You just fucking send it and see if it stays on the table.

There isn't much math to do really. Take as axioms that the obvious way to balance 2 or 3 tubes is in fact balanced, and that if you add a balanced arrangement of tubes to an already balanced arrangement, the result is still balanced.

It's just one equilateral triangle and then two pairs. The specific slots the opposing pairs are in don't matter. You can see that each sample of the triangle has a gap of 7 slots between each other.

Example of an unbalanced spinning thing: https://youtu.be/vROdVsU_K80?t=51

Centrifuges spin really fast, so you need to balance out the things they're spinning, otherwise it can fall catastrophically.

Stick everything on one side and it will effectively explode.

Centrifuge spins really fast so you need to balance where you put the samples, or else it will vibrate. The trick is to put them on the opposite side or equally spaced apart from each other.

Think of it like a tilt-a-whirl. When you don't distribute the load as best as possible and it starts spinning at an angle, someone (a test tube) will puke.

That thing spins really really fast.

If you put too many of those things in it in a not balanced way (like all at one side), it's dangerous.

The picture is balanced, but it doesn't look like it is at first glance.

Man I have seen many centrifuges in my life and none roulette tables in real life. But still my stupid ass thought this was a roulette table

All on black!