Daniel is two years older than three times Joanna's age.
If Joanna is j years old, how would you calculate Daniel's age?
Daniel is two years older than three times Joanna's age.
If Joanna is j years old, how would you calculate Daniel's age?
John packs 10 CDs in a box.
If he has 123 CDs of one type, and 45 of another, how many boxes would he need in order to pack them all while not mixing the types?
Tim is building two hamster cages in the shape of rectangular prisms. The first cage is 44 cm long, 33 cm wide and 33 cm high. The second cage has the same width, but is 10% longer and higher.
What is the difference between the volumes of the cages?
Of the 26 capital letters, how many are symmetrical along both the vertical and the horizontal axes?
Pipe 1 can empty a full tank in 1 hour. Pipe 2 can empty the tank in 2 hours.
If both pipes are used, how long will it take to empty the tank?
Kate ties the leash of her dog to the corner of a garden.
The leash is 3 meters long.
Over how many square meters can Kate's dog wander?
The number of strawberry cones sold at an ice cream store was 1 more than 3 times the number of vanilla cones sold.
A total of 601 cones were sold.
How many vanilla cones were sold?
Alex needs six tacks to fix two rectangular pictures because he can overlap the pictures.
What is the least number of tacks he needs to tack eleven pictures?
The picture shows the first five notes of the tune 'We Wish You A Merry Christmas'.
How many different melodies can be composed by these five notes?
Water flows through two pipes from F to G.
As shown, there are four taps, A, B, C, and D, which can be opened or closed.
There are 24=16 different ways of setting the taps.
How many of these 16 ways will allow water to flow from F to G?
There is a set of 10 numbers. Five numbers are selected from the set and added together.
The remaining five numbers are also added together. These two sums are then multiplied.
Find the maximum possible product of the multiplication.
John's dad pays him 80 cents for each correct answer he provides in his math homework and fines him 20 cents for each incorrect answer.
Today, John received $15 after completing 50 problems.
How many problems did John answer correctly?
Five students put their sandwiches into five paper bags. The bags are randomly distributed to the students.
What is the probability that all the five students receive the correct bag?
Eugenia's grandmother bought a new car for $55,000 in 1970.
The car depreciated in value 10% each year until 1990.
After 1990, it increased in value by 10% each year.
How much was the car worth in 2010?
I want to put exactly 4 liters of milk into a large tub with a capacity of roughly 10 or 11 liters. I have available a 5-liter bucket and two 3-liter buckets.
What is the least amount of milk needed to complete this operation?
A password consists of three digits, from 0 to 9, followed by a capital letter from an alphabet having 26 letters.
Repetition of digits is allowed.
Determine the number of different passwords that can be created.
The product of four consecutive whole numbers is 3024.
What are these numbers?
Source: Berrondom, Marie - Mathematical Games, 1983
It takes 2 cards to build a single-storey card house.
It takes 7 cards to build a 2-storey card house.
It takes 15 cards to build a 3-storey card house.
How many stories can you build with 60 cards?
Is the number of people in the world that has shaken hands with an odd number of people odd or even?
Source: Fixx, James F. - Solve It!, 1978
A lady always arrives at the train station at exactly six o'clock to pick up her husband and drive him home. One day the man arrives an hour early, starts walking home, and is picked up by the lady on his way out to the train station. They arrive at home twenty minutes earlier than usual.
How long did he walk before he met his wife?
Source: Fixx, James F. - Solve It!, 1978
It takes Alex 20 minutes to paint a fence while it takes Bill 30 minutes to paint the same fence.
How long would it have taken if they worked together?
There are 40 boys and 60 girls in Funnytown.
There are 50 men and 50 women in Funnytown.
What is the percentage of boys in the town?
For every birthday of John's life he puts as many dollars in a piggy bank as his age in months.
There are 1440 dollars in the bank.
How old is John?
Jim won a contest in which the prize was his weight in U.S. dimes (1 dime = 10 cents).
If a dime weighs 2.7 grams and if Jim weighs 54 kilograms, how much money did he win?
