Puzzle seen at the LA County Fair - can it be solved?

Spent a while at the LA county fair trying to solve this puzzle. The objective is to make the pieces fit into a square shape. We couldn’t do it, and it quite bothered me. Sorry if the photo doesn’t perfectly capture the dimensions.

One thing to note is that the large piece at the bottom and the one above and to the right of it (above the perfect square) are fused/glued together. The small perfect square seemed a little too obvious there, so we did try other configurations that didn’t include having it in that spot, but still couldn’t get it all to fit.

Another thing to note is that the pieces have a clear top side and bottom side, so what you are seeing in the photo are all the top sides up. They can be rotated but not flipped over.

I get this:
Call the parts other than the big one, square, triangle, L, kite and pointer (rectangle with triangle on top).

Big bit and square as you have them in the picture. Pointer is rotated clockwise from the picture and lays in the notch in the big piece. The L is hooked around the pointer so that the chamfered end of the L forms part of the top edge of the square. The kite has an orientation exactly as in the picture and lays against the side of the L, thus forming the top LHS corner of the square. The triangle fits the remaining space.

That seems to work with what I can guess are the dimensions. The gimmick of the puzzle is realising that the chamfered end of the L is part of the top edge of the square.

That sounds like what I got as well. I think the gimmick is that the piece you call pointer has two obvious right angles on it, but neither of those forms a corner of the square. It’s the third right angel, the corner that looks like it’s pointing, that forms the upper right corner.

Is there a way to draw this with text characters?

There’s got to be a number of sides that match up to the be same length and abut.

A number of three side sets have to be side a = side f + side m. maybe more of these three side situations than two.

But the thing is that you can’t get started with the obvious 90’s, so start forming some 90’s that also allow sides to connected together to become mere internal divisions… three sides become zero edges (of the square), resulting is a limitted number of sides forming edges of the square. Basically its easier to see which sides will fit together nicely, and then you can check to see if they produce the square’s edges and the requisite 90 degrees.

I had to draw it out, but I believe I see what you’re saying Francis… I’m not 100% sure it would have fit in practice, but on paper it looks like it potentially could. I hate that we left it unsolved, but this at least gives me a small measure of satisfaction. :smiley:

To add to Francis’s efforts, looks like the square sits at the end of the L, even though because the shapes are worn it seems the square is too large.
Lets call the quadrilaterals Qbig, Qmed, Qsmall

So left to right -
pointer (pointing into corner), triangle (long side up), Qsmall (into corner)
L (chamfered on edge), square (in middle)
Qmed, Qbig (forming the last two corners)

Does that work?

No, because you are using seven pieces and there are only six in the picture. And there are only two quadrilaterals – the square and the kite-shaped one.

Francis Vaughan’s solution

Imgur

That’s a terrible “solution”. I knew with the rounded corners and all there’d be gaps but there’s a hole in the center!

I call shenanigans.

Interesting. The original pic has significant parallax distortion that makes some of the pieces quite out of scale relative to others, something which worried me when I was trying to work it out. I wonder if doing a correction for parallax before re-sorting the pieces would improve matters or make things worse?

That’s what I got too, before peeking at yours.

By printing then cutting out, it fits a bit better but not much. There must be some distortion in the picture.

Alternately, is it possible that there’s a missing piece, a little square that fits exactly into that hole? I can easily see a small object like that wandering off from a public booth at a fair, and I can just as easily see the person manning the booth not noticing (especially if, as seems plausible, they don’t know how to solve the puzzle, either).

No, the photo does not represent the true scale. there is some distortion.

For example, when I cut out and assemble - one short edge of the triangle piece should add up to the short outside piece of the “L” plus a short edge of the Q arrowhead. In my cutout, the edge of the triangle is barely longer than the bottom outside edge of the “L”. The triangle is too small, the L and quad too big. Similarly, the pentagonal piece is too big. It is slightly too big to match the fused pieces. It is too small to match the oversized “L” on the other side.

So in photo -
Triangle too small.
“L” and Quad too big
Penta slightly too big.

I assume this is photo distortion.

I got it first try.

It’s basically the same as the previous one with two pieces shifted and their ends appear cropped off.

Shenanigans 2, Electric Boogaloo?

I took the distortion out in Photoshop before cutting them out. I promise I did not look at the other solutions before doing mine. I mean where’s the fun in that? It’s the same because it’s the only correct answer.

So basically the photo is somewhat not 100% overhead?
I took the original photo, cut it out, and found that some pieces definitely were the wrong scale.

I assume you “removed distortion” by adjusting perspective?

But, based on your result, the quadrilateral seems a bit too big still, the triangle too small, and the L is still not quite right. need to remove more distortion.

Photoshop has a Perspective Warp tool for things like this, but it’s usually for subtle adjustments and where you know more than just two corners, and I only knew one, so its an imperfect adjustment. I think you’re being too picky on what is a very worn-edged rough-as-guts puzzle board.

No, we all done good. It took me half an hour thanks to the distortion, but it seems we all came up with the same result.