Puzzle Description:

The cost of a wedding today is about the same as what you'd spend on a car.

#1: Joe (infrapinklizzard) on Mar 19, 2010 [HINT] [SPOILER]

This solves about 3/4 without problem. There's a little smile logic on the groom's hair.

But then a problem crops up on the bride's gown. (How clichéd.) And it's a doozy.

There's the "duh" answer, and as it turns out it's the right one. Most experienced solvers know that when they see a large expanse with only 1s and a few 2s, they're probably looking at a staircase or a smile. Counting the distance between the 2s will give you an idea as to where to put the largest numbers.

But I don't like it in this case. To much in the way of guessing for me to call it logic. After all, the longest distance between 2s (5) could be either of two 5s. Also, either of those two 5s could fit in other positions.

(What follows is a stream-of-consciousness effort to solve this logically. I do, eventually, but there are some dead-ends on the way. If you want to get to the correct logic, skip to the dashed line "=====" below.)

Some givens:
The bottom seven rows only have one clue each, so only one 5 (at most) could fit down there. That means the seven rows above them must hold at least one 5 (if not both). The 5 clues have one column between them, so as there are no horizontal clues larger than 2, any space between them must be white.

Does that help?... um, no.
Either (or neither) 5 can go in the bottom seven rows. Also, the 5s could be placed partially next to each other (the left in rows 17-21 the right in rows 21-25) These are incorrect, but cannot be shown so in sufficiently few steps.

How about if we try some counting... If the fives are not next to each other, then the 5|3|5|4 must take up between 14 and 17 rows (14 if they overlap on each end, 17 with no overlap - note the overlap will only be one square as there are not any 2s in adjacent rows). As our available rows max out at 15, there *must* be overlap if we do it this way.
And if there's overlap, there's two ways: a "smile" or a "staircase". A smile overlap is prohibited as there is only one clue in each column (except 18 - but we're ignoring that one for the time being). So a staircase it must be.
We have 14 rows for the staircase if we start with the left 5 at the top, 15 if we start with the 4. A quick glance shows that starting with the 4 in rows 16-19 or 17-20 won't work. Starting with the (left) 5 in row 17 will. The rest solves easily with line logic.

But can we prove that's the only way? We need to discount the 5s next to each other, with logic, not with seaching ahead
Erm...
The right 5 cannot extend above row 21. If it does, it will cause a conflict with the 4. ... Aaaand we're into guessing territory again before any real conflicts. @#$%^!! >:(


Let's try to solidify the Case for Staircase.
Since there are two 1s to be placed in row 16, but only one 1 in row 17, one of the 1s in r16 must take one of the two vertical 1s.
Since none of the horizontal 2s are in adjacent rows, at least two of the three must be overlaps (at the ends of numbers) instead of just having a 1 stuck next to it in the middle.
Aaaaaaaaargh

Try again:

=========


There are three choices for row 16.
Currently we have _¤_¤_
It could be:
(A) ¤¤X¤X
(B) X¤¤¤X
(C) X¤X¤¤

Given (A), there is nowhere to put the 5 in column 19 that will not cause a conflict. (It must cross at least two 2s at its ends or one 2 in its middle both of which are impossible since the 1 in column 18 is used already as the given.)

Given (B), then both column 16 and column 20 are fulfilled. There is only a space 3 columns wide and 13 rows high in which to place the 5|1,3|5. The only place the 5 in column 19 can fit is r23-27 (since c19r17&18 are white due to the 4 in c20). That would force the 3 in c18 down to r29, but that leaves r30 blank. It would need a (vertical) 1, but the only one that might fit (c16) is taken by the given. Thus this is impossible.

Therefore (C), r16c16&18 are black; r16c20 is white.

That fills the rest of column 16 with white.

Now look at row 30.
The 5s in c17 and c19 cannot be in that row because of the 2 clue in row 27.

The 3 in c18 cannot be in that row because it would force the 2 in row 27 into either c15-16 or c19-20. Neither will work.

Therefore the 4 in c20 must start in r30. And the rest solves easily. Whew.

Reminds me of puzzle #531. Great fun to solve.

I liked the puzzle .... did edge logic on right side making the 4,5,3 agree! Staircase was the only probability. The grooms face had only 2 possibilities. One worked, the other didn't.

What a unique image. Tough puzzle because so unexpected image. Great. Did use 2 small guesses.

I like how your puzzles convey so much with a simple line.

Nice image. I didn't quite work my way all the way through Joe's long description of solution techniques, though I noticed he'd covered most of the failed techniques I tried before peeking. His final solution technique seemed to me to be on the bleeding edge of what you can reasonably ask from a solver. I feel like adjusting a few pixels here and there might result in a puzzle that wouldn't require quite so much of a high wire act to solve.

On the other hand, there is definitely a subset of solvers who love this kind of thing more than anything else, and Joe seems to be one of them. I'm all for people making the puzzles they love.

I didn't end up with any strong feelings on the solvability of this puzzle, so I'm not going to make a ruling. Folks can vote their opinions, or if Gator has a strong opinion, he can make a ruling.

I solved the gown part from c19: 1)the bottom 3 squares are dots
2)r17&18 of c19 are also dots, otherwise there's no room for the 4 in c20
3)r19c19 is a dot, otherwise it causes a conflict with the 1's in r16
4)now you can see the r23&24 squares of c19 are black
5)then you can eliminate r20&21 of c19 to avoid conflict in c18 and the rest solves easily.

I like that phrase, Jan, "... on the bleeding edge of what you can reasonably ask from a solver."

I think that sums up this puzzle nicely.

I think we are looking too many moves ahead to be considered logically solvable.

I didn't spend THAT much on my wedding, thank heavens. My parents gave me $3000 and said that if I went over that, it'd have to come out of my non-existent savings. I made it work and I think it was wonderful! ;)

I love how this solved, Joe. Clever title. The image jumped out nicely. The logic was a little too advanced for me at the end, but guessing on the gown was pretty easy. Thanks for a fun puzzle.

I LOVE THIS PUZZLE !!!

Excellent puzzle Joe, love it!

Found to be solvable with deep lookahead by gator.

Once is was obvious that the unsolved portion was her gown, a few guesses helped to solve a nice image.

Having attended several weddings before my own, where I sat looking around and thinking what a waste for such a short period of time. The money could have been used for so many better things. So I had a very small wedding and was very happy with it and no regrets.

Good puzzle. I didn’t see the image till the end. I do not think any guessing is required.

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