[jacquesm]

Ah, jacquesm bait, ok here is my solution (left), right one is an alternative to yours.

http://imgur.com/a/h7HnB

just the tops:

http://imgur.com/a/wsqCw

[spydum]

I feel like they should be attached and not stacked?

https://imgur.com/gallery/W13nR

Fwiw: 10.3cm

[spydum]

https://i.imgur.com/zUl5AP8.jpg

Measured 10.7cm: https://i.imgur.com/I637r2v.jpg

What have you done to me!? Can't stop.

[BatFastard]

I never considered that the backplane is the same height as the inter dot distance. I thing I can think of as a possible improvement would be to put the single dot side ways, and put a grain of salt on each side. Or find a very slight indentation to put it in.

[prawn]

I really like the thinking of moving the smallest piece to the very bottom!

This would make a great quiz night team challenge or corporate team-building activity.

[jacquesm]

One of the conditions was that it should be able to stand on its own ('freestanding'), that one can't balance on the lower piece.

[lorenzosnap]

LOL. Can't wait to show those pictures to my daughter. thanks

[jacquesm]

You're welcome :) That's a nasty trick though but it is actually designed to be used that way, Lego has all kinds of interesting tricks.

Come to think of it this is an interesting game in the making, much better than most (or even all) games that lego makes:

Given x pieces from some set you get to take turns trying to make the highest combination, or, alternatively, all kids at a party are handed the same lego pieces and the winner gets some prize.

[gawin]

As a former Lego building champion I couldn't resist ;-)

http://imgur.com/a/TjXeO

[jacquesm]

Show with real parts that it remains standing. I tried building that one and could not get it to balance. Maybe you can find some position where the COG is over the little piece.