Thursday, 8 November 2012


Lateral Thinking 2

Number & Math Play

73.    How Many Students?

Q       A new school has opened with fewer than 500 students. One-third of the students is a whole number. So are one-fourth, one-fifth, and one-seventh of the students. How many students go to this school?

A       420 students: This is the only number under 500 that can be divided evenly by 3, 4, 5, and 7.
STRATEGY: Make a list.
Source:, August 27, 2000

Number & Math Play

74.    How Old?

Q       Mary is twice as old as her brother and half as old as her father. In 22 years, her brother will be half as old as his father. How old is Mary now?

A       Mary is now 22 years old.

From "an age-old puzzle" reappearing in The World's Most Amazing Puzzles by Charles Barry Townsend. New York: Sterling Publishing, 1993

Number & Math Play

75.    Hungry Hamsters

Q       Five hamsters — Arnie, Betty, Carl, Debby, and Ernie — are learning to go through a maze. Each time a hamster reaches the end of the maze, it gets a pellet of food.
So far, Arnie has gotten four more pellets than Betty; Betty has gotten seven fewer pellets than Carl; Carl has gotten five more pellets than Debby; and Debby has gotten three more pellets than Ernie. Betty and Debby have gotten ten pellets between them.
How many times has each hamster gone through the maze so far? (Each hamster has gone through more than once.)

A       Arnie has gone through 8 times, Betty 4 times, Carl 11 times, Debby 6 times, Ernie 3 times. The key fact is that Betty and Debby have gotten ten pellets between them.
There are only ten possible combinations that will add up to ten pellets, and since we know that each hamster got more than one pellet, we can eliminate four of them: Betty 0/ Debby 10, Betty 1/Debby 9, Betty 9/Debby 1, and Betty 10/Debby 0. Try the remaining six combinations. Betty 4/Debby 6 is the only one that will work.
Source: Barnes and Noble, Mensa Presents Mind Games for Kids, p.13

Number & Math Play

76.    Insects and Spiders

Q       As you know, one way to tell an insect from a spider is to count its legs. All insects have six legs, and all spiders have eight legs. So if some insects and spiders went to a dance, and there were 48 dancing legs, how many insects and how many spiders were at the dance?

A       Four insects (24 legs) and three spiders (24 legs). No other combination will work.

Lowell House, Brain Games, p.48

Number & Math Play

77.    Loose Change

Q       I have pennies, nickels, dimes, and quarters. How many of which coins should I give you if you want 1 dollar in 6 coins? How many of which coins should I give you if you want 1 dollar in 28 coins?

A       If you want 1 dollar in 6 coins, I should give you 3 quarters, 2 dimes, and 1 nickel.
If you want 1 dollar in 28 coins, I should give you 3 quarters and 25 pennies.
From The Best of Brain Teasers from Teacher Created Materials, p. 141

Number & Math Play

78.    Magic Square

Q       Fill in the missing numbers so that the numbers in every row, down, across, and diagonally, will add up to 30.
Then, for a real challenge, make up your own magic square.



Number and Math Play
79.    Minus Two
Q       How many times can you subtract the number 2 from the number 32?
A       Once. After you subtract 2 from 32, you subtract 2 from 30, from 28, and so on.
Source: Inspired by a puzzle in Mensa Presents Mighty Brain Teasers, R. Allen & J. Fulton. New York: Barnes and Noble, 1999

Number & Math Play
80.    Missing Number
Q       What is the number missing from the following sequence?
            4 7 11 18 29 47 ____ 123 199 322
A       The missing number is 76. Beginning with the third number in the sequence, each number is the sum of the two preceding numbers.
STRATEGY: Look for a pattern.
Source: Puzzle 1-3 (p. 8) in IQ Puzzles, compiled by Joe Cameron, New York: Barnes & Noble, 2000
Number & Math Play
81.    Odd One Out
Q       Which number on this square is the odd one out? Why?


A       34.
All the other numbers are evenly divisible by 3.
STRATEGY: Look for a pattern.
Source: Scholastic, Mensa Number Puzzle for Kids, puzzle 141

Number and Math Play

82.    Odd Balls

Q       Suppose you have 7 balls and 2 paper bags. How can you put an odd number of balls into each bag?

A       Put 3 balls in each bag (or put 1 ball in the first bag and five in the second). What about the seventh ball? Just don't put it into a bag at all!
Source: Usborne Brain Puzzles, p. 14

Number and Math Play

83.    Painting by the Numbers

Q       Two painters can paint two rooms in two hours. If 12 rooms have to be painted in six hours, how many painters do you need?

A       The two painters need one hour to paint one room. In six hours, the original two painters can paint six rooms. You'll have to double the number of painters to four if you want twelve rooms painted in six hours.
STRATEGY: Make it simpler.
Source: Puzzle 3-4 (p. 28) in IQ Puzzles, compiled by Joe Cameron, New York: Barnes & Noble, 2000

Number & Math Play

84.    Penny Candy

Q       Back in the days when candy cost just a few cents a piece, Alice was able to buy exactly 100 pieces of candy for a dollar. Some of her candy cost 10 cents a piece; some of her candy cost 3 cents a piece; and some of her candy cost 1 penny for 2 pieces.

How many pieces of each price candy did Alice buy?

A       5 pieces of candy at 10 cents a piece equals 50 cents
1 piece of candy at 3 cents a piece equals 3 cents
94 pieces of candy at 2 pieces for 1 penny equals 47 cents
100 pieces equals $1.00

STRATEGY: Guess and check.

Number & Math Play

85.    Pennies

Q       If someone offered you a choice between a ton of pennies and five miles of pennies lined up with touching edges, which would you take if you wanted the most money? Here are some facts to help you decide:

A penny weighs .09 ounces.
A penny's diameter is .75 inches.

