- Simplify the expression (x+a)(x–b)(x+c) ··· (x–z).
- Arrange the integers 1 through 15 in a row so that the sum of any two

adjacent integers is a perfect square. - What is the smallest number that when divided by each of the digits 1

through 9 leaves no remainder? - Find five different whole numbers, all less than nine, such that the sum

of three of them equals the sum of the other two, and also the sum of the

squares of the first three equals the sum of the squares of the other two. - Find a 6-digit number such that if you transfer the two left-most digits

to the right, the new number is double the original. - One year on the fourth of July, Samantha figured that there were 73 days

until her birthday. What are the day and month of Samantha's birthday?

If the fourth of July that year was on a Wednesday, what day of the week

was Samantha's birthday that year? - 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? - Why are the digits 8, 5, 4, 9, 1, 7, 6, 3, 2, 0 arranged in this order?
- Twin primes are prime numbers that differ by two, for example 3 and 5.

There are eight pairs of twin primes less than 100. Find them. - Mrs. Chambers is buying Christmas presents for her seven 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? - 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? - What is the weight of a fish that weighs six pounds plus half its weight?
- The Yankees and the Tigers play five baseball games. They each win three.

No ties or disputed games were involved. How could this be? - Two fathers and two sons own 21 horses. They're moving to different

parts of the country and want to divide the horses equally among

themselves. How is this possible? - Write the number twelve thousand twelve hundred twelve in simplest form.
- How many balls are needed for a single elimination Ping-Pong tournament

if a new ball is used for each match and there are eight participants?

12 participants? 25 participants? N participants? - 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? - 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? - 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? - 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 three

faces, two faces, one face, and no faces? - An ant is determined to climb a flagpole that is 18 feet tall. Each day

the ant climbs five feet, but each night he slips back three feet. When

will the ant reach the top of the flagpole? - What is the smallest number of coins needed to give exact change for any

amount less than a dollar? - Write 25 as the sum of consecutive integers.
- When does 10 + 4 = 2?
- A rectangular flag has three vertical stripes of equal width. If

adjacent stripes may not be the same color, how many different flags may

be made with cloth of five colors? - Find four 3-digit numbers that are the sum of the cubes of their digits.
- Find the simplest operation that will make 606 greater by 50%.
- Divide 60 into four parts such that the first increased by four, the

decreased by four, the third multiplied by four, and the fourth divided

by four, are all the same number. - Find 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. - Three men play a game in which the loser doubles the money of each of the

other two. After three games each has lost once, and each has $24. How

much did each have to start? - 159 X 48 = 7632 -- Find another pair of numerals with a product such that

each non-zero digit is used once and only once. - Find three numbers such that their sum is a square and the sum of any

pair is also a square. - 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. - a X b X c = 1729. Each letter names a prime number. Find them.
- 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? - It takes four seconds for a clock to strike three times. How long will

it take to strike eleven times? - Two cars are behind two cars, two cars are ahead of two cars, and two

cars are between two cars. What is the least number of cars? - If it takes 3 ½ minutes to fry one egg, how long will it take to fry four?
- That man's father is my father's son. Who is that man?
- What is the fewest 40,000-mile tires you would need to drive a car

130,000 miles? - What is the largest number expressed with exactly four 1s and no other

digits? - What is the ones digit of 31,003?
- What bowling score is achieved with alternating strikes and spares? Does

it matter whether a strike or spare comes first? - Write 1000 using eight 8s.
- A regular octahedron has faces that are equilateral triangles. What

geometric figure is formed if the centers of the adjacent triangles are

connected? - Find all 2-digit numbers that with their reversals sum to perfect squares.
- 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? - Express 100 using five 5s.
- The difference between two numbers is 40. The difference between their

squares is 4800. What are the numbers? - Cora has a penny, a nickel, a dime, and a half-dollar. How many

different amounts can she make using these coins? - What are the next four numbers in this progression? 12,1,1,1,2,1,3,....
- Write 18 as the sum of consecutive integers.
- What cube has surface area equal to its volume?
- How many 2-digit numbers have a 5 as a digit?
- Find n such that n, n+99, and n+200 each are square numbers.
- How many times a day does the hands of a clock make a 47° angle?
- What part of ½ sq ft is ½ ft square?
- How many times is the digit 9 used in writing the numerals from 1 to 100?
- What is the probability of rolling a pair of standard dice and obtaining

a sum divisible by three? - Use each of the digits once and only once to compose two fractions whose

sum is 1. - What is the largest amount of change you can have and still not be able

to change a dollar? - What combination of whole numbers that adds up to 12 has the greatest

product? - How many different scores is it possible to make in three rolls of two

standard dice? - In 1980, Laura's age was the square root of the year in which she was

born. How old was she? - A grocer has a balance and four weights with which he can correctly weigh

any whole number of kilograms from 1 to 40. What weights does he have? - How many 3-digit numbers are palindromes?
- Find three numbers such that the product of any two added to the third

gives a square. - Find four whole numbers whose sum is equal to their product.
- If I have a penny, a nickel, a dime, and a quarter, how many different

amounts can I pay without requiring change? - The difference between the squares of two consecutive odd numbers is 40.

What are the numbers? - 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? - 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 four in line? - 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 two 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? - Find a 2-digit number that is twice the product of its digits.
- Express 100 as the product of two factors in which all the digits are

contained in order. - 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? - 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? - 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? - Harry has three sisters and five brothers. His sister Harriet has S

sisters and B brothers. What is the product of S and B? - 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? - 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 three friends have? - Find 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. - Three men play a game in which the loser doubles the money of each of the

other two. After 3 games each player has lost once, and each has $24.

How much did each player have to start? - Mrs. Chambers is buying Christmas presents for her seven 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? - Twin primes are prime numbers that differ by two, for example, 3 and 5.

There are eight pairs of twin primes less than 100. Name them. - 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?