Two problems that were on my job application

After a night of wild revelry, a group of local intoxicated hoodlums stumble into a children's playground. One of these hoodlums, Phil, climbs to the middle of a spin-around carousel and his friends push the carousel so it rotates once every five seconds. Phil, who is trying not to get sick, holds a flashlight motionless in his hand.

There is a straight path running by the playground that, at its closest point, is 30 meters from the middle of the carousel. Unknown to Phil, there are two cops facing him on the path, shocked at the spectacle. One of them is standing on the path at the point closest to the carousel, while the other is standing 60 meters down the path. At approximately what speed (in meters per second) does the spot illuminated by the flashlight traverse each of the cops' bodies? State speed at the closest cop first.


A rustic village contains one million married couples and no children. Each couple has exactly one child per year. Each couple wants a girl, but also wants to minimize the number of children they have, so they will continue to have children until they have their first girl. Assume that children are equally likely to be born male or female. Let p(t) be the percentage of children that are female at the end of year t. What is p(t)? "Can't tell" is a potential answer if you don't have sufficient information.


Let's see how fast you guys can answer these.

>>2-8
You guys are making the question a lot harder than necessary.
p(T) = 1/2 for all T [on average at least]

yr 1: half male, half female
yr 2: previous gender distribution is 1:1, and the gender distribution of newly born children is (surprise!) 1:1.  Combine these 2 sets, and the total gender distribution is still 1:1
...
yr N: rinse and repeat