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1. |
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Arrange
the integers 1 through 15 in a row so that the sum of any 2 adjacent
integers is a perfect square.
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2. |
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What is
the smallest number that when divided by each of the digits 1 through 9
leaves no remainder?
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3. |
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Find 5 different whole numbers, all less than 9, such that the sum of
3 of them equals the sum of the other 2, and such that the sum of the
squares of the first 3 equals the sum of the squares of the other 2.
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4. |
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Find a
6-digit number such that if you transfer the 2 left-most digits to the
right, the new number is double the original.
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5. |
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One year
on the 4th of July, Samantha figured that there were 73 days until her
birthday. What are the day and the month of Samantha's birthday? If the
4th of July that year was on a Wednesday, what day of the week was
Samantha's birthday that year?
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6. |
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In a
gaggle of geese and a flock of sheep, there are 98 eyes and 162 legs.
How many geese and how many sheep are there?
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7. |
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Why are
the digits 8, 5, 4, 9, 1, 7, 6, 3, 2, 0 arranged in this order?
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8. |
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Twin
primes are prime numbers that differ by 2, for example 3 and 5. There
are 8 pairs of twin primes less than 100. Find them.
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9. |
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Mrs.
Chambers is buying Christmas presents for her 7 children to give each
other. If each child gives one present to each of the others, how many
presents will Mrs. Chambers have to buy?
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10. |
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If the
eggs in a basket are counted by 2s, 3s, 5s, or 7s, there is one egg left
each time. What is the smallest number of eggs that could be in the
basket?
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11. |
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What is
the weight of a fish that weighs 6 pounds plus half its weight?
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12. |
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The
Yankees and the Tigers play 5 baseball games. They each win 3. No ties
or disputed games were involved. How could this be?
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13. |
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Two
fathers and 2 sons own 21 horses. They are moving to different parts of
the country and want to divide the horses equally among themselves. How
is this possible?
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14. |
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Write the
number twelve thousand twelve hundred twelve in simplest form.
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15. |
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How many
balls are needed for a single elimination Ping-Pong tournament if a new
ball is used for each match and there are 8 participants? 12
participants? 25 participants? N participants?
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16. |
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My age
this year is a multiple of 7 and next year it will be a multiple of 5. I
am not yet 50; can you tell how old I am? What if you know that I am
over 30?
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17. |
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I have
$1.15 in coins, but I cannot make change for a dollar, a half-dollar, a
quarter, a dime, or a nickel. What coins do I have?
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18. |
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A clock
strikes the hour on the hour. It strikes twice on each half hour and
once on each quarter hour. How many times does it strike in each 24-hour
period?
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19. |
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A wooden
cube is painted orange on all sides. It is then sliced into 27 equal
smaller cubes. How many of the smaller cubes are orange on 3 faces, 2
faces, one face, and no faces?
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20. |
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An ant is
determined to climb a flagpole that is 18 ft tall. Each day the ant
climbs 5 ft, but each night he slips back 3 ft. When will the ant reach
the top of the flagpole?
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21. |
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What is
the smallest number of coins needed to give exact change for any amount
less than a dollar?
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22. |
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Write 25
as the sum of consecutive integers.
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23. |
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When does
10 + 4 = 2?
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24. |
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A
rectangular flag has 3 vertical stripes of equal width. If adjacent
stripes may not be the same color, how many different flags may be made
with cloth of 5 colors?
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25. |
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Find four
3-digit numbers that are the sum of the cubes of their digits.
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26. |
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Find the
simplest operation that will make 606 greater by 50%.
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27. |
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Divide 60
into 4 parts such that the first increased by 4, the second decreased by
4, the third multiplied by 4, and the fourth divided by 4, are all the
same number.
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answer |
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28. |
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There is a
2-digit number such that its square and its fifth power contain together
all the digits from 1 to 9, each once and only once. Find it.
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answer |
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29. |
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Three men
play a game in which the loser doubles the money of each of the other 2.
After 3 games each has lost once, and each has $24. How much did each
have to start?
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30. |
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159 X 48 =
7632
Find another pair of numerals with a product such that each non-zero
digit is used once and only once.
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answer |
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31. |
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Find 3
numbers such that their sum is a square and the sum of any pair is also
a square.
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32. |
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Ramanujan's number is the smallest number that can be written two
different ways as the sum of two cubes. Find Ramanujan's number and the
two ways it can be written as the sum of two cubes.
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answer |
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33. |
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a X b X c
= 1729. Each letter names a prime number. Find them.
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34. |
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30 people
numbered 1 to 30 are equally spaced around a circular table. What is the
number of the person seated directly across from the person numbered 23?
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answer |
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35. |
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It takes 4
seconds for a clock to strike 3 times. How long will it take to strike
11 times?
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answer |
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36. |
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Two cars
are behind 2 cars, 2 cars are ahead of 2 cars, and 2 cars are between 2
cars. What is the least number of cars?
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answer |
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37. |
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If it
takes 3 ½ minutes to fry one egg, how long will it take to fry 4 eggs?
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answer |
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38. |
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That man's
father is my father's son. Who is that man?
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answer |
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39. |
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What is
the fewest 40,000-mile tires you would need to drive a car 130,000
miles?
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40. |
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What is
the largest number expressed with exactly four 1s and no other digits?
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41. |
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What is
the ones digit of 31,003?