A       Five miles of pennies are worth more than the ton of pennies. Use a calculator to find the inches in a mile, then 5 miles. 316,800 inches divided by .75 inches = 422,400 pennies, or $4,224. 1 ton = 32,000 ounces divided by .09 ounces = 355,555.55 pennies, or $3,555.56.      

Number & Math Play

86.    Piano Lessons

Q       Abigail, Bettina, Cynthia, and Dahlia all began piano lessons last year. Cynthia took twice as many lessons as Bettina. Abigail took 4 lessons more than Dahlia but 3 fewer than Cynthia. Dahlia took 15 lessons altogether.

            How many lessons did Bettina take?

A       Bettina took 11 lessons.
Let A stand for Abigail, B for Bettina, and so on. C = 2B A = D + 4 = C - 3 D = 15
Since D = 15, you know that A = 19. You also know that C - 3 = 19, which means that C = 22. And since C = 2B, 22 = 2B, which means that B = 11.
Source: Inspired by a similar puzzle in Unriddling by Alvin Schwartz, New York: Lippincott, 1983

Number & Math Play
87.    Pick a Pair
Q       Ben has socks in five different colors: two pairs of blue socks, two pairs of black, three pairs of brown, four pairs of green, and four pairs of white. Ben, who is not very neat, doesn't bother to pair up his socks when he puts them away. He just throws them in the drawer. Now Ben is packing to go away for the weekend, but there's been a power failure and he can't see the socks in his drawer.
How many socks does he have to take out of his drawer to be sure he has at least two that will make a pair?
A       The answer is six socks. If Ben takes out five socks, he could have one of each color, with no two matching colors. But if he takes out six socks, two have to be the same color, since there are only five colors. (Sorry we tricked you with all that unnecessary information!)

Number & Math Play
88.    Profit or Loss?
Q       Jill brought home a poster from her trip. She had paid $25 for it. Liu saw the poster and gave Jill $35 for it. A few days later, Jill bought the poster back for $45. Then she sold it again, this time to her cousin Allie for $55.
Did Jill make money on her transactions, or lose money?
A       Add up all the money that Jill spent — $25 and $45 for a total of $70. Then add up all the money Jill got for the poster — $35 and $55 for a total of $90. Jill came out ahead by $20.
Source: Inspired by a puzzle in Put on Your Thinking Cap, Helen Jill Fletcher. New York: Abelard-Schuman, 1968
Number & Math Play
89.    Puzzle about Puzzles
Q       Ann, a very competitive person, decides to give herself 2 points for every crossword puzzle in her daily newspaper that she completes correctly and to forfeit 3 points for every crossword in the paper that she completes incorrectly or cannot complete.
After 30 days of working the puzzles, Ann has a score of zero. How many puzzles has she solved correctly?
A       Ann solved 18 puzzles correctly; therefore, at 2 points a puzzle, she earned 36 points. But Ann failed to solve 12 correctly; therefore, at 3 points a puzzle, she lost 36 points.
In order to arrive at a total of 0 points, the total points for correctly and incorrectly solved puzzles must be equal. Since Ann loses more points for an incorrect puzzle than she gains for a correct one, you know she has to solve more correctly than incorrectly. That means she has to have more than 15 correct puzzles and less than 15 incorrect ones, since the total number of puzzles is 30.
Try out 16 correct (gain 32 points) and 14 incorrect (lose 42 points). That's wrong because it would leave Ann with -10 points. Try 17 correct (gain 34 points) and 13 incorrect (lose 39 points). It still doesn't come out even. Try 18 correct (gain 36 points) and 12 incorrect (lose 36 points). Bingo!
Source: Carter & Russell, Classic Brain Teasers, p.53

Number & Math Play
90.    Rain, Rain, Every Day
Q       Randy's science project was making a rain gauge to measure the amount of rain for one week. It rained each day that week, starting on Monday, and each day the amount of rain in the gauge doubled. By the following Sunday, the rain gauge was completely filled. On which day was the rain gauge half-filled?
A       Randy's rain gauge was half-filled on Saturday. It doubled on Sunday, to become completely filled.
STRATEGY: Draw a picture.
Source: Usborne Brain Puzzles, p. 6

Number and Math Play
91.    Right in the Middle
Q       The numbers in the middle column are related in some way to the numbers in the left and right columns. How are they related?
A       In each row, the middle number is the product of the number on its left and the number on its right, but backwards.
STRATEGY: Look for a pattern.
Source: Scholastic, Mensa Number Puzzle for Kids, puzzle 184

Number & Math Play
92.    Roman Values
Q       What is the second to the largest number and the second to the smallest number that you can make if you have one each of the following Roman numerals?
A       The second to the largest number is LXIV (64); the second to the smallest number is XLVI (46).
STRATEGY: Make a list.
I = 1
V = 5
L = 50
X = 10
The only combinations are: 44, 46, 64, 66
Inspired by a puzzle in Mighty Mini Mind Bogglers, K. C. Richards, New York: Sterling, 1999
Number & Math Play
93.    Sale!
Q       An online shopping site reduced the price of one computer model by 25 percent for a sale. By what percentage of the sales price must it be increased to put the computer model back at its original price?
A       Suppose the computer originally cost $100.00. With the 25% deduction, it would cost $75.00. To bring the price back to the original $100.00, you'd have to add $25.00, which is 1/3 of $75 — or 33.3%.
Source: Cameron, IQ Puzzles, p. 40
Number & Math Play
94.    Six Daughters
Q       Mr. Seibold has 6 daughters. Each daughter is 4 years older than her next younger sister. The oldest daughter is 3 times as old than her youngest sister.
How old is each of the daughters?
A       From youngest to oldest, the 6 daughters are 10, 14, 18, 22, 26, and 30.
Source: Inspired by a puzzle in Put on Your Thinking Cap, Helen Jill Fletcher. New York: Abelard-Schuman, 1968