Anna had an average score of 90 on her first ten tests.
Her average after all twelve tests was 80.
What was the average score of her last two tests?
The sum of three different positive integers is 33.
The smallest and the largest integers differ by 22.
How many different 3-number sets satisfy the conditions?
Juice is poured from a full 1 L bottle into an empty glass until both the glass and the bottle are 80% full.
What is the volume of the glass?
Mrs. Smith has 80 birds: geese, hens and ducks.
The ratio of geese to hens is 3:1.
60% of the birds are ducks.
How many geese does Mrs. Smith have?
It takes six people 48 hours to paint a house.
How long would it take to paint the house if three people were added in the middle of the project?
A girl is 10 years old.
She is five times older than her dog.
In how many years will she be twice as old as her dog?
Figure out the smallest difference between two four-digit integers, each contains all of the digits 6 ,7, 8 and 9?
How many crosses can you place on a Tic-tac-toe board without making three-in-a-row in any direction?
Eight students travel in a car.
They speak English, French and Spanish.
Everybody speaks two languages.
Four students speak French.
Five students speak Spanish.
How many students speak English?
Roman numerals are a numeral system of Ancient Rome based on letters of the alphabet.
For example, XCVII is 97 (100 – 10 + 7).
Which year that has passed consists of the largest number of symbols when expressed in Roman numerals?
Mathematical Pie , 1984
In a football tournament every team plays a match against every other team once and only once.
If 120 matches are played in total, how many teams participated?
How many different lines that extend to infinity in both directions can you draw through any two of these ten points?
I throw a fair die until 1 is obtained.
What is the probability that this will happen on the second throw?
A straight line and two circles are drawn to form several bounded regions.
For example, the picture on the right shows 4 bounded regions.
What number of regions is NOT possible?
If each row and each column of the square must contain exactly one triangle, circle, pentagon, and rhombus, which shape must be placed in the empty white cell?
Twenty-two performers have numbers 1 to 22.
A couple finds that their numbers add to a perfect square.
What is the largest possible difference between the two numbers?
A 200-dollar stock loses $40 of its value for a week.
What percent of increase will recover all of its lost value?
Anna began eating 25 jellybeans at a rate of 1 every 5 minutes.
Eleven minutes later, Bill joined her, and ate at a rate of 1 every 4 minutes.
Who ate more jellybeans?
A company initially planned for sixty people to complete a project in 100 days.
If the number of people is decreased by 10, what is the delay in the time to completion for the project?
John is going to repair his house. There are three major activities:
electrical installation takes 3 man-days;
sanitary installation takes 4 man-days; and
garden work takes 5 man-days.
His neighbor Mary agrees to participate in the project. They have the same skills and productivity, but refuse to work on the same activity at the same time.
What is the shortest project duration if they work together?
Four sisters are all 30 months apart in age.
The total of their ages is equal to 31 years.
How old is the youngest sister?
The difference between a two-digit number and the two-digit number obtained by interchanging the positions of its digits is 72.
What is the sum of the two digits of that number?
John received a pay raise due to extraordinary performance.
He decided to not to work on Friday so that his overall pay would remain unchanged.
What is the pay raise?
An amoeba is a shapeless unicellular organism.
An amoeba propagates by simple division into two amoebas; each split takes 3 minutes to complete.
At noon, 0.1% of a Petri dish was filled with amoebas.
At what time will the dish be full?
Ninety-nine percent of John's nuts and 99% of a nut cost as much as all his nuts. How many nuts does he have?
The ratio of goats to tigers in a zoo is 3:2.
There are a total of 100 animals in the zoo.
10% of the animals are goats and tigers.
How many goats are in the zoo?
Anna spent $8.99 on groceries. She bought three liters of milk and 20 cereal bars.
Three cereal bars cost the same as one liter of milk.
How much does one cereal bar cost?
Which statement is CORRECT?
Here,
'even' is an even number;
'odd' is an odd number;
{Evens} = 2Z = {..., -6, -4, -2, 0, 2, 4, 6, ...}
{Odds} = 2Z + 1 = {..., -5, -3, -1, 1, 3, 5, ...}.
