The area of the first page of a 100-page book is 666 square centimeters.
What is the area of all pages on one side?
The mass of Earth is 5.9742 x 1024kg,
the mass of Venus is 4.8685 x 1024kg.
The mass of Mars 6.4185 x 1023kg.
The mass of Moon is 7.3477 x 1022kg
What is largest mass from the following?
The total weight of Bob and his sister Anna is 155 kilograms. Bob's weight is 2 kilograms more than twice Anna's weight.
What is Anna's weight?
A group of 7 adults and 8 young children want to rent sailing boats. Each boat holds 3 people, and there must be at least one adult in each boat.
How many boats will the team need?
Alex, Bill, and Craig have a combined weight of 120 kilograms.
Alex weighs 40 kilograms and Bill weighs seven-eighths of Alex's weight.
What is Craig's weight in kilograms?
Anna wants to earn exactly 5 points.
The ducks give different points.
How many different ducks will she take?
A letter in the English alphabet has four times as many letters after it as before it.
Find the letter.
The sum of four consecutive numbers is 2010.
What is the sum of all the digits of these four numbers?
12 students are evenly spaced on the circumference of a big circle.
They are numbered from 1 to 12.
Which number is opposite 8?
Eugenia is 9 year-old.
What is the largest number of birthdays she can celebrate in 1,111 consecutive days?
There are 4 cards with numbers. They are arranged from smallest to largest.
The difference between any two neighboring numbers is the same.
The value of the third card is:
The length of a soccer pitch is 110 meters and the width is 66 meters.
The diameter of the soccer ball is 22 centimeters (0.22 meter).
How many soccer balls are needed to fill the pitch?
Three boys put $52, $60, and $70 in a piggy bank.
Alex is 100 cm tall.
Bill is 20% taller than Alex.
Craig is 20% taller than Bill.
How should the money be split if it is distributed as a ratio that is proportional to the heights of the children?
Alex paints twice as fast as Bill and three times as fast as Craig.
It takes them 30 minutes to paint a fence.
How long would it take Alex if he works alone?
The pages of a book are consecutively numbered from 1 through 999.
How many digits are there in this numbering?
There are 72 rabbits in Funnytown.
The population of rabbits in Funnytown doubles every 8 months.
How long ago was the population of rabbits less than ten?
Each child in a family has at least 3 brothers and 4 sisters.
What is the smallest number of children their parents might have?
The time on a digital clock reads 9:43.
What is the shortest length of time, in minutes, until all of the digits are equal to each other?
Five apples weigh the same as 24 eggs.
Two pineapples weigh the same as 32 eggs.
How many apples weigh the same as three pineapples?
Swiss trains leave from Zurich for Geneva every hour.
The trip takes three hours.
Each train waits one hour at the destination city and then returns back.
After another one hour break, it starts the trip again.
How many trains are needed to cover a period of twenty-four hours?
A cube consists of small black and white cubes.
Two small cubes of the same color never share a common face.
Which number is the greatest?
I enclosed 9 apple trees using a large square fence.
What is the smallest number of square fences I need to add in order to separate all the trees?
A number is said to be perfect if it is equal to the sum of its divisors.
For example, 6 is a perfect number because 1 + 2 + 3 = 6 .
What is the next perfect number?
The matchsticks make four small squares and one big square.
How many matchsticks do I need to remove so that there are no squares in the picture?
Find the minimum number.
There are three mothers and three daughters in a group of people.
Each mother has a daughter in the group.
What is the smallest possible number of people in the group?
Each child in a family has at least one brother, two sisters, and two parents.
What is the fewest number of children their parents might have?
In a football tournament, every team plays a match against every other team once and only once.
If 6 matches are played in total, how many teams participated?
Two hundred employees work for company XYZ, where the ratio of men to women is 11 to 9.
If 30 men leave the company and 10 women are hired, what is the new ratio of men to women?
X = 2 x 2 x 3 x 5 x 7 x 7 x 11 x 13 x 17 x 19
is not evenly divisible by a number.
Which is the number?
I want to move just one matchstick to make the equation correct.
From which part will I take the matchstick?
2889 digits are used to number the pages of a book beginning at page 1.
How many pages does the book have?
Four sisters are all 2 years apart in age.
The total of their ages is equal to 28 years.
How old is the youngest sister?
My neighbor works 5 days per week and sells three times more flowers on Friday than the other days. How much does she sell on Friday if she earns $4900 in flower sales every week.
In a competition, 16 teams play each of the other teams twice.
What is the total number of games played during the competition?
What is the largest possible number of pieces you can produce if you cut a round pizza by 4 straight cuts?
Note: you can move the pieces.
Anna bought jellybeans. She gave 9/11 of them to Bill.
If Anna kept 18 jellybeans, how many jellybeans did she buy in total?
Eight people pay $6.50 each for a meal in a restaurant.
They leave a 10% tip for the waiter.
How much change do they receive from 3 $20 notes?
The photograph courtesy of Roland Sauter
A student has 2 shirts (black and white), 2 pants (black and white), 2 ties (black and white), and 2 hats (black and white) to choose from.