Number & Math Play
95.    Spiders and Insects
Q       Once the spiders and the insects played a game of tag. To be fair, the insects were allowed to have more members on their team, because an insect has fewer legs than a spider. (As you know, a spider has eight legs, while an insect has only six.) Altogether, there were 20 heads and 136 legs in the game.
How many insects were playing? How many spiders?
A       8 spiders, 12 insects
You know there are 20 animals, and more insects. If all were insects, there would be 120 legs. But there are 136, which means that 16 additional legs must belong to spiders. Since each spider gets 2 of those 16 legs, divide 16 by 2 to get 8 spiders. Subtract 8 from 20 to get 12 insects.
STRATEGY: Work backwards.
Source: Barnes and Noble, 100 Numerical Games, Pierre Berloquin

Number & Math Play
96.    Stack 'Em Up
Q       Kenny had an after-school job at the Pet Food Emporium. His boss told him to stack 35 cartons of dog food so that each row of cartons would have one more than the row above it. How many rows of cartons did Kenny have when he was finished?
A       7 rows. 8 cartons in the bottom row, 2 in the top
Number and Math Play
97.    Summit
Q       You are at a point near the top of a mountain that you have been climbing. In normal conditions, you would need to take only 5 more steps forward to reach the summit. Today, though, the wind is posing problems. For each 2 steps you take forward, the wind pushes you back 1 step. What is the total number of forward steps that you will have to take from this point to reach the summit in this windy weather?
A       Allowing for being pushed backward, you will have to take a total of 8 forward steps to reach the summit. STRATEGY: Draw a picture or diagram.

Number & Math Play
98.    Super Sevens
Q       For each of the seven rows, insert the mathematical symbols (+, -, ÷, ×) that will make the equation correct for someone calculating from left to right. Here's an example with the symbols already inserted:
7 × 7 - 7 ÷ 7 = 6
7 7 7 7 = 9
7 7 7 7 = 15
7 7 7 7 = 56
7 7 7 7 = 63
7 7 7 7 = 91
7 7 7 7 = 147
7 7 7 7 = 294
A                   7 + 7 ÷ 7 + 7 = 9
7 ÷ 7 + 7 + 7 = 15
7 ÷ 7 + 7 × 7 = 56
7 × 7 + 7 + 7 = 63
7 + 7 × 7 - 7 = 91
7 + 7 + 7 × 7 = 147
7 × 7 - 7 × 7 = 294
Source: Will Shortz's Best Brain Busters, p. 97 (and other sources)
Number & Math Play
99.    The Largest Roman
Q       What is the largest number you can express in Roman numerals if you have one each of the following letters? (NOTE: You cannot use any of the letters as powers or exponents.)
C   D   I   L   M   V   X
A                    MDCLXVI (1,666)

Number & Math Play
100.  The Wall
Q       If the Jones twins can build a wall five bricks long and five bricks high in 1 minute, how long will it take them to build a wall ten bricks long and ten bricks high?
A       The first wall has 25 bricks. The second wall has 100 bricks — four times as many. So it will take four times as long — that is, four minutes.
Source: David Adler, Easy Math Puzzles
Number & Math Play
101.  Teaming Up
Q       In Ms. Quimby's class, everyone plays on a team. There are five more soccer players than baseball players. There are three more students on the track team than on the baseball team. There are two more football players than hockey players. There are three more students on the track team than on the football team. The number of baseball and football players equals 8.
How many players are on each team? How many students are there in the class?
A       The three key pieces of information are (1) there are three more students on the track team than on the baseball team; (2) there are three more students on the track team than on the football team (therefore the number of students on the baseball team and the football team are the same); and (3) the number of baseball and the number of football players equals 8. Since the two numbers are equal, there must be four players on each team. Now it's easy to figure out the rest.
Source: Barnes and Noble, Mensa Presents Mind Games for Kids, p. 89
Number & Math Play
102.  Time Difference
Q       Larry's flight is supposed to leave Sydney, Australia, at 1 p.m. on Thursday, September 9. What time and what day will Larry get to New York City?
New York is twelve hours behind Sydney; that is, it's twelve hours later in Sydney than in New York City. The flight from Sydney to Los Angeles takes 14 hours, Larry's layover in Los Angeles is 2 hours, and the flight from L.A. to New York is 5 hours. Assume there are no delays.
A       Larry will get to New York City on Thursday, September 9, at 10 p.m.
Source: Karen C. Richards, Mighty Mini Mind Bogglers, p. 79

Number & Math Play
103.  Time Puzzle
Q       Two hours ago, it was as many hours after one o'clock in the afternoon as it was before one o'clock in the morning.
What time is it now?
A       It's now nine o'clock in the evening.

Number and Math Play
104.  Time to Paint the Floor
Q       If it takes Polly the Painter 1 hour to paint a bedroom floor that is 9 feet wide and 12 feet long, how long will it take her to paint the living room floor, which is twice as wide and twice as long?
A       Four hours. The size of a room that measures 9’ x 12’ is 108 square feet. A room that is twice as long and twice as wide will measure 18’ by 24’, which makes 432 square feet. That makes the living room 4 times the size of the bedroom, so it will take 4 times as long to paint.
Number & Math Play
105.  Time Will Tell
Q       Picture a regular (analog) clockface — with the numerals 1 to 12 correctly positioned.
Where would you draw a straight line to split the clockface in half in such a way that the sum of the numbers on one side of the line will equal the sum of the numbers on the other side of the line?
A       Draw a straight line that begins on the left side of the clockface between 9 and 10 and cuts across the clockface to the right side between 3 and 4. The sum of the numbers above the line equals 39, and the sum of the numbers below the line equals 39.
Based on a puzzle in The World's Best Puzzles by Charles Barry Townsend. New York: Sterling Publishing, 1986.

