1.
Two friends decide to get together; so they start
riding bikes towards each other. They plan to meet
halfway. Each is riding at 6 MPH. They live 36 miles
apart. One of them has a pet carrier pigeon and
it starts flying the instant the friends start traveling.
The pigeon flies back and forth at 18 MPH between
the 2 friends until the friends meet. How far does
the pigeon travel?
2. Nick and John were exercising when the subject
of weight came up. Nick had no problem telling
John his weight, but John said he had more "mass"
than he wanted. He wouldn't come right out and
reveal his weight; so he told Nick this riddle.
" I weigh 147 pounds plus half of my weight,"
he said. How much does he weigh?

3. A farmer knows that 20 of his hens, housed
in 3 coops, will hatch 30 eggs in 18 days. How
long will it take 30 hens, housed in 4 coops to
hatch the same number of eggs?

4. How can you measure 1 gallon of juice out
of a barrel, if all you have available is a 3-gallon
and a 5-gallon pitcher?

5. Students at Monty High with a class size under
of 30 took a math test. One third of the class
got a "B", one quarter a "B-",
one sixth a "C", and one eighth failed.
The remainder of the students got an "A"
How many students got an "A"?

6. When manufacturing bars of soap, the cutting
machine produces scraps. The scraps from 11 bars
of soap can be made into one extra bar. What is
the total number of bars that can be made after
cutting 250 bars of soap?

7. Kerry loves dumplings. He can eat 32 of them
in an hour. His brother Pete needs 3 hours to
eat the same amount. How long will it take them
both together to eat 32 dumplings?

8. Joan and Jane are sisters. Jean is Joan's
daughter and 12 years younger than her aunt. Joan
is twice as old as Jean. Four years ago, Joan
was the same age as Jane is now, and Jane was
twice as old as her niece. How old is Jean?

9. Find a simple method of solving:

6751X + 3249Y = 26751

3249X + 6751Y = 23249

10. Divide 110 into two parts so that one will
be 150 percent of the other. What are the 2 numbers?

11. At a sports banquet there are one hundred
athletes. Each one is either a football or basketball
player. At least one is a football player. Given
any two of the athletes, at least one is a basketball
player. How many of the athletes are football
players?

12. The following number is the only one of its
kind. Can you figure out what is so special about
it? 8,549,176,320

13. Jennifer took a test that had 20 questions.
The total grade was computed by awarding 10 points
for each correct answer and deducting 5 points
for each incorrect answer. Jennifer answered all
20 questions and received a score of 125. How
many wrong answers did she have?

14. A box of candy bars can be divided equally
(without cutting anything) among 2, 3, or 7 people.
What is the least number of candy bars the box
could contain?

15. Using standard mathematical symbols, e.g.
+, -, x, etc., rearrange (4) fives to equal the
numbers one to ten. For example, 5/5 + 5 - 5 =
1, 5/5 + 5/5 = 2, etc.

16. Use each of the digits 1, 2, 3, 4, 5 and
6 once only, in this multiplication problem to
make it correct.

? ?

x ?

——

? ? ?

17. Bob is ten years older than his brother Stan.
There was a time when Bob was three times as old
as Stan. What was Stan's age when Bob was three
times as old?

18. Can you replace the question marks with
three math symbols to make the following equation
correct:

(2 ? 3) ? (6 ? 2) ? (3 ? 1) = 5

19. Can you find four consecutive prime numbers
that add up to 220?

20. If I buy an apple and a banana, the cost
will be $1.19. If I buy an apple and a pear, the
cost will be $1.45. If I buy a banana and a pear,
the cost will be $1.40. What are the individual
prices?

21. A two-digit number when read from left to
right, is 4.5 times less than the same number
read from right to left. What is the number?

22. Barry went to a sporting goods store with
$100 to buy some golf equipment. If he spent $40
on a new driver, 20% of what was left on a new
putter, 1/8 of his original money on golf balls,
and 31/71 of what was left of his money on a golf
cart, how much money does he have left?

23. If 3 salesman can sell three stoves in 7
minutes, how many stoves can six salesmen sell
in seventy minutes?

24. You have a cake which you must cut into 8
equal pieces. You may make only 3 cuts. How will
do this?

25. Which number when added to 5/4 gives the
same result as when it is multiplied 5/4?

26. In the square below, a rule applies both
from top to bottom and from left to right. Find
the rule and figure out the missing number.

6 2 4

2 ? 0

4 0 4

27. What is the missing number in this arrangement?

1 2 3 4 5

1 3 7 15 31

1 4 13 40 121

1 5 21 85 ???

28. A fish is fifteen inches long. Its head is
as long as its tail. If the head were twice as
long as it really is, the head and tail would
together be as long as what's in between. How
long is each part of the fish?

29. Arrange the ten digits 0 to 9 in three arithmetical
sums, using three of the four operations of addition,
subtraction, multiplication, and division, and
using no signs except the ordinary ones implying
those operations. Here is an example to make it
quite clear (note that the example is not correct):

3 + 4 = 7 9 - 8 = 1 5 X 6 = 30

30. Several cartons of candy are being shipped
from a manufacturer to warehouses where they will
be prepackaged to sell to stores. The candy in
each carton needs to be divided equally among
3, 4, 5, or 7 stores. What is the least number
of pieces of candy that each carton can have?

