guardian sis. However, since r8c7 is limited to 45, and since it sees four members of the guardian set, it is much more efficient to transport the (4)r8c7 into the sis, and remove four of the 5's.

Guardian 5's with a transported 4

The guardian sis and transportation logic follows:

  • Guardian sis (5):[r1c4, r7c6, r8c13,r7c9,r9c7]
  • The AIC: (4=5)r8c7-(5):[r8c13,r7c9,r9c7]=(5)[r1c4, r7c6]
  • => sis[(4)r8c7,(5)r1c4,(5)r7c6]
From this point, the deduction is fairly simple (for this puzzle!)

Step 4 chains transported guardian sis to derive (5)r1c4=(6)r5c4

Below, but for the trivalue transported sis and the double forbidding done by the potential 6 at r6c6, this would be nothing but a standard AIC. Finally, I am able, however, to transparently map all of the weak inferences, and all but the transported guardian strong inference set.

Transported guardian sis chained up

As AIC, one could write:

  • (5)r1c4=G[AIC]-(6)r6c6=(6)r5c4
  • [AIC]: (6)r6c12=(6-4)r4c1=(4)r4c3-(4)r1c3=(4)r1c7-(4)r8c7=G(5-1)r7c6=(1)r6c6
Below find a short TM (triangular matrix) that performs precisely the same task.

6B5 r5c4 r6c6
6B4 r6r4c1
4r4 c1c3
4r1 c3 c7
1c6 r6 r7
TG 5r1c4 4r8c75r7c6

The conclusion: (5)r1c4=(6)r5c4 => r1c4≠6. This now solves many cells by naked and hidden singles. All the sixes, all the ones, all the fours, and a few of the others.

Step 5 short skyscraper with candidate 9

scraping 9s

Above, the standard run of the mill AIC:

  • (9): r5c3=r7c3-r7c9=r6c9 => r6c1≠9 & r5c7≠9
The puzzle now solves using only naked singles.

Easter Monster Solution

Done

Parting Shots

This puzzle was more difficult than I care to tackle often. However, the ideas that it forced upon me may prove to be useful in the future when faced with a puzzle devoid of suitably bi-value, bi-location sis. The main ideas used herein, summarized:

  • Derived sis can be used again later. Even very complex ones help to focus searches.
  • Any tool in the toolbox is suitable for the creation of derived sis
  • Matrices are not only a useful tool for explaining a deduction, but the concept of counting that they infer is useful in locating long, complex chain-like nets.
The matrix type, Mixed Block Matrix is an invention that can reduce matrix size. Although Andrei and Bruno have proven that all sudoku eliminations can be justified using Block Triangular Matrices, Mixed Block Matrices can significantly shorten the deductive path. Moreover, they can more efficiently prove all of the derived sis available from one set of native sis. For this reason, they show some promise towards a more efficient resolution of a puzzle such as the Easter Monster. I am fairly certain that just such a more efficient and quicker solution path exists for this puzzle. By quicker, I mean much quicker!

Thanks for your patience with this ridiculous solving path!




3 Comments
Indicate which comments you would like to be able to see

Hi STEVE,

CONGRATULATION ! Thank you for your very very ... good work. But now very very... hard work for me and someone...
08/Dec/07 3:12 AM
 |  |
Hi ttt!

Thanks!

Not sure how good it is. It was difficult, though!

I am even more certain now of a better solution path, however - it adds a new wrinkle!

Hint: one more AUR not previously considered!
08/Dec/07 9:55 PM
 |  |
I would appreciate comments regarding www.stolaf.edu/people/hansonr/sudoku/easter_monster.htm
which I believe to be a quite easy solution to the Easter Monster based on Medusa chains and a few new ideas.
Bob Hanson
hansonr@stolaf.edu
26/Feb/08 4:08 AM
 |  |
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