Easter Monster

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Easter Monster

Postby ArkieTech » Mon Apr 15, 2019 12:34 am

Challenge: Find minimum number of added Givens to make puzzle solvable with a single advanced move.

Code: Select all
 *-----------*
 |1..|...|..2|
 |.9.|4..|.5.|
 |..6|...|7..|
 |---+---+---|
 |.5.|9.3|...|
 |...|.7.|...|
 |...|85.|.4.|
 |---+---+---|
 |7..|...|6..|
 |.3.|..9|.8.|
 |..2|...|..1|
 *-----------*
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Re: Easter Monster

Postby Leren » Mon Apr 15, 2019 3:10 am

Nice challenge. For my first attempt I added r1c3 = 4 and r1c7 = 9 and the puzzle solves with basics plus BUG+1.

1.4...9.2.9.4...5...6...7...5.9.3.......7.......85..4.7.....6...3...9.8...2.....1

Code: Select all
*--------------------------------*
| 1 7 #4 | 36   8  5  |#9  36 2  |
| 2 9  3 | 4    16 7  | 18 5  68 |
| 5 8  6 |*1-23 9  12 | 7  13 4  |
|--------+------------+----------|
| 4 5  1 | 9    26 3  | 28 7  68 |
| 9 2  8 | 16   7  4  | 3  16 5  |
| 3 6  7 | 8    5  12 | 12 4  9  |
|--------+------------+----------|
| 7 1  9 | 5    4  8  | 6  2  3  |
| 6 3  5 | 12   12 9  | 4  8  7  |
| 8 4  2 | 7    3  6  | 5  9  1  |
*--------------------------------*

I subsequently checked every extra single Given placement without success, so I suppose the answer is 2, although I would suspect that there is more than one way to achieve this.

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Last edited by Leren on Mon Apr 15, 2019 6:00 am, edited 1 time in total.
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Re: Easter Monster

Postby RSW » Mon Apr 15, 2019 4:59 am

With 8r3c2 and 3r3c8, it's all basics. So, I assume that there must be a single given for an advanced technique.
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Re: Easter Monster

Postby Leren » Mon Apr 15, 2019 5:55 am

Nice catch RSW. With an extra 4 in r1c3 the puzzle solves with singles. I found another 3 extra Givens singles solution at one stage but couldn't reproduce it.

I've checked all the single extra Givens cases but nothing seemed to work out. I'm not even sure whether my BUG+1 is an "advanced" technique or not.

So I think the answer is 2 extra Givens, but if you pick the right ones, an "advanced" technique is not necessarily required.

I have a sneaking feeling that Golden Nugget, Champagne Dry, Platinum Blonde or some other famous puzzle will be in our near future.

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Re: Easter Monster

Postby SpAce » Mon Apr 15, 2019 8:43 am

6r1c8 & 4r9c2 : solvable with a split-chain (or other simple nets).

Doesn't look like adding just one given works for this challenge (or it would require some very interesting move) so my answer is two (like Leren's). 4r9c2 seems to be the most powerful added given by itself (yields 10 singles with one move, and solved with just two more).
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Re: Easter Monster

Postby Leren » Mon Apr 15, 2019 10:40 am

Found 8 more BUG+1 two extra Givens solutions : 9 r1c7 + (7 r1c2 or 2 r5c2 or 6 r6c2 or 4 r9c2 or 3 r2c3 or 7 r2c6 or 7 r6c3 or 6 r9c6). Leren
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Re: Easter Monster

Postby 999_Springs » Mon Apr 15, 2019 8:26 pm

i remember doing something like this a long time ago with the easter monster puzzle, it must have been 2009-2010 because i do remember that whatever i wrote got lost in the big forum crash.

i don't remember how i came up with this exactly, but my solution idea was to systematically try out all possibilities of r4c8 and r8c4

here is the pm grid after the infamous sk loop and secondary eliminations
Code: Select all
 +----------------------+----------------------+----------------------+
 | 1      478    3458   | 3567   389    5678   | 3489   369    2      |
 | 238    9      378    | 4      126    1267   | 138    5      368    |
 | 3458   248    6      | 1235   389    1258   | 7      139    3489   |
 +----------------------+----------------------+----------------------+
 | 2468   5      1478   | 9      126    3      | 128    1267A  678    |
 | 3489   126    3489   | 126    7      4      | 3589   126    3589   |
 | 2369   1267   1379   | 8      5      126    | 1239   4      3679   |
 +----------------------+----------------------+----------------------+
 | 7      148    4589   | 1235   348    12458  | 6      239    3459   |
 | 456    3      145    | 1267B  126    9      | 245    8      457    |
 | 4589   468    2      | 3567   348    45678  | 3459   379    1      |
 +----------------------+----------------------+----------------------+

i have marked cells r4c8 and r8c4 with A and B. notice that the strong links on 7 in c8, r8 and b9 mean that either A or B must be 7, but not both. this gives us 6 possibilities

A,B = 1,7; 2,7; 6,7; 7,1; 7,2; 7,6

out of these 6 possibilities, 3 of these resolve to a contradiction using basics and turbot fish, 1 gives a contradiction using basics plus turbot fish and an xy-wing, while the other 2 give a contradiction - or solution - using no more than basics and one or two wing patterns (combos of 3 strong and 3-4 weak links with their own names). nothing more is needed, and the end result is what i think is a pretty nice solution to the easter monster with just a simple case breakdown and no chains at all :)

edit: to answer the op's question, this is equivalent to saying that 2r8c4 solves the puzzle by itself with the sk loop and a couple of wings, which while not a one-step solution is still quite nice. however, this approach also considers what happens if you don't assume 2r8c4 as well
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