Friday, January 4, 2013

A Piece of Cake

Did you bake a cake for a New Year party? Or bought a fancy cake and stored it in the refrigerator to reveal just after midnight for a sweet new year. Imagine that you take the cake plate out and one piece is missing. Help find this piece. You may want to print this puzzle out to look closer.

Your answers accepted any time until midnight on Sunday on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.


Thad said...

Look at the picture upside down and you'll find the missing piece. :-P

Anonymous said...

Your cake picture is a bit of an optical illusion. For one, you can see the top and bottom edges of the back of the cake while looking at from the front of the cake, the view shown in your picture.

With the optical illusion, it is possible to see the triangular piece that looks cut out of the cake at first glance (the triangle section shown in the front of the cake) as actually being a piece of the cake that is standing on its side with the black triangle being the bottom of the piece, and the adjacent parallelograms being two of the piece's sides.


Jerome Cherry's wife said...

Being a non-math type, when I look at this drawing and squint my eyes I can see there is not a piece of cake missing at all, but a piece of cake has been cut and laid on end with the center facing it remains in place in the cake. The lines that do not match up on the drawing which I assume are only to give the cake the illusion of dimensions.

Jerome said...

The cake magically turns vertically. That's where the hidden piece is. A wonderful optical illusion.

I'm not sure about the vertical. I can only hold the image for less than 1/2 a second, so I'm guessing.

Anonymous said...

I think this is an optical illusion. The "missing piece can either be looked at as a piece that is actually missing or it can be looked at as a piece that is actually right n "front" of the cake with the back even with the circumference and the point of the piece pointed straight opposite of the usual way a piece would point with the point in the center of the cake. Actually the piece may even look like it is pointing straight up.


Ilya said...

At first I wasn't sure, but my son who loves cakes confirmed it for me. We think the piece was cut out and then put on its cylindrical side, so it's pointing upwards with the angled tip.

Annoe said...

When I continue to look at the spot where the cake is missing I suddenly see the missing piece from the perspective from under the plate. The missing piece is at the back of the plate!!

Maria said...

You did it - the missing piece is there but can be spotted by either turning the picture upside down or carefully concentrating on the plate. The missing piece has black coloring (chocolate?) at the top. Puzzle point for everyone.

Why optical illusions are connected to math?
Look at this picture - it is just a collection of black and white regions. But our brain is expert at making sense from it. Even more, it creates different interpretation of this picture depending which way we look at it! It analyses shapes, colors, context and uses previous experiences to map all this into a 3D scene.

If we can figure out how our brain does it, we can teach computers to do it and sit and relax while computers are doing some mundane, complex or dangerous jobs for us: automatically identifying defected parts, going into radioactive areas to shut the valves, analyzing MRI to detect cancerous tumors and much more. We are actually quite ahead in all of these.

Who does this? Mathematicians that are studying our visual system and simulating it with math algorithms.

I am not sure who is the author of this specific illusion. It seems that Martin Gardner placed it in one of his books, but it has likely been created by someone else.

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