31. Kevin flew to Puzzle land at the fantastic
speed of 1000 miles per hour. There he picked
up his friend and flew back, burdened by the extra
weight, at only 500 miles per hour. What was his
average speed?

32. What is the number that is 5 more than the
number which is one-fifth of one-fifth of one-half
of 1050?

33. The following multiplication example uses
every digit from 0 to 9 once (not counting the
intermediate steps). Fill in the missing numbers.

7 x x

4 x

x x x x x

34. There are 7 tennis balls which are identical
in all aspects except that one of them weighs
slightly less than the other 6. How can you identify
the one that weighs less on a balance scale with
no more than 2 separate weighings?

35. Fill in the missing numbers in the following
series:

101 99 102 98 103 97 ? ?

36. Can you arrange the odd digits 1, 3, 5, 7,
and 9, and the even digits, 2, 4, 6, and 8, in
such a way that the odd ones add up to the same
as the even ones? You can use arithmetical signs
and decimals, but the idea is to try and arrive
at the simplest possible solution. There are,
of course, many possible answers.

37. Many years ago when gasoline was only 46
cents a gallon, I stopped to fill up my car. I
gave the attendant a $20.00 bill and waited for
my change. Unexpectedly, he charged me for the
number of gallons that the car needed instead
of the dollar amount. (for example if the car
took 8.4 gallons he would have charged me $8.40.
Because he did this, I received less in change
than I should have. The funny thing is that I
had received in change exactly the amount that
I should have been charged for the gas in the
first place. Remembering that the cash indicator
on a gas pump will only charge to the nearest
half-cent, how many gallons of gas did I buy that
day?

38. What is the four-digit number (no zeros)
in which the third digit is the number of "winds,"
the first digit is one-half of the third, the
second digit is double the third and the last
digit is one-half the sum of the first three?

39. What would be the next number in the following
sequence?

11 1,331 161,051 19,487,171 ?

40. The square of 13 is 169. Take the last digit
of the square, 9, and place it in the middle,
making 196. This is the square of 14, the next
number above 13. What are the next numbers which
also have this property?

41. The following multiplication example uses
every digit from 0 to 9 at least once. Letters
have been substituted for the digits. Can you
replace the letters and make the original multiplication
problem?

B O G

x B O G

L Y L E

G G U L

T U O O

U N I T O E

42. There are several ways to come up with 100
by using the digits 0 through 9. One way is: 0
+ 1 + 2 + 3 + 4 + 5 + 6 + 7 + (8 x 9) = 100. Another
way is 78 3/6 + 21 45/90. Can you come up with
2 more ways?

43. If 1/2 of 16 were 13, what would 1/3 of
32 be?

44. Sheilah is now two-thirds of Sally's age.
In six years, Sheilah will be four-fifths of Sally's
age. In 15 years, Sheilah will be seven-eighths
as old as sister Sally. If they are both under
the age of ten, how old are they now?

45. You have a huge box of beautiful decorated
tiles, enough to provide a border in two rooms.
You really can't figure out how to arrange them,
however. If you set a border of two tiles all
around, there's one left over; if you set three
tiles all around, or four, or five, or six, there's
still one tile left over. Finally; you try a block
of seven tiles for each corner, and you come out
even. What is the smallest number of tiles you
could have to get this result?

46. A car company sold 150 cars in a special
6-day tent sale offer. Each day the company sold
6 more cars than the day before. How many cars
were sold on the 6th day?

47. When the two met, one was half the other's
age plus seven years. Ten years later, when they
married, the bride was thirty, but this time one
was nine-tenths the age of the other. How old
was the groom? ( no fractions, no partial years---whole
numbers only.)

48. Mona and Allen went shopping for groceries.
They spent half of what they had plus $2.00 at
the butcher shop. At the dairy, they spent half
of what was left, plus $5.00. At the bakery, they
spent half of what was left. The remaining $5.00
was spent on coffee and cake. How much did they
start with?

49. Take the number of your fingers (10) multiplied
by the number of you toes (10) divided by one
half and add it to the number of months in a year.
What is the total?

50. A mother and father have six sons and each
son has one sister. How many people are in that
family?

51. Jenn has half the Beanie Babies that Mollie
has. Allison has 3 times as many as Jenn. Together
they have 72. How many Beanie Babies does each
girl have?

52. Kevin is 14 inches taller than George. The
difference between Kevin and Richard is two inches
less than between Richard and George. Kevin at
6'6" is the tallest. How tall are Richard
and George?

53. A baseball team had just won the championship
game and the players wanted to congratulate each
other. They began shaking hands, but each player
only shook hands with every other player just
once. There are, of course, only 9 players on
a baseball team. How many times did the players
shake hands?

54. A jar has 4 amoebas in it to start. Amoebas
split their cells in two ( therefore doubling
in size) once every minute. The jar will be completely
filled in 10 minutes. How long would it take to
fill the same sized jar if had 8 amoebas in it
to start?

55. There are 100 golfers in the local match
play contest. If a player loses a match, he is
immediately eliminated from the contest. How many
matches will be played to determine the winner?

56. Two trains are on a head on collision course.
The trains are currently 65 miles apart. The north
bound train is traveling at 55 miles per hour
and the south bound train is traveling at 80 miles
per hour. What is the distance between the trains
two minutes before they collide?