How many different outfits can be assembled?
John read a 294-page book in 2 weeks. He read every day including weekends.
How quickly does John read?
Jim is training for a race. He uses this map to find possible routes. He choose 4 routes.
Find the longest route.
The diagram shows some of the results of a six-person contest, each player having just one match against each other player.
An arrow pointing from one player to another means that the first player defeated the second player in their match.
What is the largest number?
David built a display stack using 8 layers of cans.
How many cans did he need to build the eighth layer of the stack?
The Chinese Calendar is based on a twelve-year cycle.
Each year in the cycle corresponds to an animal:
Tiger, Rabbit, Dragon, Snake, Horse, Sheep, Monkey, Rooster, Dog, Pig, Rat and Ox.
The order of the animals never changes.
The year 2010 in the Chinese calendar is the Year of the Tiger.
Which animal marked the year 2111?
What is the smallest integer that can be written entirely with zeros and 2s and is evenly divisible by 30?
44 students are evenly spaced on the circumference of a big circle.
They are numbered from 1 to 44.
Which number is opposite 37?
Ninety-nine people stand in a line (queue) to buy tickets to a match.
There are enough tickets for each person to purchase two tickets.
Each person in the beginning of the queue buys five tickets until there are none left.
How many people do not receive any tickets?
Dick is three years older than two times Joanna's age.
If Joanna is j years old, how would you calculate Dick's age?
With the cash in her pocket, Mrs. Smith can either exactly afford ice cream cones for all her family including the baby and animals OR three huge cigars for her beloved husband John.
A cigar is worth $7.
Find the price of an ice cream cone.
NOTE: Smoking is harmful to your health.
If 3 of every 120 astronauts are NOT married, then what is the percentage of all astronauts that are married?
Multiply the largest two-digit number by the smallest two-digit number and add 100.
What is the result?
Tricky Equation Puzzle: the equation below is wrong:
12 + 3 = 4
Which numeral has to be moved to make the equation correct?
Roman numerals are a numeral system of Ancient Rome based on letters of the alphabet.
For example, XCVII is 97 (100 – 10 + 7).
What is the value of CCCLV?
A glass holds 180 ml of juice when it is one third empty.
How much does it hold when it is one third full?
In a class of 42 children there are twice as many girls as boys and twice as many boys as redheads.
How many redheads are there?
In a paper box, two thirds of the pieces of fruit are apples.
The rest are oranges.
My guests ate three quarters of the apples and three fifths of the oranges.
How many pieces of fruit are still in the box?
Anna, now 18 years old, is three times as old as her brother.
How old will she be when she is twice as old as her brother?
A boat can hold a maximum of two people.
The width of a lake is about 200 meters from the South bank to the North bank.
What is the minimum distance the boat must travel to transport 7 people across the lake.
A basket full of coconuts weighs 39kg.
A half-full basket weighs 21kg.
How many kilograms of coconuts fit into the basket?
Evguenia tried to sell her car for $50,000.
Nobody bought it. She decided to discount it by 40%.
What is the new price of the car?
A swimming school costs $129 a month, but costs $1,390 annually if you pay the yearly fee at the beginning.
How much do you save if you pay the yearly fee at the beginning?
In a country, students attend school 200 days in a year.
What part of the year do they attend school?
I bought 3 ice-creams.
I gave the cashier $20 and got $9.50 change.
What is the price of an ice-cream?
A hockey league consists of 6 teams, with 100 players in total.
Each team has at least 15 players.
What is the largest possible number of players in a team?
Gerry drove 210 miles from home to his college and used 14 gallons of gasoline.
His girlfriend, Jane, drove 200 miles from her home to the college and used 12 gallons of gasoline.
Whose car had better gas mileage?
The 136 sixth graders and their 8 teachers will be taking a trip together.
If each bus holds 36 passengers, how many buses does the school need to use?
Three U.S. coins add up to $1.
If one of them is not a half dollar, what is the smallest-value coin?
Gerry wants to share the chocolate bar equally with five of his friends by breaking it into equal pieces.
How many pieces does each friend get?
In a pizzeria, you pay $7 for each of the first three pizzas, and $6 for the following pizzas.
How many pizzas did Gerry's band buy, if they paid $45?
I choose a positive integer, add 3, multiply by 6 and divide the result by itself and receive an odd number.
What was the original number?
Kate has five haystacks in one field and one haystack in another.
How many haystacks would she have if she combined them all in one?
Jane lives exactly in the middle on a short street.
How many houses are there in the street if her house number is 6?
Andrew is shorter than Blake but taller than Carter.
Dylan is taller than Ethan but shorter than Andrew.
Who is the tallest?
Jane races on a circular track.
Her bicycle tire has a circumference of 1.5 m. She rides 18 laps of 400m.
How many full rotations will her tire make?
The unit price of a thingamajig is $3.50.
If I buy 10, the unit price drops to $2.00.
At what quantity does it become more costly to buy them singly than to just buy 10?
