A fly is in a cubical room of side 2m. It starts from one corner of the floor and goes to the centre of the ceiling. Unfortunately, the fly cannot fly. So it has to crawl along the floor, walls or ceiling to reach there. What is the length of the shortest path for the fly to reach there?

A friend of mine wanted 285 gold coins to be packed and sealed in pouches (each of which is reasonably expensive). Another friend of mine wants to trade gold coins with diamonds. However the second friend has not decided how many gold coins would he like to trade for diamonds. He might trade any number of gold coins (between 1 to 285) depending on his requirement at that moment. What is the minimum number of pouches my first friend should use to pack and seal the gold coins so that he'll be able to trade the coins with my other friend without having to open any pouch later?

Well, this is not so much of a "puzzle" but something general that we come across everyday. Have a look at the shape of a tooth-paste or a ointment-tube cap. It usually is a conical frustum (a cut-off tapered cone) and not always a regular cylindrical shape.

Do you think there is any particular reason why these caps are conical frustum in shape?