World's 200 Hardest Brain Teasers (2 page)

There are actually now six ways to solve the problem, and in this book I’ll show the simplest one. See if you can figure it out. Turn to page 182 for the answer!

Given a triangle ABC, side AB = side AC. Draw a line from C to side AB. Call that line CD. Now draw a line from B to side AC. Call that line BE. Let angle EBC = 60 degrees, angle BCD = 70 degrees, angle ABE = 20 degrees, and angle DCE = 10 degrees. Now draw line DE. Find angle EDC. Do not do this trigonometrically; do it geometrically to get an exact answer.

Dr. Gary R. Gruber

Here is a collection of my most interesting and mind-improving brain teasers. Many of the answers should give you a strategy for thinking, which will carry over to many other problems and provide you with thinking and problem-solving methods. There is no time limit for these questions (with exceptions as noted). Be aware that there may be more than one way to arrive at an answer to a question.

Just remember, a person who can solve problems efficiently either knows a particular strategy for the type of problem or extracts something from the problem that is curious to him or her and that leads to the next step toward a solution.

1.     Two U.S. coins add up to 30 cents. If one of them is not a nickel, what are the two coins?

2.     Make
one word
from all the following jumbled letters:

o r e n o d w

3.     In miles per hour, what is the average rate of a car going 20 mph and traveling back the same distance at 60 mph?

(a) 30

(b) 40

(c) 50

(d) 60

(e) cannot be determined unless the distance is given

4.     If you don’t know the meaning of the word PRECURSORY, which of the following words do you think means the opposite of PRECURSORY?

(a) flamboyant

(b) succeeding

(c) cautious

(d) simple

(e) not planned

5.     An explorer found a silver coin marked 7 BC. He was told it was a forgery. Why?

6.     I have only nickels, dimes, and quarters and have at least one of each type of coin. The total number of coins I have is fifteen and the total value of all the coins is $1.00. How many of each coin do I have?

7.     A malicious computer program informs a user that it has “kidnapped” an important file and that what happens to the file will be based on the next statement to be typed by the user. If the user types a false statement it will delete the file, and if the user types a true statement it will change the file’s name so it can never be found. The user types a statement that makes the computer unable to perform or shut down. What could the user have typed?

8.     Terry is half as old as Alice was when Alice was five years older than Terry is now. How old is Terry now?

9.     IMAGINARY NUMBERS is to REAL NUMBERS as

(a) spiritual : global

(b) infinite : finite

(c) prime : rational

(d) negative : positive

(e) disordered : ordered

10.   In 40 seconds or less, and without using a calculator, figure out which is greater: 354 x 357 or 355 x 356.

11.   The price of a watch at a department store has been discounted 20 percent and then an additional 30 percent after the first discount was applied. Would the final discounted price have been lower if there had been a single discount of 50 percent? Why or why not?

12.   A lawyer argued for $1,000,000 damages based on the following claim: His client went to an art museum, where he saw a painting of Marie Antoinette on a guillotine. He fell asleep and dreamed of the painting. At the museum’s closing time, a guard tapped him on the neck just as he dreamed of the guillotine beheading Marie Antoinette. The tap provoked immediate cardiac arrest and a fatal heart attack immediately following, because he associated the tap with the guillotine blade. Why did the judge dismiss the case?

13.   “Many more people who smoke develop lung cancer than those who do not smoke.” What research would possibly show that cigarette smoking does not cause cancer?

14.   Suppose I have 40 blue socks and 40 brown socks in a drawer. If I reach into the drawer without looking at the socks, what is the smallest amount of socks I must take out to make sure that I have a pair of socks of the same color?

(a) 2

(b) 3

(c) 4

(d) 40

(e) 41

15.   What day follows the day before yesterday if two days from now will be Sunday?

16.   MUSIC : VIOLIN ::

(a) notes : composer

(b) sound : musical instrument

(c) crayon : drawing

(d) furniture : carpentry tools

(e) symphony : piano

17.   What is the next number in the following sequence:

0 0 1 2 2 4 3 6 4 8 5 ?