Number & Math Play
106.  Tug of War
Q       The young farm animals have been playing tug of war. With 3 piglets on one side and 2 kids (young goats) on the other side, the game ended in a tie. Similarly, with 3 calves on one side and 4 kids on the other side, the game ended in a tie. Which side, if either, will win if one side has 5 piglets and the other side has 2 calves?
A       The 5 piglets will win. If there were only 4 piglets on one side and 2 calves on the other side, it would be a tie.
Here's one way to solve the puzzle. The puzzle tells you the following:
  2 kids = 3 piglets
  3 calves = 4 kids
Those facts mean the following are also true:
  4 kids equal 6 piglets
  3 calves equal 6 piglets
Therefore, 1 calf = 2 piglets. It follows that 2 calves = 4 piglets. If 2 calves and 4 piglets would tie, then 5 piglets would beat 2 calves.
Source: Karen C. Richards, Mighty Mini Mind Bogglers, p. 11

Number & Math Play
107.  Two Legs, Four Legs
Q       A puzzle maker looks out a window into his back yard. He sees a mix of boys and cats. He counts 22 heads and 68 legs. He wants YOU to figure out how many boys are in the yard.
A       The boys plus the cats have a total of 22 heads. Or B + C = 22. Subtracting C from each side of the preceding results in a value for B of 22 - C.
The boys' legs equal two times the number of boys, the cats' legs equal four times the number of cats, and the total number of legs equals 68. Or 2B + 4C = 68. Using the value for B already calculated, the last equation can be rewritten as 2 (22 - C) + 4C = 68, or 44 - 2C + 4C = 68, which, by addition and subtraction, becomes 2C = 24, or C = 12.
There are 12 cats and 10 boys in the back yard.
From a puzzle in Puzzles, Patterns, and Pastimes: From the World of Mathematics by Charles F. Linn. Garden City: Doubleday, 1969
Number and Math Play
108.  Uphill, Downhill
Q       Grandma walked up a hill at the rate of 2 miles an hour, turned around as soon as she got to the top, and walked down the hill at the rate of 4 miles an hour. The whole trip took her 6 hours. How many miles is it to the top of the hill?
A       Here's one of several ways to figure out the answer: Grandma walked 1 mile up the hill in 30 minutes and 1 mile down in 15 minutes. In other words, 1 mile took her 45 minutes round trip. The whole trip took her 6 hours, or 360 minutes; if you divide the overall time (360 minutes) by the time it took to do 1 mile (45 minutes), you find out that the overall length of the hill is 8 miles.
STRATEGY: Make it simpler.
Source: Inspired by a puzzle in The Adler Book of Puzzles and Riddles, or Sam Loyd Up-to-Date, Irving and Peggy Adler. New York: John Day, 1962
Number & Math Play
109.  Walking the Dogs
Q       A group of kids got together and started a dog-walking business. They got lots of clients right away, so that when they all walked their dogs together, there were twelve heads and forty legs. How many kids and how many dogs were out walking?

A       If all 12 heads belonged to kids, there would be 24 legs (2 legs for each head). But there are 40 legs. That leaves 16 legs, or 8 pairs of legs that must belong to dogs. So there are 8 dogs. Subtract 8 from 12 (since everyone has only one head), and that leaves 4 kids.

Number and Math Play
110.  What Time Is It?
Q      What is the number missing from the following sequence?

By figuring out the relationship of these watch settings to one another, you should be able to determine what time will show up on Watch E.
WATCH A   5:23
WATCH B   8:26
WATCH C   12:30
WATCH D   5:35
WATCH E   ______

A       The hours move ahead 3, 4, and 5 hours. The minutes move ahead 3, 4, and 5 minutes. The time WATCH E will show is 11:41, 6 hours and 6 minutes beyond 5:35.

STRATEGY: Look for a pattern.
Source: Inspired by a puzzle in Mensa Presents Mighty Brain Teasers, R. Allen & J. Fulton. New York: Barnes and Noble, 1999

Number and Math Play
111.  What's the Fewest?
Q       Some kids are playing hide and seek in a park where there are seven trees. One of the kids is “It,” and the others are all hiding behind trees. Of course, you can’t see them, because they’re hiding. See if you can figure out the fewest possible kids hiding, using the following information:
A girl is hiding to the left of a boy.
A boy is hiding to the left of a boy.
Two boys are hiding to the right of a girl.
A       The fewest kids hiding is 3. A girl is on the left; to her right is a boy; to his right is another boy.
            STRATEGY: Draw a picture or diagram.

Number & Math Play
112.    What's So Special?
Q       What's special about the number 2520?
            HINT: The answer has something to do with the numbers 1 through 10.
A       The number 2520 is the smallest number that can be divided evenly by each of the numbers 1 through 10.
Source: Carter & Russell, Classic Brain Puzzlers, p. 57

