Off The Edge

I still blog, I swear. Anyway, I suppose I should put up the solution for the plane puzzle from last time.

There is a standard puzzle of this form where you have camels going into a desert and you have to feed them, bananas or something, but each camel can only carry a finite amount of food. Suppose a camel can carry enough food to go 90 meters (I choose 90 so I can take fractions of it easily), then with two camels you head out 45 meters, transfer all the food from camel 2 to camel 1 and can then go another 90 meters with camel 1 making a total of 135 meters. With 3 camels we can go 30 meters out, move all the food from camel 3 to 2 and 1 and then make it another 135 on top of the 30 for a total of 165. In general if one camel can carry the food for distance x, then the n^th camel adds an extra x/n to your total distance.

Anyway, then with our planes we can use this sort of strategy to go 1+1/2+1/3 times the distance half-way around the world, but that is only 11/6, so we are short. The solution to this is to make use of the fact that the puzzle is happening on the world, so we can go around the other way. Use two planes to go 3/2 the distance of one plane (that is 3/4 of the way around the world) and have the other plane meet you by going the last bit in the other direction.

Its not much of a puzzle, but its sort of cute and I thought it was a neat variation on a standard puzzle.

Flying Along

Ok, time for a new puzzle. I found this one a few months ago over at Tanya Khovanova's math blog:

You are sitting at the equator and you have three planes. You would like to fly around the equator. Each plane is full of gas and each has enough gas to take you half way around. Planes can transfer gas between themselves mid-air. You have friends, so that you can fly more than one plane at once. How do you fly around the equator?

Its sort of like an old puzzle involving camels going into the desert and you only have a finite amount of food for them, but a bit of a twist on this one. Anyway, thats it for now.