What you Need
What to do
The idea is to build a bridge across a 21cm chasm which will hold as much weight as possible, using only one sheet of A4 paper. You can use some tape to hold it together, but not to act as part of the structure.
What may happen
A sheet of paper doesn't make a very good bridge, and can't even hold its own weight.
A square tube is quite rigid until it folds slideways into a parallelagram when it becomes only slightly stronger than the sheet of paper, supporting a little over 100g of water
A triangular tube doesn't collapse sideways and supported about 300g of water
A round tube supported about 1.2kg of water
A triangle made of two tubes and a strip of paper supported over 2kg of water - at which point we ran out of water!
Why does it happen?
Paper is an interesting material, it is very strong in tension - if you clamp it correctly a sheet of A4 paper will support over 200kg. However it is very flexible, so if you compress paper it will just buckle and fail at very low forces.
Paper is so flexible, not because the material is particularly soft, but because it is so thin. If you bend something the material on the outside of the curve is stretched and the material on the inside of the curve is compressed.
If the beam is very shallow, the change in length is very small, so you aren't stretching or compressing the material very much, and it doesn't push back hard. On the other hand, a thick beam will have very large changes in length, so it will be very stiff.
This means that a major way of making a beam bridge stiffer is to make it deeper. One obvious way to do this is to make a square tube. This would be very stiff if it didn't have a major weakness.
There is nothing to stop the square turning into a parallelogram and going flat, and therefore very flexible.
A triangular beam is a lot stronger, because the triangle can't change shape without distorting its sides. However because the sides are very flat, they can bend and allow the corner to buckle under load.
A tube is very strong because the paper is all curved in one direction and it can't curve in another without stretching or tearing. However if you use it as a beam you are squashing it, and eventually it will go flat enough to bend in the wrong direction
A tube however is very strong is straight compression, as there is no force trying to flatten it. so if you can devise a structure with tubes in compression and something else in tension it can be very strong.
One way of doing this is to make a triangle out of two tubes and a strip of paper to hold the bases together at the bottom. This is very strong although if you wanted to make the structure stand up on its own you would probably have to give it more legs.