Stack identical flat objects so they project over an edge as far as possible
quantamagazine.org
quantamagazine.org
It looks impossible, doesn't it? But it is really quite easy.
Step 1: Find 5 blocks with 4 short and one long. You can test by putting several upright on a table with one laid across with pressure. The ones that slide are short, the ones that don't are long.
Step 2: Put the tall upright in the middle, the 4 short around it in a base. Place 2 blocks whose middle crosses the tall one, standing on the others as a base.
Step 3: Pile up your structure. Try to keep it from being off balance as you go, but you have a surprising amount of leeway.
Step 4: Test the base, find which are loose and which are tight. Manipulate the pile until all 4 at the base are loose.
Step 5: (Expect a 50% success rate.) Slide the base out. Everything is now balanced on one!
Step 6: (For fun.) Put the remaining 4 on the very top.
Step 7: Take pictures, show people, etc. Your structure is unstable and can collapse very easily. Which gives you opportunity to build another. :-)
A fun variation is to have 2 starting points, and build piles that extend both ways. You can make a surprisingly long bridge!
And yeah, what I do is just a trick. The end result looks impossible but not much skill is involved.
I have done it at other conferences and explained the technique, so it could have been someone who learned it from me.
The hard part is balancing the structure on a single block, which is standing on end.
Q'aplaH!
I also allowed blocks to stand on their end, but in retrospect, that might not be a very effective strategy.
For those who aren't familiar, they are wood blocks sort of like Jenga blocks but with a length:width:height ratio of 5:3:1 which is very useful for building structures. They are made with quality wood and are cut precisely.
The fun part is using them to build bridges and domes. I always have fun seeing how far I can build make a bridge span, which is why I came across this article in the first place.
My 4yo and I have previously played the "cantilever game" too. Adults get involved when we play "improbable structures" - that quickly gets competitive!
http://www.greenhatworkshop.com/
I'm in the UK and didn't realise it was a European thing.
http://www.maa.org/sites/default/files/pdf/upload_library/22...
The bottom block hanging over the table with a heavy weight on the top right edge means the whole system is prone to tipping, and moving the bottom block back so we're just worried about the next edge higher up means that the system is, on average, less prone to tip over. It turns out to be easy to calculate the difference in tippyness/torque between these two cases, so we can use this to calculate how far the block can hang over.
One block obviously balances at 1/2, and has a center of mass at the edge. Two blocks obviously still have a center of mass at the edge - else they would tip, or could go closer to the edge without tipping. But how far out is this second block hanging?
If we put the second block flush with the edge of the table, it has a center of mass at -1/2 and a mass of 1, and the top block has a center of mass at 0 and a mass of 1. So the center of mass of the system is at -1/4 and we can shift it this far to the right. With 3 blocks, we have a mass of 2 blocks with the center at position 0, and another block below with a center of mass at -1/2 and a mass of 1, for a system centered at -1/6th (and so on for more blocks). We always shift it over in the end, but it makes the math of how far to shift it easier to compute if we start with it backed up a bit.
http://www.maa.org/sites/default/files/pdf/upload_library/22...
I didn't realize popular science magazines get to call dibs on such problems.
https://www.amazon.com/crazy-cantilever-other-science-experi...