(Thingamajig is something whose name you have forgotten or do not know.)
Author: Leslie Green
6 boys and 12 girls attend prom at the Cool High School. If each of the boys dances once with each of the girls and the boys were always occupied, how many dances occur in total?
(NOTE: We are not counting the individual couples. We just count the number of dance sessions, regardless of how many couples are on the dance floor.)
The playing cards shown need to be sorted into increasing order with the lowest card on the left. Each move consists of picking up a card and inserting it anywhere in the line, including at the beginning or at the end. The cards slide sideways to allow a card to fit in between if necessary.
Which is the fewest number of moves possible?
Author: Leslie Green
If Edgar cleans his teeth twice per week and changes the toothbrush every time he uses it, how many brushes does he need every year?
What is the main difference between the pictures on the left page and on the right page?
The problem is similar to 100 Bongard Problems on visual pattern recognition.
If you pick 3 apples a day and you eat 4 apples every fifth day, how many apples will you have after 5 weeks?
Eight apples are worth three oranges.
I bought all these fruits for $5.
How much would 24 apples and 24 oranges cost altogether?
There are rabbits and eagles in a zoo.
There are 29 heads and legs in total.
How many animals are there?
On an island, kids always tell the truth and the adults always lie.
Which of them could make the following statement?
"I always lie."
In 2 seconds, Benny Bunny jumps 4 meters.
How long does it take Benny Bunny to jump a 50 meters race?
In the game of noughts and crosses (tic-tac-toe) the winner is the player who gets three of their symbols in a straight line, with each player placing their symbol alternately.
In this game, noughts has started and it is now the turn of crosses to make their move.
Which move by crosses carelessly forces a win for noughts?
Author: Leslie Green
These guys gallop at speed of 25 km/h and walk on foot 10 times slower.
How much time does it take for them to ride to a stable, which is 5 km away and come back on foot?
How many seconds are there in the second hour of the second day of the second month of the second year of the second century?
When my car's tank is a quarter empty my car can drive 240km more than when it is a quarter full.
How many kilometers can it drive when the tank is full?
One third of the solar panels must be repaired.
If the set is a rectangle 32 panels in length and 15 panels in width, how many panels must be repaired?
Three parrots sleep one after another.
Sunny sleeps 3 hours, then
Buddy sleeps 4 hours, and then
Twitty sleeps 5 hours, then Sunny takes the lead again.
How much time does Buddy sleep per day?
Two pineapples together weigh 2kg.
If the larger pineapple costs $3 and the smaller $2, how much does the larger pineapple weigh, assuming that pineapples are priced at a fixed value of dollars per kilogram?
John works one 42 hour week in Switzerland and one 35 hour week in France.
What is the difference between his Swiss and French weekly income if he earns 20 Euros per hour in both countries?
Leslie Green asks:
I would like to weigh myself, but neither of the two bathroom scales available to me can take my somewhat chunky weight. Also, both are broken in the sense that they have zero offsets, and the zero offset button does not work. I have checked the scales with a 20kg weight, and both read correctly when their offset is taken into account.
The left scale reads +1.1kg when unloaded. The right scale reads -0.6kg when unloaded.
I stand on both scales at the same time, one leg on each, although my weight distribution is not necessarily equal.
The left scale reads 48.1kg and the right scale reads 37.3kg.
What is my actual weight?
Jane has invited several guests to her party, but is unsure if the total headcount will be 6, 7 or 8. She wants to prepare a fruit dessert such that regardless of how many people show up, she can serve all the collected cherries equally to everyone.
What is the minimum number of cherries she will need to collect?
Gerry dries grapes and obtains 6 kg of raisins out of 21 kg of grapes.
How many kilograms of grapes are needed in order to get 8 kg of raisins?
In the Smith's family every child has at least one brother and at least two sisters.
What is the smallest possible number of children in the Smith's family?
Anna, Betty and Cindy have 36 apples between them.
Betty gives 7 apples to Cindy, Cindy gives 6 apples to Anna, and Anna gives 2 apples to Betty.
Now each of them has the same number of apples.
How many apples did Cindy have initially?
How many phrases below are spelled the same written forward as backward?
Samples of Palindromes
Madam, I’m Adam
Top of spot
No lemon, no melon
Two fathers, two sons, and two doctors had a healthy breakfast.
Each person ate an apple.
What is the least possible number of apples that have been eaten?
With uncharacteristically mathematical insight, John's dad has realised that there is a cost associated with being an unpaid taxi service for John.
John's dad has costed this as $3 for fuel plus an arbitrary $3 "annoyance cost", since John's trips seem to increasingly occur during live sports events on TV.
If a new bicycle costs $200, after how many of these trips will John's dad feel that he is profiting by just giving John a new bicycle, allowing John to make his own way?
by Leslie Green
I recently heard a riddle, and I wrote down what I heard.
"What can be black and white, but is red all over?"
Gerry has $7, Jane $20, and Kate as much as Gerry and Jane together.
If they put their money together and share it equally among them, how much more money does Gerry get?