The Quotient of Murder (Professor Sophie Knowles) (25 page)

FUN
(EXERCISES) First, here’s the answer to the math riddle in Chapter 24.

Bruce asks, “What’s the difference between a new penny and an old quarter?”

A: Twenty-four cents!

Sophie Knowles doesn’t expect that everyone will be able to unwind with arithmetic, but she feels that doing puzzles, brainteasers, and mental arithmetic keeps you sharp, and improves your memory and your powers of observation. Here are some samples of puzzles and games that exercise your wits.

Browse in your bookstore, library, and online for more brainteasers, and have some fun!

BRAINTEASER

Here’s a combination of wordplay and number play. What do the items in the following list have in common?

Too bad I hid a boot.

2002

Was it a car or a cat I saw?

111,111,111 x 111,111,111

1. 1.
   Here’s an ancient riddle, The Riddle of the Sphinx. (Be aware that metaphors are often used in riddles!) In Greek mythology, the Sphinx sat outside of Thebes and asked this riddle of all travelers who came by. If the traveler failed to solve the riddle, the Sphinx killed him. And if the traveler answered the riddle correctly, then the Sphinx would destroy herself.
   What goes on four legs in the morning, on two legs at noon, and on three legs in the evening?
   
2. 2.
   Here’s a cute riddle that physics professor Ted Morrell might introduce when he’s in a good mood:
   Where does bad lighting end up?
   

(Hint: It sounds like the place where Big Dog and Einstein are headed!)

1. 1.
   Okay, Sophie admits this is not really a puzzle, but a simple algebra problem that might have been taken from your middle-school textbook. But Sophie gets a great deal of pleasure when numbers work out right. She hopes you do, too. Try it!
   

A car travels at a speed of 64 mph and its fuel consumption is 28 mpg. It has an 11-gallon tank, which was full when it started but at that very moment began to leak fuel. After 112 miles the car stops with a completely empty tank. How many gallons per hour was it losing?

1. 2.
   A short, easy math puzzle: Move only one digit in the following expression to make a correct equation.
   

62 – 63 = 1

1. 3.
   Have a little fun at a party with this calendar “trick.”
   

Ask a friend to choose four days that form a square in any month on a calendar. Then, ask the friend to tell you only the sum of the four days. Using basic algebra, you’ll be able to tell her which four days she picked.

ANSWERS

ANSWER TO BRAINTEASER

All the items in the list are palindromes—a word, phrase, verse, or sentence, that reads the same backward or forward. Note that 111,111,111 x 111,111,111 = 12,345,678,987,654,321. (The answer is a palindrome, though the equation taken as a whole is not.)

ANSWER TO RIDDLE #1

A man, who crawls on all fours as a baby, walks on two legs as an adult, and walks with a cane in old age.

ANSWER TO RIDDLE #2

The riddle that Ted might use when he’s in a good mood.

Where does bad lighting end up?

In a prism!

ANSWER TO MATH PUZZLE #1

The Speeding Car

A
NSWER
:
4 gallons per hour.

SOLUTION:

Distance ÷ Speed = Time for the trip.

The car took 112 miles ÷ 64 mph = 1.75 hours to travel the 112 miles In that time, the car used 112 miles ÷ 28 miles per gallon = 4 gallons of fuel.

The car started with 11 gallons of fuel; thus, 7 gallons of fuel were lost (leaked) in 1.75 hours.

Therefore, the car was losing fuel at a rate of 7 gallons ÷ 1.75 hours = 4 gallons per hour.

ANSWER TO MATH PUZZLE #2:

The tricky equation

2
6
– 63 = 1

ANSWER TO MATH PUZZLE #3: Fun with Calendars Let x be the first date your friend chose. (Sophie says not to groan; it’s easy and fun!) The next day will be x + 1, of course. That’s the top row of the square. The first number in the bottom row of the square will be x + 7 (the first date, plus 7 days); the second number in the bottom row of the square will be x + 8.

Forming the equation, we have: x + x + 1 + x + 7 + x + 8 = T (total given to you by your friend).

Simplifying:

4 x + 16 = T

This is as far as we need to go!

You can see that no matter what x (the first date) is, to figure out what it is, simply subtract 16 from the Total, and then divide by 4.

For a method that’s easier to remember, simplify the last equation further, by dividing by 4: x + 4 = T/4

You can find x, then, by dividing the total by 4, then subtracting 4.

Try it and let Sophie know how it goes!