Eleven men met at a conference.
Each man shook hands with each of the other men exactly once.
How many handshakes took place?
For every birthday, John's parents put as many dollars in a piggy bank as his age in years.
The total in the piggy bank is $120.
How old is he?
Eugenia, the magician, receives a 50% discount every time she asks for the price.
She bought a $200 puppy for less than $1.
How many times did she ask for the price?
A melon slice weighs 5kg, and 96% of the weight is from water.
After lying in the sun, the water makes up 75% of the weight.
Estimate the new weight of the slice in kg.
For every birthday of John's life he puts as many dollars in a piggy bank as his age in months.
There are 1092 dollars in the bank.
How old is John?
A password consists of four digits and the repetition of digits is not allowed.
Determine the number of different passwords that can be created.
Here, a password consists of four capital letters from A to Z.
How many passwords are there that read the same backwards as forwards?
Anna had an average score of 90 on her first nine tests.
Her average after all ten tests was 91.
What was the score on her last test?
If nine hens can lay six eggs in two days, how many hens would be needed to lay 20 eggs in three days?
Tree diagrams present the hierarchical structure of schools or companies.
Which diagram has the largest number of hierarchical levels?
Anna ran in the north direction at a speed of 3 miles per hour, Bobby ran west at a speed of 4 miles per hour, and their dog, Rex, was running between them at a speed of 9 miles per hour.
What was the distance between the children in one hour?
Several students want to rent a car for the next weekend.
If each contributes $19, they lack $10.
If each contributes $21, they have an extra $10.
How many students are there?
Seventy-five percent of the apples in a box and seventy-five percent of an apple cost the same as all of the apples in the box.
How many apples are there in the box?
I want to move just two matchsticks to make the equation correct.
How many different ways are there to do this?
Twelve years ago, Bill was twice as old as Anna.
Twelve years on from now, she will be 7/10 of his age.
How old is Anna now?
A boy has as many sisters as brothers, but each of his sisters has three times more brothers than sisters.
How many sisters are there in the family?
A four-letter word can be written forward, backward or upside down while remaining the same word.
What is the first letter of the word?
Mount Everest is the Earth's highest mountain with a peak at 8,848 meters (29,029 ft) above sea level.
Indian mathematician Radhanath Sikdar was the first to identify Everest as the world's highest peak in 1852. Edmund Hillary and Tenzing Norgay reached the summit on 29 May 1953.
What was the highest mountain in the world before Mount Everest was discovered?
The numbers are the total of the values of the symbols within each column and row.
What should replace the question mark?
A car weighs 997kg when empty and 1234kg when John, his sister Jane, and their two parents are inside.
Find the weight of the parents if they are twice as heavy as the children.
The pie chart represents the results of an election.
The least lucky candidate received 10%, while the most lucky candidate won the election, receiving three times as many votes as the second-placed candidate.
What percentage of votes did the winner receive?
Metro Card prices: a single ride is $2.5 and a 7-day Metro Card costs $29.
How much will you save weekly using the 7-day Metro Card if you ride 3 times every day except Saturday and Sunday?
At the beginning, the girl rode 6 km in the first 15 minutes and then 4 km in the next 10 minutes.
Which statement is true?
The diagram shows the lowest point and the highest point of our planet.
What place is the closer for John who lives in London?
Source: Nelson Thornes New Maths in Action. 2004
Mrs. Smith has three sons who played hockey, two sons who played basketball, one of these sons played two sports, and one son who smokes and does not play any sports.
How many sons does she have?
NOTE: Smoking is harmful to your health.
According to Wikipedia Mrs. Vassilyeva holds the record for most children: she gave birth to a total of 69 children: sixteen pairs of twins, seven sets of triplets and four sets of quadruplets between 1725 and 1765, in a total of 27 births.
How many single children were born?
How many days does Bob work every year if he does not work on weekends and has a 3-week summer vacation and 7 days of official holidays?