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42. |
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What
bowling score is achieved with alternating strikes and spares? Does it
matter whether a strike or spare comes first?
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43. |
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Write 1000
using eight 8s.
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44. |
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A regular
octahedron has faces that are equilateral triangles. What geometric
figure is formed if the centers of the adjacent triangles are connected?
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45. |
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Find all
2-digit numbers that with their reversals sum to perfect squares.
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46. |
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If 120
seats are arranged in a row, what is the least number of seats that must
be occupied so that the next person seated must sit next to someone?
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47. |
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Express
100 using five 5s.
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48. |
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The
difference between 2 numbers is 40. The difference between their squares
is 4800. What are the numbers?
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49. |
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Cora has a
penny, a nickel, a dime, and a half-dollar. How many different amounts
can she make using these coins?
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50. |
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What are
the next 4 numbers in this progression?
12,1,1,1,2,1,3,....
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51. |
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Write 18
as the sum of consecutive integers.
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52. |
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What cube
has surface area equal to its volume?
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53. |
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How many
2-digit numbers have a 5 as a digit?
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54. |
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Find n
such that n, n+99, and n+200 each are square numbers.
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55. |
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How many
times a day does the hands of a clock make a 47° angle?
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56. |
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What part
of ½ sq ft is ½ ft square?
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57. |
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How many
times is the digit 9 used in writing the numerals from 1 to 100?
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58. |
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What is
the probability of rolling a pair of standard dice and obtaining a sum
divisible by 3?
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59. |
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Use each
of the digits once and only once to compose 2 fractions whose sum is 1.
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60. |
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What is
the largest amount of change you can have and still not be able to
change a dollar?
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61. |
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What
combination of whole numbers that adds up to 12 has the greatest
product?
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62. |
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How many
different scores is it possible to make in 3 rolls of 2 standard dice?
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63. |
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In 1980,
Laura's age was the square root of the year in which she was born. How
old was she?
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64. |
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A grocer
has a balance and 4 weights. With them he can correctly weigh any whole
number of kilograms from 1 to 40. What weights does he have?
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65. |
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How many
3-digit numbers are palindromes?
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66. |
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Find 3
numbers such that the product of any 2 added to the third gives a
square.
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67. |
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Find 4
whole numbers whose sum is equal to their product.
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68. |
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If I have
a penny, a nickel, a dime, and a quarter, how many different amounts can
I pay without requiring change?
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69. |
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The
difference between the squares of 2 consecutive odd numbers is 40. What
are the numbers?
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70. |
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Five
friends are comparing heights. Joe is 5" taller than Sue. Sue is 8"
shorter than Bob, who is 6" taller than Tom. Mary is 5' 3" tall and 2"
shorter than the next shortest person. How tall is Tom?
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71. |
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Abigail,
Beth, Chuck, and Dave are waiting in a single file line at the movie
theater. Chuck is ahead of Dave but behind one other person. Abigail is
ahead of Beth who is ahead of one other person. What is the order of the
4 in line?
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72. |
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A girl
bought some pencils, erasers, and paper clips at the school supply
store. The pencils cost $.10 each, the erasers cost $.05 each, and the
paperclips are 2 for a penny. If she bought a hundred items for a total
cost of $1.00, how many items of each kind did she buy?
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73. |
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Find a
2-digit number that is twice the product of its digits.
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74. |
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Express
100 as the product of 2 factors in which all the digits are contained in
order.
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75. |
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A box
contains pennies, nickels, and dimes. If each nickel is replaced with a
quarter, the amount doubles. If each dime is replaced by a quarter, the
amount will also double. What is the smallest possible amount in the
box?
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76. |
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Twenty-four (24) is one short of a square and its double is also one
short of a square, what is the next number with the same property?
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77. |
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Amoebas
grow by simple division, each split taking one minute. If, starting from
a single amoeba, a container fills to capacity in an hour, when will it
be half full?
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78. |
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Harry has
3 sisters and 5 brothers. His sister Harriet has S sisters and B
brothers. What is the product of S and B?
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79. |
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A 4 x 4 x
4 cubical box contains 64 identical cubes that exactly fill the box. How
many of these small cubes touch a side or the bottom of the box?
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80. |
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Three
generous friends, each with some cash, redistribute their money as
follows: Amy gives enough money to Jan and Toy to double the amount that
each has. Jan then gives enough to Amy and Toy to double their amounts.
Finally, Toy gives Amy and Jan enough to double their amounts. If Toy
has $36 when they begin and $36 when they end, what is the total amount
that the 3 friends have?
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81. |
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There is a
2-digit number such that its square and its fifth power contain together
all the digits from 1–9, each once and only once. Find it.
Check answer |
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82. |
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Three men
play a game in which the loser doubles the money of each of the other 2.
After 3 games each player has lost once, and each has $24. How much did
each player have to start?
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83. |
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Mrs.
Chambers is buying Christmas presents for her 7 children to give to one
another. If each child gives one present to each of the others, how many
presents will Mrs. Chambers have to buy?
Check answer |
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84. |
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Twin
primes are prime numbers that differ by 2, for example, 3 and 5. There
are 8 pairs of twin primes less than 100. Name them.
Check answer |
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85. |
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If the eggs in a basket are counted by 2s, 3s, 5s, or 7s, and there
is one egg left each time, then what is the smallest number of eggs that
could be in the basket?
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