How about this one:

Assume an arbitrarily high coefficient of friction between all surfaces. Can you stack the blocks on the table such that at least one block is wholly below the top of the table?

I think I have an answer to this, but I've only worked it through in my head, so there's a good chance I'm wrong!

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cousin_it 6 days ago | parent | next [-]

If the blocks are thin enough, I think it's possible. Stack three blocks. Position the left edge of the stack on the edge of the table, so it's hanging downward at a slight angle, and stack enough blocks on top that it holds. Now slide the middle block 2/3 of the way out. The friction should still hold.

I think it's also possible for other shapes, all the way up to square blocks. But you need to build a bunch of nested "clamp" arrangements, instead of just one.

	▲	jeffparsons 5 days ago \| parent [-]
		That's basically the direction I was going in my head. I just remembered we have a bunch of Kapla blocks in the house, so I may be able to do this "IRL"!

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amelius 6 days ago | parent | prev | next [-]

> Assume an arbitrarily high coefficient of friction between all surfaces

Yes but in practice that means using glue, at which point you might as well glue everything together into a single piece.

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Liftyee 6 days ago | parent | next [-]

The difference is that glue can withstand tension which changes a lot. Even infinite friction still requires a non-negative contact force (i.e. the surfaces are not being pulled apart).

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IAmBroom 6 days ago | parent | prev [-]

Not glue, necessarily. The coefficient of friction is not about surface adhesion. It is kinetic; glue is an additional static component.

	▲	amelius 6 days ago \| parent [-]
		Are you talking about changing the geometry of the blocks?

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dooglius 6 days ago | parent | prev | next [-]

I don't see how. Consider the block of minimum altitude, what's stopping it from falling?

	▲	jeffparsons 3 days ago \| parent [-]
		I didn't specify the challenge clearly. I meant to allow blocks in any orientation, as long as they would be stable. So you can, for example, have blocks sloping down from the edge of the table by sandwiching one end of them between two other blocks with enough vertical distance between them, and enough weight on top.

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cluckindan 6 days ago | parent | prev | next [-]

Sure, just use gauge blocks!

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WithinReason 6 days ago | parent | prev [-]

Turn the stack from the article by 89°