How many days does Bob work in 40 years of his career if he does not work on weekends and has a 3-week summer vacation and 7 days of official holidays?
A $1 bill measures 156 mm long and weighs approximately 1 gram.
How much does a million dollars in $1 bills weigh?
Gerry and Jane spent a week on an island and they ate only coconuts.
Gerry had already eaten half of the coconuts when Jane ate half of the remaining coconuts plus four more.
There are no coconuts left.
How many coconuts did they have?
A hospital needs 168 pills to treat 6 patients for 2 weeks.
How many pills does it need to treat 8 patients for 3 weeks?
In a room, there are 3 bosses, 2 wives, and a plumber who works for the government.
What is the least possible number of people in there?
If the height of the tower is 88 mm, how many pens are needed to build a tower that is 1000 mm high?
Sales for a business doubled or tripled every year and increased from 1 million dollars to 36 million dollars.
How many times did the sales double in that period of time?
When Pinocchio lies, his nose gets twice as long.
When he tells the truth, his nose gets 1 cm shorter.
His nose was 1 cm long in the morning, and it is 10 cm long in the evening.
What is the least number of lies he could have told today?
Three parrots yell at Gerry every 2, 3 and 4 seconds, respectively.
If they start yelling at Gerry at 6:00:00, how many seconds will elapse until they yell at Gerry at the same time again?
Bob works for 40 years. He does not work on weekends, has a 3-week summer vacation, and 7 days of official holidays. The average hourly rate is $12.5 and he works 8 hours per day.
What is his total income?
Leslie Green asks:
It is difficult to see a 2% price difference between food items in two different food stores, but the difference becomes noticeable over time.
If the weekly family shopping bill is $200, how much money does a 2% reduction make over the course of a year.
Most solids expand when heated and contract when cooled.
Does a hole in a shaft of metal get bigger or smaller when you heat the metal?
If 30 students occupy 2/3 of the seats in the classroom, how many students would occupy 4/5 of the seats in the classroom?
A triggerfish with a snout like a pig is the national fish of Hawaii and its name is
humuhumunukunukuapua’a
How many times does the word have to be written to write the letter "u" more than 100 times?
Photo source: Wikipedia
Answer the traditional English-language nursery rhyme in the form of a riddle:
"As I was going to St Ives
I met a man with seven wives
Each wife carried seven sacks
Each sack carried seven cats
Cats, sacks, man, and wives
How many were going to St Ives?"
Leslie Green commented: "This is a variant of a traditional old rhyming puzzle, often interpreted as a trick question by assuming that the group was travelling away from St Ives.
Here we explicitly state that the narrator travels more rapidly than the cat-carrying crowd, and catches them up on their way to St Ives."
According to The New York Times the average New Yorker produces nearly three pounds of garbage every day.
If the average weight of a New Yorker is 165 pounds, how many times does he/she produce the garbage that is equals to his/her weight every year?
A 52-page newspaper "The Daily Dog News" consists of 13 double sheets. Edgar chooses one of these sheets at random and adds the four page numbers of the sheet.
What sum does he get?
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.
M. Bongard (1924 – 1971) was a Russian computer scientist. His tests played an important role in the disciplines of cognitive psychology and cognitive science. Bongard died in 1971 during a hiking expedition in the Pamir Mountains.
I am listening to a 1-hour audiobook.
If I play the same audiobook at 1.25x speed, then how many minutes will it run?
Their names start with letters A, B, and C.
The girl says "My name starts with A."
The boy says "My name starts with B."
The dog says "Woof."
If we know that at least one of them lied, what is the first letter of the girl?
I am 180 cm tall.
If snow falls at a rate of 0.1 cm every 6 minutes, then how many days will it take for 180 cm of snow to fall?
Brainteaser: A word becomes shorter when you add two letters to it.
How many letter are there in the word?
While going from home to a shop, Jane counted nineteen parked cars on the left side and saw a river bank on the opposite side. While returning back to her home, she counted nineteen parked cars on the right side.
How many cars are parked there between her home and the shop?
A white hen lays an egg every third day.
