From L to Cube

Geometry Level 3

True or False: It is possible to take $9$ L-shape pieces below and rearrange them to make a $3 \times 3 \times 3$ cube.

True False

1 solution

David Vreken
Aug 12, 2020

The following animation shows one of the many different ways of doing this:

Fantastic. Love the animation. What did you use to create it?

I was fully expecting this not to be possible, spent ages looking for a colouring proof, then finally actually tried it. I wonder how many different ways there are?

Chris Lewis - 10 months ago

Thanks! I just used a combination of MS Paint and www.ezgif.com.

Yes, it's peculiar that the L-shape can't be used to make the $3 \times 3 \times 1$ box, but can to make the $3 \times 3 \times 3$ cube.

I'm not sure how many different ways there are to solve it. I may need to think about that some more.

David Vreken - 10 months ago

I guess this is the only way excluding rotations and reflections. Not sure though...

Mahdi Raza - 10 months ago

@David Vreken The animation is just 🤩🤯🙌.

Just like Chris, even I was thinking this to be false

Mahdi Raza - 10 months ago

Thanks, I'm glad you liked it!

David Vreken - 10 months ago

The colors have no meaning,right? I mean with 3 different colors it is not possible such that each face of the big cube has a uniform color?

Guy Fox - 9 months, 3 weeks ago

The colors are just for shadowing to make it look three dimensional

David Vreken - 9 months, 3 weeks ago

Because I was trying to find out if it is possible with your given color set, assuming opposite faces have the same colors, but was unable to find a positive solution.

Guy Fox - 9 months, 3 weeks ago

From L to Cube

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