Number & Math Play
113.  What's Your Sign?
Q       In the equation below, replace each question mark with one of the four mathematical signs: +,-, ×, or ÷. Each sign can be used only once. Fill in the blanks to solve the equation. (Hint: the first sign is +.)
7 ? 5 ? 4 ? 7 ? 6 = 15
A                   (7 + 5) ÷ 4 × 7 - 6 = 15
If the first sign is +, there are only 6 possible combinations. You can get the answer by trying each one of them out. There is only one correct answer.
Source: Barnes and Noble, Mensa Mind Games for Kids, p. 18
Number and Math Play
114.    Wheel of Fortune
Q       A game wheel shows the numbers 1 to 36. Figure out on which 2-digit number Lucy has landed given the following facts:
The number is divisible by 3.
The sum of the digits in this number lies between 4 and 8.
It is an odd number.
When the digits in this number are multiplied together, the total lies between 4 and 8.
A       Lucy has landed on 15. Make a list of numbers 1- 36 that are divisible by 3. Cross out all that are even. This leaves 9, 15, 21, 27, and 33. 9, 21, and 27 have a “sum of digits” less than 4 or more than 8. But, 1 x 5 = 5 and 3x 3 = 9.
STRATEGY: Make a list and search for a pattern.
Word & Letter Play
115.  When, Oh, When?
Q       Ken promised Ben today to tell him a big secret on the day before five days from the day after tomorrow. Today is Saturday, October 21. On what day and date will Ken tell Ben the secret?
A       Ken will tell Ben the secret on Friday, October 27
Number and Math Play
116.  Where's the Fruit Juice?
Q          A catering company sells large containers of iced tea and large containers of fruit juice. Right now the company has six containers, each holding the following amounts:
Container A: 30 quarts
Container B: 32 quarts
Container C: 36 quarts
Container D: 38 quarts
Container E: 40 quarts
Container F: 62 quarts
Five of the containers hold iced tea, and one container holds fruit juice.
Two customers come into the shop. The first customer buys two containers of iced tea. The second customer buys twice as much tea as the first customer. Which container is holding the fruit juice?

A       Container E holds the fruit juice. The second customer can buy twice as much as the first customer if the first customer buys Containers A and C (for a total of 66 gallons) and the second customer buys Containers B, D, and F (for a total of 132 gallons). Therefore, the remaining container—E—must hold the fruit juice.
STRATEGY: Make a list of possibilities

Number & Math Play
117.  Which Wages?
Q       A man applied for a job. The woman who interviewed him offered him two pay rates: a straight rate of $100 a day or a pay rate that would begin at one cent the first day and then double each day. The second rate meant the man would earn two cents the second day, four cents the third day, eight cents the fourth day, and so on. The man chose the second rate, and the woman hired him.
Tell why, and prove your case.
A       The woman hired the man because she wanted a smart employee, and he was smart enough to figure out that he would accumulate much more money at the second pay rate as soon as he got to the 18th day of work. It's true that at Day 10, the first rate would pay him a total of $1,000, for the first 10 days and the second rate would pay him a total of only $10.23 for the same ten days. By day 19, however, the first rate would earn him a total of $1,900, but the second rate would earn him $2,621.44 just for that day! And the man's earnings would keep increasing by leaps and bounds.
Source: The Best of Brain Teasers from Teacher Created Materials, p.127
Number & Math Play
118.  Wrap It Up
Q       You have 100 yards of ribbon on a spool, and you need 100 lengths of ribbon 1 yard long. It takes you 1 second to measure and cut each yard. How long will it take you to come up with the 100 pieces of ribbon?
A       It will take you 99 seconds. Each cut, including the 99th, produces two pieces of ribbon.
Source: Carter & Russell, Classic Brain Puzzlers, p. 80

119.  Catchy Code
Q       The message below is written in code. Each letter of the alphabet is represented by a sign and a number. The words are separated by lines like this:
 ___. See if you can break the code and read the message.
            This is a catchy one, so here are two hints:
Hint 1: Do the signs look familiar? Think about where you’ve seen them. That’s the key.
Hint 2: Notice that the only numbers that appear in the code are 1, 2, and 3. They stand for rows—row 1, row 2, and row 3.
(To get you started, ^1 stands for Y, ^2 stands for H, and ^3 stands for N.)
(2 (1 (1 *2 ___ $2 (1 $1 ___ %1 ^2 #1 @2 #1 ___@2 *1 %2 ^3 @2
___(1 ^3 ___ ^1 (1 &1 $1 ___ #3 (1 &3 )1 &1 %1 #1 $1 ___
*2 #1 ^1 %3 (1 !2 $1 #2.
A       The answer is: Look for these signs on your computer keyboard. And that’s also the key to the code. !2 stands for the letter A because A is down two rows (going diagonally from left to right) from the exclamation point on your keyboard. !1 would stand for the letter Q, and !3 would stand for the letter Z. Here’s the whole code:
!1 = Q; !2 = A; !3 = Z
@1 = W; @2 = S; @3 = X
#1 = E; #2 = D; #3 = C
$1 = R; $2 = F; $3 = V
%1 = T; %2 = G; %3 = B
^1 = Y; ^2 = H; ^3 = N
&1 = U; &2 = J; &3 = M
*1 = I; *2 = K;
(1 = O; (2 = L
)1 = P

120.  Doggies
Q       The dog named Jam is heavier than the dog named Jelly.
Copper weighs more than Brandy but less than Pumpkin.
Brandy weighs more than Jelly.
Pumpkin weighs less than Jam.
List the dogs in the order of their weights, starting with the heaviest.
A       The heaviest dog is Jam, the next heaviest is Pumpkin, the next heaviest is Copper, the next heaviest is Brandy, and the least heavy (or the lightest) is Jelly.
            STRATEGY: Guess and check -- write each name on note-cards and move them to test sequence

121.  Escape Hatch
Q       SETTING: A prison cell with a dirt floor, stone walls, no window but a skylight very high up in the ceiling; no furniture except for a mattress
ACTION: The prisoner who was in the cell manages to escape through the skylight.
            QUESTION: How did the prisoner escape?
A       First, the prisoner dug a hole in the dirt floor. Second, the prisoner piled the dirt from the hole against the wall. Third, the prisoner climbed the pile of dirt and escaped through the skylight.
Based on a puzzle in More Puzzles for Pleasure and Leisure by Thomas L. Hirsch. New York: Abelard-Schuman, 1974.

