Mental Exercise

1. Three Meetings. Ms. Tepper had three meetings in a high-rise office building. Her first meeting was with Mr. Abel on a certain floor. At the end of this meeting, she asked Mr. Abel if he knew what floor, Mr. Baker was on, her next appointment in the same building. "Yes, starting from this floor, go to the floor that is half way to the ground. His office is just to the right of the elevator doors." In her meeting with Mr. Baker, she once again was told that her next appointment with Mr. Carr was halfway down to the ground. After this last appointment, she went down one floor and left the building. What floor was her first appointment on?

2. American Companies. Consider each of the following words with the underscore character representing a missing letter or letters. Within each word, each occurrence of the underscores represents the exact same letter or letters. They each spell the name of a company. 
For example, _oda_ = Kodak

What are these company names?

_ero_
e_ro_
_ear_
_son & _son

3. Famous Brothers. The following two lists show the names of famous brothers. Match the name of a well-known brother on the left to his famous sibling on the right. For extra credit, what is the family name of each pair (one pair doesn't have a family name).

4. Geometric Figures. Imagine an equilateral triangle (all three sides are the same length), a square, and a circle that all have the same area. Which has the largest perimeter, which has the smallest perimeter?

5. Mystery Triplets. There is a game called Tri-bond where you are presented with three items or words and you must think of a word or idea that connects them. For example, consider the three words horse, house, and butter. They are all connected by the word fly, they can each be combined with fly to form new words: housefly, horsefly and butterfly. Consider each of the following four triplets. Each one is connected, can you figure out what the connection is?

6. Boys or Girls. Imagine an island that is permanently isolated from the outside world. Suppose that families favor boy children in such a way that they will continue to have children until they have a boy, then they will stop having children. Each birth has a fifty-fifty chance of producing a boy or a girl. All other factors being equal, after a thousand generations, what is the ration of males to females in the population of the island?

Answers

1. Ms. Tepper starts out on the fifth floor, down two floors to the third floor for her second meeting which leaves her two floors from the first (ground) floor. From the third floor, down one floor to her third meeting on the second floor. The second floor is one floor above the first (ground) floor.

2. The company names are: Xerox, Enron, Sears, Johnson & Johnson.

3. George and Ira Gershwin, Wilbur and Orville Wright, John and Bobby Kennedy, Eng and Change Bunker (original Siamese Twins), Cain and Abel.

4. The circle has the shortest perimeter, then the square then the triangle.

5. Knife, cheese, musical note: they can all be sharp. Mexico, York, Jersey: all correspond to U.S. States beginning with "New." Black, Brown, Teddy: are all types of bear. Baby, Wisdom, Canine: are all types of teeth.

6. Each individual birth has a fifty-fifty chance of producing either gender. This results in a population of equal proportions of males and females. The parent's behavior does nothing to change that.