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Guest Message by DevFuse

# James33

Member Since 04 Jun 2012
Offline Last Active Yesterday, 10:05 PM

### The Ant Walk

02 July 2012 - 01:40 PM

I don't claim to have made this puzzle, nor do I have a solution.

The is a circle of radius 3 meters with an ant in the centre. The ant picks a direction randomly, all angles have an equal probability. It walks in this direction for 1 meter before fogetting where it was going and chosing another direction randomly. This could go on forever, but on average how many meters has the ant travelled before it exists the circle?

Computers are allowed, but I do want to see a mathematical solution.

### Equations with the Floor Function

09 June 2012 - 04:24 PM

For those that don't know, the floor function which I will denote by [x] is the largest integer less than or equal to x so for example [6]=6, [8.7]=8 and [-4.3]=5. Solving equations using this function can be very interesting and there are often loads of ways to do it.

An easier one to start off:

Solve -6x^2+[x^4]+19=0

This one is harder;

Solve [x^3]-x^2+6[x]=23