122.  Flat Tire
Q       Two friends were driving on the highway when they got a flat tire. First they took off the hubcap. Then they unscrewed the four lug nuts — the screws that hold the tire in place. They put the inverted hubcap down on the road and carefully placed the lug nuts inside the hubcap. Then they removed the flat.
As they were in the process of putting on the spare tire, another car came along, hitting the hubcap and scattering the four lug nuts where they could not be found. The driver of the other car felt sorry, so he stopped to help. The two friends followed his advice, and in a little while they were back on the road again. What did the man tell them?
A       The man told the two friends to take one lug nut off each of the other three tires and use them to hold the spare tire in place. (Later they could buy four more lug nuts so that each tire would have four again.)

123.  Getting Across
Q       Ms. Waters and her twins, Danny and Anny, want to cross from the east side of the river to the west side in a canoe. But the canoe can hold no more than 200 pounds. Ms. Waters weighs 160 pounds, and Danny and Anny weigh 100 pounds each.
How can all three of them reach the other side of the river in the canoe?
A       First the twins paddle to the west side of the river. Anny stays on the west side, and Danny comes back. Mrs. Waters rows alone to the west side, leaving Danny on the east side. Finally, Anny comes back for Danny.
Together, they paddle to the west side of the river. (You can reverse Anny and Danny-it doesn't matter which one goes first.)

124.  How Many Were Going To Saint Ives?
Q       This is a very old rhyming riddle. See if you can answer it by reading and thinking very carefully.
As I was going to Saint Ives,
I crossed the path of seven wives.
Every wife had seven sacks,
Every sack had seven cats,
Every cat had seven kittens,
Kittens, cats, sacks, wives,
How many were going to Saint Ives?
A       Only one person was going to Saint Ives.
If he or she crossed the path of the seven wives, then the kittens, cats, sacks, and wives were all going in a different direction!
(If everyone was going in the same direction, however, the answer would be 2,801 — 7 wives, 49 sacks, 343 cats, and 2,401 kittens equal 2,800. Then you have to add one more for the person speaking the words of the riddle.)

125.  Moving Day
Q       The Masters family is moving to a new house. They have a dog, a cat, and a pet mouse, but the animals don't get along in the car, so they can take only one at a time.
Then there are other problems. They can't leave the dog alone with the cat, because the dog chases the cat if no one is watching. And they can't leave the cat and the mouse together, because...well, you know what would happen if they did.
How can the Masters family get all three of their pets to their new house?
A       They take the cat to the new house, leaving the dog and the mouse at the old house. They return to the old house and take the mouse to the new house. They take the cat back to the old house, leave it there, and take the dog to the new house. Then they return to the old house for the cat.

126.  Mystery Twins
Q       Two babies born on the same day in the same year with the same mother and father are not twins.
Can you explain how this can be?
A       The two babies are two of a set of triplets.

127.  Not Enough Time
Q       Larry insists that he does not have enough time to go to school more than 17 days a year. He comes to this conclusion based on the following list that he put together.
Number of days
per year
Sleep (8 hours a day)
Meals (2 hours a day)
Summer vacation
Recreation (2 hours a day)
Inspired by the list, Larry claims he has only 17 days left in the year for school. What's wrong with his thinking?
A       Larry's categories overlap. For example, he has counted 60 days for vacation, during which time he will both eat and sleep, activities that he has already counted separately. The 60 vacation days also include weekends, another category that he has already counted separately. He should not count the same periods of time more than once.
Inspired by a puzzle in Mathematical Puzzles by Martin Gardner. New York: Thomas Y. Crowell Company, 1961.

128.  Puzzling Relations
Q       A man named George was hurrying to get ready for a dinner party when Dan rang his doorbell.
"I'm just rushing off to a dinner party," said George, "but I'm sure it would be fine if you came along."
So the two went off together. When they arrived at the party, George, who always enjoyed getting people to use their heads, introduced Dan to the other guests with the following rhyme:
"Brothers and sisters have I none,
But this man's father is my father's son."
How were George and Dan related?
A       Dan was George's son.

129.  Relabeling
Q       In front of you are three covered cartons. One is labeled mustard packets; one is labeled ketchup packets; one is labeled mustard and ketchup packets. None of the cartons is correctly labeled.
How can you relabel the cartons correctly if all you're allowed to do is close your eyes, reach into one carton, take out one packet, and then look at it?
A       You can solve this brainteaser by one of the following scenarios:
You already know the carton mislabeled mustard and ketchup packets must contain only mustard packets or only ketchup packets. If the packet you open is mustard, you should relabel the carton you took it from mustard packets. Since you've already used up the label mustard packets, the carton mislabeled ketchup packets cannot possibly contain only mustard packets; since it is mislabeled, it can't contain only ketchup packets; so you should relabel it mustard and ketchup packets. Therefore, the remaining carton to be relabeled as ketchup packets; it's the only possibility left.
You already know the carton mislabeled mustard and ketchup packets must contain only mustard packets or only ketchup packets. If the packet you open is ketchup, you should relabel the carton you took it from ketchup packets. Since you've already used up the label ketchup packets, the carton mislabeled mustard packets cannot possibly contain only ketchup packets; since it is mislabeled, it can't contain only mustard packets; so you should relabel it mustard and ketchup packets. Therefore, the remaining carton to be relabeled as mustard packets; it's the only possibility left.
Based on a brainteaser posted on April 8, 1999, on

130.  Ripping Pages
Q       If you ripped the following pages out of a book, how many separate sheets of paper would you remove? The page numbers are 4, 5, 24, 47, and 48.

