Suppose we place 1000 tiny bugs on a meter stick. Once placed, each bug starts moving either to the left or to the right at a constant speed of 1 meter per minute.

If two bugs run into each other, then they both immediately change directions and continue moving at 1 meter per minute.

Once a bug reaches either end of the ruler, it falls off the ruler.

Considering all possible initial configurations of the bugs, what is the maximum amount of time you need to wait before the ruler is bug-free?

Originally posted by davegage Suppose we place 1000 tiny bugs on a meter stick. Once placed, each bug starts moving either to the left or to the right at a constant speed of 1 meter per minute.

If two bugs run into each other, then they both immediately change directions and continue moving at 1 meter per minute.

Once a bug reaches either end of the ruler, it falls off the ru ...[text shortened]... s of the bugs, what is the maximum amount of time you need to wait before the ruler is bug-free?

Are the bugs evenly spaced to begin with. If so, are they spaced 10 to the centimetre? Are they spaced with equal chance of facing left/right?

Originally posted by Alcra Are the bugs evenly spaced to begin with. If so, are they spaced 10 to the centimetre? Are they spaced with equal chance of facing left/right?

The bugs are not necessarily evenly spaced. They can be initially distributed along the ruler in any arbitrary fashion.

The probability that any one bug faces right (or left) initially is also unrestricted.

The problem is to find the maximum amount of time that it could possibly take for all of the bugs to fall off the ruler, so you may want to think about what starting configuration is limiting in this sense.

my hint would be that it is very easy to overthink this problem...