[lenazegher]

> Whatever the make-up of the tower below, if it is stable, we can always place the top brick so that it extends half way into the void.

I don't understand the meaning of this statement. If a brick extending halfway into the void is stable, and we can place a brick extending halfway into the void on any stable brick, then we can create an infinitely overhanging tower by placing an infinite series of bricks each of which extends halfway over the void relative to the tower beneath it.

Clearly this is not the case. What does 'stable' mean (precisely) in the above quote?

[ambrop7]

I think the reasoning is wrong here. Obviously a tower could be stable, but still applying force to an edge of the top could make it collapse.

What's actually happening is that at each step, you already have a max-overhang tower of N bricks, then you add another brick below, to produce a max-overhang tower of N+1 bricks. Because the old N-brick tower is stable, you can place it anywhere on the new bottom brick as long as its center of gravity is not off the edge of the new brick.

[garethadams]

Think of it the other way around.

The top brick can be placed so that its centre of mass is positioned over the edge of the brick below. This two block system is stable.

The two block system can be placed on a third block so that the centre of mass of the two blocks is positioned over the edge of the third block. This three block system is then stable.

From there, it's turtles all the way down

[Dylan16807]

But the extension mechanism has nothing to do with placing the top brick. It seems like a mistake in the writeup.

[cjh_]

If you do this so that the top brick is overhanging by half it's length and then place another brick on it, the first brick is no longer the top brick so this no longer applies.