A black hen lays an egg every second day.
How many eggs in total do a white hen and a black hen lay in November?
Gerry works 2 hours per day on Monday, Tuesday and Friday, and 3 hours per day on Wednesday and Thursday. He does not work on Saturday and Sunday. He earns $264.
How much does he earn per hour?
A wall is being built with bricks of 10 cm height. The joints between the bricks are filled with a mortar (cement) layer that is 1 cm thick. Bricks are placed so that each joint is at the midpoint of a brick in the row below. In every other row 2 half bricks are placed at the ends. The two half bricks are made from a single brick. Imagine that the wall is 2 bricks wide.
What is the minimum number of bricks needed to build such a wall that is higher than 200cm?
The picture shows a project plan. Arrows indicate where an activity must be finished before the next activity can start. The number shows the duration of the activity in days.
What is the duration of the project?
Last year my piggy bank weighed 800 grams.
This year it weighed 1 kg (1000 grams).
With what percentage did its weight increase?
Swiss car sharing system Mobility provides its 133,000 customers with 3,000 vehicles. They are usually red.
On average, production of a new car generates emissions of CO2 of 15,000 kg = 15 tons.
If all these customers refuse to use the car-sharing system and buy a new car, how much additional CO2 is emitted into the atmosphere?
Benny Bunny has three types of carrots of lengths 10cm, 15cm and 17cm.
What is the least number of carrots he can use to mark out a distance of 111cm?
Five gentlemen ran in an election.
Four hundred people voted.
The winner beat his opponents by 1, 2, 3, and 4 votes, respectively.
How many percent of the votes did he receive?
Leslie Green asks:
Here is a number sequence with a definite mathematical rule to move from one number to the next.
2, 5, 23, 47, 95
The tricky thing is that one number (not necessarily at the end) has been deleted from the sequence, but which number?
(Hint: This is just mathematics. It works in any language, not just English.)
Having just won the lottery, Jeff has gone from tossing burgers for a living to being a multi-millionaire. Sadly his wealth has increased faster than his EQ (Emotional Quotient) can handle. He demands that the bath in his new mansion be ripped out and replaced by one twice as big. When the tradesmen try to make suggestions he just shuts them up angrily, and tells them to do exactly what he asked for, no more and no less, without adding in any complexity.
Jeff gets in the bath whilst filling it, but as it gets nearly full it breaks through the ceiling and plummets onto the marble floor below.
What went wrong?
Author: Leslie Green
Twenty-five students go to school in a bus.
Each girl is sitting with a boy, and a third of the boys are sitting separately.
How many boys are there in the bus?
Granny gives a full bottle of natural juice in return for five empty bottles.
You have 33 empty bottles and you can use them to get full juice bottles.
How many filled bottles will you be able to drink?
One-fourth of the cars in a car park are 4x4.
Another car arrives and now one-third of the cars are 4x4.
How many cars are now in the car park?
The cards have a number or letter on one side and a color on the other side.
Every card that shows an even number on one side has the color green on the other side.
How many cards do you need to flip to be sure that the rule is valid for all the cards?
An even number is an integer which is evenly divisible by 2 : 0, 2, 4, 6, 8, . . .
Leslie Green asks:
What is the secret message in the text below?
Mary Evans eventually took Michael, Ewan, and Tom Maudsley into Downton, not into Glasgow’s heavy traffic.
Which statement is NOT correct?
How many cubes will balance one sphere?
How many generations forward must you go in order to have more than one thousand ancestors?
How many of the first 100 integers are divisible by either 2 or 3?
What does the algorithm say?
Thinking outside the box: 
A boy scored 28 times or 35% in a series of kicks. 
How many steps are required to break the Swiss chocolate bar into 1 x 1 pieces? 
Estimate what part of the rectangle is blue.
Adding a letter to a word makes it odd. 
What is half an hour added to 0.45 hours? 
Len's number is 31. 
A brick weighs 5 pounds and half a brick. 
Which proverb has a different meaning than the other three?
Something gets wetter the more it dries.