A       You would have four sheets of paper. The odd pages of a book are on the right side, and the even pages are on the left. Therefore, pages 47 and 48 are opposite sides of the same sheet of paper.
Source: Sterling Pocket Puzzlers, Brain Teasers, p.20

131.  Round vs. Square
Q       Why is it better for manhole covers to be round rather than square?
A       You can turn a square manhole cover sideways and drop it down the diagonal of the manhole. You cannot drop a round manhole cover down the manhole. Therefore, round manhole covers are safer and more practical than square ones.
Based on "Manhole Covers," found at
, which cites Challenging Lateral Thinking Puzzles by Paul Sloane and Des MacHale, distributed by Cassell in the UK and by Capricorn Link in Australia.

132.  Sisters & Brothers
Q       Suppose I have two siblings, and at least one of them is a girl. What are the odds that I have two sisters? Supposing I have two siblings, and the older one is a boy. What are the odds that I have two brothers?
A       The probability that both are girls is 1/3. (The odds that both are girls is 1 to 2- one way it can be true against two ways it can not.) There are four possibilities when considering the gender of two siblings: girl-girl, girl-boy, boy-girl, and boy-boy. Given that I have one sister, the boy-boy combination is impossible. So in this case, there are three possible combinations, and only one with both girls.
In the second case, the probability of having two brothers is 1/2. (The odds are "even" - 1 to 1.) The same four possibilities for gender must be considered. Girl- girl is not possible from the given information. The statement "the older one is a boy" also eliminates the girl-boy option. This leaves only two choices.
STRATEGY: Draw a picture or diagram.

133.  The Barbershop Puzzle
Q       A traveler arrives in a small town and decides he wants to get a haircut. According to the manager of the hotel where he's staying, there are only two barbershops in town — one on East Street and one on West Street. The traveler goes to check out both shops. The East Street barbershop is a mess, and the barber has the worst haircut the traveler has ever seen. The West Street barbershop is neat and clean; its barber's hair looks as good as a movie star's.
Which barbershop does the traveler go to for his haircut, and why?
A       The traveler goes to have his hair cut at the barbershop on East Street. He figures that since there are only two barbershops in town the East Street barber must have his hair cut by the West Street barber and vice versa. So if the traveler wants to look as good as the West Street barber (the one with the good haircut), he'd better go to the man who cuts the West Street barber's hair-the East Street barber.
By the way, the reason the West Street barbershop is so clean and neat is that it seldom gets customers.
Source: A Haircut in Horse Town, p.64 (and other sources)

134.  There's Something Fishy Going On
Q       Although each of the following sentences sounds okay at first, there's really something wrong with each one of them. Read the sentences and explain why each one is a little "fishy."
1.            No one goes to that restaurant any more because it's too crowded.
2.            I'm glad I don't like spinach, because if I liked it, I'd eat it, and it tastes awful.
3.           If you can't read this sign, ask for help.
A       1. If no one goes to the restaurant, it can't be crowded.
            2. If the person did like spinach, he or she wouldn't think it tasted awful.
3. If the person can't read the sign, she or her won't know that it says to ask for help.

135. Toast for Three
Q       Dad is preparing breakfast for his three children—Dan, Ed, and Frank. Each boy wants Dad to toast 1 slice of bread for him. The family’s toaster holds only 2 slices of bread and toasts only 1 side at a time. The person who toasts bread has to toast one side of a slice of bread, take out the slice, turn it over, and put it back in the toaster to toast the other side. It takes exactly 1 minute to toast 1 side of a piece of bread. Dad has figured out how to toast 3 slices on both sides in only 3 minutes. How does he do it?
A       First minute: Dad toasts Dan’s bread on side 1 and Ed’s bread on side 1. Then he removes Dan’s slice, turns it around, and puts it back in the toaster. He puts Ed’s slice aside and puts Frank’s bread in the toaster.

Second minute: Dad toasts Dan’s bread on side 2 and Frank’s bread on side 1. He removes both slices, turns Frank’s around, and puts it back in the toaster. He gives Dan his toast and puts Ed’s slice back in the toaster.

Third minute: Dad toasts Frank’s slice on side 2 and Ed’s slice on side 2. Then he serves those slices to Frank and Ed.

136.  True or False?
Q       Read the following statement in capital letters and think about whether it is true or false.
What do you think? Explain what makes this statement so confusing.
A       If the statement is true, then it must be false; but if it's false, then it's true! The word for such a statement that contradicts itself
is paradox. By the way, this is probably the only statement you can make that is neither true nor false.

Spatial Awareness
137.  A Penny Apiece
Q       Cut a big circle out of a sheet of paper. Place seven pennies on the paper circle as follows:
1.     Place six pennies, evenly spaced, around the outer edge of the circle. Label the top penny "A," and the others, "B," "C," "D," "E," and "F," going clockwise around the circle.
2.     Place one penny in the middle of the circle. Label it "G."
Now divide the circle into sections by drawing three straight lines so that there is only one penny in each section.
A       Begin by drawing a horizontal line across the circle, just below penny G.
Next, draw a diagonal line beginning just to the left of penny A, passing to the right of penny G, and just beneath penny C.
Then draw another diagonal line beginning just to the right of penny A, passing to the left of penny G, and just beneath penny E.
Penny G should end up in a small triangle all by itself.
Source: Sterling, Math Tricks, Puzzles & Games, p.45

Spatial Awareness
138.  Cups Up
Q       Take three paper cups and put them in a row. Turn the first and third cups upside down, but leave the middle cup right side up. Your task is to get all the cups right side up, but you must follow these rules:
You have only three moves.
For each move, you must turn over two cups at a time—never one at a time.
A       First move: Turn over the first and second cups.
Second move: Turn over the first and third cups.
Third move: Turn over the first and second cups.
Now they should all be right side up.
STRATEGY: Act it out.

