# What is the largest cube that can fit through a 1ft by 1ft square hole in a wall?

I know it is bigger than a 1ft cube, but exactly how big? How would you figure this out or prove it?

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• 1 x 1 x 1....1 ft cube

• You could feed through an infinitely large cube.

It would be simply 1x1ft square and really long.

• use the measurement formula... 3,4,5, which is 90 DEGREES WHEN MEASURED...

• If it's a cube its 1ftx1ftx1ft.

If it is 1 ft x 1 ft x infinity it's not a cube.

• "square hole"?

• I can't prove it, 'cause it's not so.

The diagonal of a cube (corner to corner) is a greater distance than any of its edges. Which mean that the cube can only fit through that square when it is aligned with the edges. Any tilt whatsoever would disallow it from passing through.

• You can't do better than a cube that is 1 ft on each side. The projections of a cube are either a rectangle or a hexagon but the smallest projected area is when a face is directly parallel to the surface which results in a square. Any other rotation results in a larger shadow and hence would need a larger hole.

In other words, if you have a 1 ft by 1 ft square, the largest cube that fits through is 1 ft by 1 ft by 1 ft.

You're not talking about Prince Rupert's Cube are you? That's a different question. That says a cube that is about 1.06066 ft. on each side will fit through a 1 ft cube.

• 1 x 1 x 1....1 ft cube

• Do you think that the answer depends on the thickness of the wall?

• sq root 6 on each edge