1

## Passing Second Place

In the final stretch of a road race, you pass the 2nd-place runner right before crossing the finish line. What place do you finish in?

2

A completely black dog was strolling down Main street during a total blackout affecting the entire town. Not a single streetlight had been on for hours. As the dog crosses the center of the road a Buick Skylark with 2 broken headlights speeds towards it, but manages to swerve out of the way just in time. How could the driver see the dog to swerve in time?

3

You are a cook in a remote area with no clocks or other way of keeping time other than a four-minute and a seven-minute hourglass. On the stove is a pot of boiling water. Jill asks you to cook a nine-minute egg in exactly 9 minutes, and you know she is a perfectionist and can tell if you undercook or overcook the egg by even a few seconds. How can you cook the egg for exactly 9 minutes?

4

## Engineers and Managers

You have just purchased a small company called Company X. Company X has N employees, and everyone is either an engineer or a manager. You know for sure that there are more engineers than managers at the company.

Everyone at Company X knows everyone else's position, and you are able to ask any employee about the position of any other employee. For example, you could approach employee A and ask "Is employee B an engineer or a manager?" You can only direct your question to one employee at a time, and can only ask about one other employee at a time. You're allowed to ask the same employee multiple questions if you want.

Your goal is to find at least one engineer to solve a huge problem that has just hit the company's factory. The problem is so urgent that you only have time to ask N-1 total questions.

The major problem with questioning the employees, however, is that while the engineers will always tell you the truth about other employees' roles, the managers may lie to you if they like. You can assume that the managers will do their best to confuse you.

How can you find at least one engineer by asking at most N-1 questions?

5

My daughter has as many sisters as she has brothers. Each of her brothers has twice as many sisters as brothers. How many sons and daughters do I have?