Question

I don't mean to resurrect an old problem, but I will anyways. :)

"Suppose we have two towns A and B and that the distance between them AB takes 12 hours to cover. If every hour a bus starts coming from A and B, how many buses coming from point B will be seen by a bus coming from point A?"

We are to assume that a bus is said to be "seen coming from point B by a bus coming from point A" if the bus from A has not yet reached B. Also assume that there are no buses on the road before we begin tracking the bus from A.

Answer 1

I argue that the answer is 12 as follows. We begin tracking a bus from A at some hour, say 10:00am, this will be denoted as t = 0 (the bus is beginning to leave point A). Then, the point B will be reached at 10:00pm, that is t = 12. Now, we wish to know how many buses coming from point B will be seen by our bus from point A. This can be answered by asking how many buses are generated at point B in the interval t = [0,12), where 12 is not included since the bus from A will have arrived at B at t = 12 so that no more buses will be counted. Since buses leave B at integer hours, there must be 12 buses generated during this interval (the number of integers from 0 to 11).

Any critiques would be greatly appreciated. This is a fun problem. :)

Answer 2

@wio

Answer 3

consider the last meet, at 10:00 pm, the A bus stops at point B and the 12th bus from B is starting. Since A bus reaches the terminal B, can we count that meet as one or not?

Answer 4

I agree that one is debatable. If we are strict with the assumption that "seen coming from point B by a bus coming from point A" if the bus from A has not yet reached B, then no we cannot count that bus. :)

Answer 5

But, your interpretation was how I did it the first time. :) in that case we would certainly get 13.