Can you guess what the challenge is?

The paper is 30 cm x 41 cm and 90 g/m2.

The cardboard is basically what you get in a pizza box, cut into 7.5cm squares.

Those are AA Duracell batteries. You must put an equal amount of batteries on each floor and the floors must be equally spaced throughout the tower.

My (not rhetorical) question is: in order to use these sorts of materials to meet (something like) Hoffman's challenge, how big would you need the piece of paper & cardboard squares to be? (You can also specify the grade of paper if you like.)

Ideally, you will keep the floor heights and bases [spans] equal, so that the structure is a series of cubes, but I'm willing to hear why that's unreasonable.

If you want more or bigger (or smaller) batteries, just ask!

You can also cut holes in the paper as you choose to weaken the walls.

You can (and probably should) connect the tower to the base (the big piece of cardboard) using as much tape as you like. If you need a bigger or heavier base, that can also be arranged.

The structure must be strong enough in its initial state to let me poke a hole through the paper with the scissors at any point.

The structure must also be strong enough to let me shift the base about 10% of the width of the tower back and forth instantaneously (simulating an earthquake). I think that makes any "wind testing" moot.

The initiating failure must be brought about using the scissors in the ordinary way, cutting the paper, cardboard, or tape as much as you like somewhere in the top 20% of the structure.

This event must cause the whole structure to be destroyed. (It's not good enough that all the floors and batteries end up at the bottom of the tube, which remains stranding.)

The solution using the smallest piece of paper wins.

(Note: you are of course free to ignore this challenge, ridicule it, or meet it as you choose. Once it occurred to me I thought it was too good to keep to myself. I don't think I'm going to be able to meet it with the 30x40cm piece of paper I have. But I'm going to try.)

[EDIT: The thing I like about this challenge is that it lets us scale

**up **instead of down. That is, if we can't get the 41 cm tower to progressively collapse because gravity doesn't scale well, we can imagine it -- or even build it -- bigger until we reach floor heights where a gravity-driven collapse becomes possible.]