(a) 6

(b) 8

(c) 10

(d) 12

(e) 14

18.   GEORGE WASHINGTON : CHERRY TREE ::

(a) Jonas Salk : polio vaccine

(b) Abraham Lincoln : emancipation

(c) Thomas Edison : lightbulb

(d) Thomas Jefferson : constitution

(e) John Hancock : signature

19.   A triangle has sides of lengths A, B, and C. Which is true?

(a) C minus B is always greater than A

(b) C minus B is always less than A

(c) C minus B is always equal to A

(d) None of the above comparisons can be made between C minus B and A.

20.   The following characteristics apply to a group of people in a room: Fourteen are blonds, eight are blue-eyed, and two are neither blond nor blue-eyed. If five of the people are blue-eyed blonds, how many people are in the room?

(a) 3

(b) 17

(c) 19

(d) 24

(e) 29

21.   Suppose you have a 12-hour digital clock where the number representing the hour is always the same as the number representing the minute. That is, the clock can only show times like 8:08, 9:09, 10:10, etc. What is the smallest time difference between two such times?

(a) 101 minutes

(b) 61 minutes

(c) 60 minutes

(d) 49 minutes

(e) 11 minutes

22.   A square, ABCD, is inscribed in a quarter-circle where B is on the circumference of the circle and D is the center of the circle. What is the length of diagonal AC of the square if the circle’s radius is 5?

(a) 3

(b) 4

(c) 5

(d) 6

(e) The length cannot be determined.

23.   50 x 50 x 50 x…(where there are a hundred 50s) is how many times 100 x 100 x 100 x…(where there are fifty 100s)?

(a) 25 x 25 x 25 x…(where there are fifty 25s)

(b) 4 x 4 x 4 x…(where there are fifty 4s)

(c) 2 x 2 x 2 x.(where there are fifty 2s)

(d) 1 time

(e) None of these answers is correct.

24.   How could you figure out the meaning of the word INEXTRICABLE?

25.   A doctor’s son’s father was not a doctor. How is this possible?

26.   What’s wrong with this advertisement: “Shop early and avoid the crowds.”

27.   You are competing in a linear race and overtake the runner in second place.

In which position are you now?

(a) first

(b) second

(c) third

(d) fourth

(e) cannot be determined

28.   Bonnie’s father has five daughters but has no sons. Four of the daughters are named Chacha, Cheche, Chichi, and Chocho. What is the fifth daughter’s name?

(a) Chuchu

(b) Chochu

(c) Chuchy

(d) Chochy

(e) none of the above

29.   HELMET : HEAD ::

(a) sword : warrior

(b) umbrella : clothing

(c) shoe : sock

(d) watch : wrist

(e) thimble : finger

30.   Suppose a four-digit number is an exact multiple of 9 and three of the four digits are 1, 2, and 3. What is the fourth digit?

31.   A knight wants to marry a princess and she wants to marry him. However, the king demands that the knight draw one of two slips of paper from a box. The king says one will say “Death” and the other “Marriage.” The princess whispers to her suitor that both slips say “Death.” What could the knight do to wed the princess?

32.   There are four people in a line. Sarah is between Barry and Mary. Mary is in front of two other people, and John is directly in front of Mary. Who’s first in line, second, third, and fourth?

33.   Which is greater, one-half the surface area of a ball with radius 3” or the area of a circle with radius 3”?

34.   In the following subtraction problem, each letter uniquely represents one digit from 0 to 9. At least one digit is not 0. Find the values of A, B, and C.

35.   What is the next letter in the following series: y z v w s t p q ?

(a) l

(b) m

(c) n

(d) o

(e) p

36.   What is the value of
x
in the diagram below?

37.   If A = 250 percent of B, what percent of A is B?

(a) 1/250 percent

(b) 25 percent

(c) 40 percent

(d) 50 percent

(e) 125 percent

38.   Suppose a car goes uphill a certain distance at the rate of A miles per hour. Then the car travels downhill the same distance at a rate of B miles per hour. Which is greater, the average of the rates A and B, or the average rate of the car for the whole trip (uphill and downhill)? Assume that the value of A is not the same as the value of B.

39.   Put these statements in the right order:

(a) The ship stopped to anchor in Commander Bay.

(b) A boy awoke and saw a sea lion.

(c) A boy went ashore and napped in a meadow.

(d) A boy did not tell what he had seen.

(e) A boy got a job on a ship.