Mental Exercise

Pocket Change. I asked Prof. Permutate if he had change for a dollar. He said yes, but in order to get the change, I had to tell him how much money he had in his pocket. He provided the following facts.

> The professor's pocket is only filled with nickels, dimes and quarters.
Ø The professor can make change for 65 cents in every possible combination of nickels, dimes, and quarters.
> Remove any single coin from the professor's pocket, and the second fact above is no longer true.

Millionaire Odds. The TV game show Who Wants to Be a Millionaire gives contestants a chance to win money by answering multiple choice questions. The questions always present four possible answers and the contestant has to choose the correct one. If a contestant gets stuck, he can use a "lifeline" to help answer the questions. One of the lifelines, called 50-50, removes two of the wrong answers. Suppose the contestant has, in his own mind, eliminated two of the four answers. What are the odds that the computer will remove the two choices that the contestant has already eliminated.

A. 50% 
B. One-third
C. 33% 
D. 1/4

Halls-of-Fame. Many are familiar with the major U.S. sports and intellectual endeavors. Match each hall-of-fame with the city where it is located.

Anagram Composer.  Consider the following list of words. The letters of each word can be rearranged to form the name of a famous musical composer. Who are the composers?
phonic
butchers
harlem
drive
gnawed
oz tram

Equal Opposites. There are two different eight-letter words that are opposites. The final four letters of both words are identical. Name the words.

Difference Triangles. Consider the following triangle of numbers on the left:

Any number that is below two other numbers is the difference between those two numbers. Now, fill in the question marks to make the triangle on the right have the same property.

Answers

Pocket Change.  The key point here is that you need at least 13 nickels, at least 6 dimes, and at least 2 quarters. This is a total of 65 cents + 60 cents + 50 cents = $1.75.

Millionaire Odds.  There are three wrong answers to choose from, so there are three different ways for the computer to remove two wrong answers and leave one of the wrong answer on the list for the contestant to choose. Of the three different ways, one of them will remove the answers a contestant has excluded. The answer is B. one-third.

Halls-of-Fame.

Anagram Composer. 
phonic = Chopin 
butchers = Schubert; 
harlem = Mahler 
drive = Verdi
gnawed = Wagner 
oz mart = Mozart

Equal Opposites. The words are positive and negative.

Difference Triangles.