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#1: Jan Wolter (jan) on Oct 28, 2004 [HINT]

If you start with the fact that there is only one possible solution to this puzzle, make a key observation, and reflect a bit, this puzzle becomes very easy. Without that clue, it's very difficult.

Since we're given that there's a unique solution, and the clues are symmetric, we know from the start that the solution is symmetric. That helps.

Great picture, but a bit too difficult without using that symmetry (and pretty easy once you actually do!).

Sat in my "not done" box for months until I read the comments and tried symmetry!

One of the best! Very enjoyable.

I always try to go with logic alone, as opposed to educated guesses and symmetry. I gave in and used symmetry as it seemed the only viable way to solve, am I incorrect?

great puzzle, I'd be interested to know if there are any on a larger scale with the same subject matter

I also had to use symmetry to solve this one.

The "has only one solution" comment in the title is supposed to be a license to use symmetry, since given that fact, it is a logical necessity that the puzzle have the same kinds of symmetry as the clues. I don't think this puzzle is very solvable without symmetry.

nice puz, Jan

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I can hear Steve Martin singing softly in the background. :)

I've tried this from scratch 4 times now. Even with hints, I've been unable to find a solution. I'm sure it's solvable as some above have mentioned that they've done so, but for me it remains completely unsolvable. Looks like it would be a great puzzle if not for the extremely high difficulty.

Look at the horizontal clues. If it's something like 3 2 2 3, then you know there's a dot in the center (since it's been made pretty clear that this is symmetrical). If the clues are something like 1 4 6 4 1, then the 6 is centered in the middle of the row.

Really great puzzle. Took carefullness, and was a fun solve.

It's a neat picture, but I have to say I found my solution to be unsatisfying. From the start, you observe
1. that the column numbers on top are symmetric, and
2. the numbers for every row are palindromes.
From what I see, these are necessary conditions for a left-right symmetric picture, but NOT sufficient. And yet, I could only solve the puzzle by assuming symmetry from the start and thus using the logic the wrong direction. Is there any way to strengthen these two conditions to guarantee a symmetric image?

Only if you have the information given by the title of the puzzle: there is only one solution.

Given the symmetry of the clues, we know that the mirror image of any solution must be a solution. So if there is only one solution, then it must be symmetric, because it must be its own mirror image.

A wonderful image and once I knew it was symmetric, the solve went nicely

solved,due to the symmetry

I solved it first using symmetry, then as an additional challenge, I solved it a second time using just logic (no guessing or symmetry based assumptions).

It is possible to solve without using symmetry. The key is the first row. Deep lookahead shows that the r1c1 must be a dot, and similarly for the upper right corner. Then line logic gives you the whole row. From there you can work the puzzle out, until the very end, at which point you have be very careful for the last eight squares of his nose and eyes.

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