Bing's House - A math riddle




Bing's House - A mathematical riddle.
Imagine a disk made of some elastic substance. You can start shrinking it, little by little, making it smaller and smaller, until - if you contined long enough, you would be left with a point.

The same thing can happen if you have a solid ball or cube.
An object that can be shrunk like that is called "contractible". You will notice that a ring is not contractible, because you can't "get rid" of the hole. The rule is that while you contract your object, you cannot go through points not previously occupied by your object. I will also mention that you ARE allowed to "inflate" your object as part of the contracting process. After all, you can take the point you got after you shrunk the disc and stretch it back to a disk form.

I present Bing's house. The object in the picture (thinking of it as two story house with internal chimneys connected to the walls) is contractible. The riddle is to find out how to contract it to a point. As opposed to my previous math riddle, the Quiangle, you cannot solve the riddle on the blocks. However, it can help visualize the setting. Note that the transparent pieces count as solid plates. I made them transparent so that the insides would be clear.

I would also mention that if you look at the model you will see that, like the Mobius Strip, it has only one side. For a full video explanation (5 minutes, not too long) of this property, you can visit my  Mobius Strip demonstrator.

If you want to play around with a 3D Model, it should be possible here.
Thank you!
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Name Bing's House - A math riddle
Designer LegoOri
Designed 2019
Parts 276
Theme Creator > Model
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