Spatial Awareness
139.  Exactly Two
Q       Draw a grid made up of six horizontal squares and six vertical squares.
The grid will have 36 squares. Place 12 pennies on the grid, one to a square, so that each of the six horizontals, each of the six verticals, and each of the two diagonals contains exactly two pennies.
A       Here are three solutions. Are there more?
Solution 1

Solution 2

Solution 1

Based on a puzzle in More Puzzles for Pleasure and Leisure by Thomas L. Hirsch. New York: Abelard-Schuman, 1974.

Spatial Awareness
140.  Pennies on a Grid
Q       In the grid below, you'll find four Xs in a row and three Xs in a row. (One row of Xs is vertical and the other is horizontal.) Your challenge is to make 3 rows of 3 Xs by moving only one X. (Hint: Use pennies so that you can try out different strategies.)




A       Move the x in boldface type to the box marked either a or b.






Spatial Awareness
141.  Two Moves
Q       Can you change two rows of Xs into a circle by moving only two of the Xs?
Go from this:
                                  X   X   X
                               X   X   X 
to this:

                                    X   X 
                               X             X
                                   X    X
by moving only two Xs.
Hint: Try it by using pennies. But remember, you can move only two of the pennies. The others stay exactly where they are!
A       Move the X at the right in the top row and the X in the middle of the bottom row to the position of the bottom two Xs in the circle

Spatial Awareness
142.  Three Moves
Q       There are 10 letters in the triangle. Change the triangle so that it points down. Move one letter at a time. You have only three moves. (Hint: Lay 10 pennies out so that they match the letters in the triangle. Then you can try out different moves.)
       B C
      D E F
     G H I J
A       Move G so that it is next to B. Move J so that it is next to C. Switch A from the top to the bottom of the triangle to make the point.
       B C
      D E F
     G H I J
     G B C J
      D E F
       H I
Source: Lowell House, Brain Games, p. 37

Word & Letter Play
143.  A?
Q       If you start with the number one and use only integers (whole numbers), how far do you have to count before you need to use the letter a in spelling a number?
A       You have to count up to one thousand.
Source: Based on a puzzle in More Puzzles for Pleasure and Leisure by Thomas L. Hirsch. New York: Abelard-Schuman, 1974

Word & Letter Play
144.  A Different Alphabet
Q       Which letter comes next?
A  C  F  J  O  
A       The next letter is U. The series moves forward by skipping 1 letter of the alphabet and then 2 letters and then 3 and so on.
Source: Cameron, IQ Puzzles, p.9

Word & Letter Play
145.  A Skinny Riddle
Q       What is being described in this riddle?
When I am filled,
I can point the way.
When I am empty,
Nothing moves me.
A       A glove

Word & Letter Play
146.  A to Z
Q       Use all twenty-six letters of the English alphabet to complete the following 13 words, but use each letter only once.
·         b a __ __ a i n
·         l __ __ g e r
·         d y __ __ s t y
·         __ __ g o t e
·         s a __ __ a t i o n
·         d i __ __ p a n
·         p u m __ __ i n
·         d e __ __ a y
·         b o __ __ a r
·         d i __ __ i t
·         s u n __ __ r n
·         o b l __ __ u e
·         l i __ __ o f f
·         bargain
·         lodger
·         dynasty
·         zygote
·         salvation
·         dishpan
·         pumpkin
·         deejay
·         boxcar
·         dimwit
·         sunburn
·         oblique
·         liftoff
Source: p. 94 in Big Book of Games II, New York: Workman, 1988.

Word & Letter Play
147.  All in the Family
Q    These words all belong to the same logical family because they have something in common:
·         footloose
·         committed
·         successful
·         address
·         millennium
Which of the following words belong to the same family?
·         silly
·         ancestor
·         millstone
·         heedless
A       Heedless. (All the words in the family have two pairs of double letters.)

Word & Letter Play
148.  Alphabet Challenge
Q       Use all twenty-six letters of the alphabet to complete the following eleven words, but use each letter only once in the course of this puzzle.
To keep track of which letters you use, print this page and cross off the letters:
1.     __ a __ z
2.     __ u i e __
3.     __ u __ c a
4.     e __ t r __
5.     __ i o __ __ n
6.     __ a __ __ f u l
7.     __ r o __ __
8.     __ e __ __ a t
9.     __ __ a l a
10.  __ o l a __
11. __ o r c __ p i n e
1.     jazz
2.     quiet
3.     yucca
4.     extra
5.     violin
6.     bashful
7.     grown
8.     defeat
9.     koala
10.  molar
11.  porcupine
From The Best of Brain Teasers. Westminster, CA: Teacher Created Materials, Inc., 1999.

Word and Letter Play
149.  Anagram Rhyme
Q       Will Shortz, a famous puzzle master, created this one: For each of the following four words, come up with another English word that uses all THE SAME letters but in a different order. The four words you come up with will rhyme with one another.
·         ONSET
·         NEWS
·         WRONG
·         HORNET
·         STONE
·         SEWN
·         GROWN
·         THRONE
STRATEGY: Look for a pattern in the letters – what is the same in each that could rhyme?

Word & Letter Play
150.  X and Y
Q       Finish each of the following three-word expressions. Some of the expressions are used as verbs, some as nouns, and some as adjectives.
1.     eat and
2.     huff and
3.     mix and
4.     rise and
5.     twist and
6.     slash and
7.     wash and
8.     watch and
9.     bait and
10.  tar and
1.     drink or run
2.     puff
3.     match
4.     fall or shine
5.     shout or turn
6.     burn
7.     wear or dry
8.     wait
9.     switch
10.  feather
Other answers may be possible.
From The Best of Brain Teasers from Teacher Created Materials, p. 19

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