A recipe to make a cake for 66 people uses 3333 grams of sugar.
How much sugar would be required to serve 88 people?
The price of a T-shirt on sale is $19.99.
The store reduced the original price by 20%.
Estimate the original price of the T-shirt.
Tom drives for 3 days.
On the second day he drives 2 km more than a quarter of the distance he drove on the first day.
On the third day he drives 3 times as far as he did on the second day.
If he drove a total of 888 km, what distance did he drive on the first day?
Anna's income is seven-eighths that of Beatrice. Anna's expenses are seven-eighths those of Beatrice.
The girls spend less than they earn.
Who saves more money?
Anna wants to score exactly 33 points.
The ducks give different points.
How many ducks will she take?
Remember, there may be more than one correct answer.
The diagram shows some of the results of a six-person contest. There are two matches left for everybody.
An arrow pointing from one player to another signifies that the first player defeated the second player in the match. For example, player A defeated player C in their match.
Which player has the most difficult matches left to play?
Jane and Gerry are playing a card game.
Without looking, a card is drawn from the cards shown here. If an even number card is drawn, Jane wins. If an odd number card is drawn, Gerry wins.
Is this a fair game?
John read a 165-page book in 11 days. Every day, he read 1 page more than the day before.
How many pages did he read on the first day?
The left 11-tooth gear turns at 124 revolutions per minute.
The middle gear has 22 teeth. The third gear has 44 teeth.
At how many revolutions per minute is the third gear turning?
The first six numbers in a sequence are shown on the right.
What is the 66th number in the sequence?
A class of 44 students is divided into 4 groups.
Each group contains at least 2 students.
Which of the following statements is always true?
How many years ago did you have more than one thousand ancestors?
Assume that the time lag between two generations is 25 years. Try to find the minimal possible value.
There is a set of 9 numbers: 1,2,3,4,5,6,7,8,9.
Five numbers are selected from the set and added together.
The remaining four numbers are also added together. These two sums are then multiplied.
What is the maximum possible product?
I arrange five marbles randomly in a ring.
There are two green and three blue marbles.
What is the probability that no two green marbles are adjacent?
A girl was born in the 20th century.
Take away from her year of birth the sum of the four numerals that make it up.
You will end up with a number divisible by X.
Source: Berrondom, Marie Mathematical Games, 1983
The matchsticks make a spiral that goes clockwise.
How many matchsticks do I need to move to make the spiral go counterclockwise?
Find the minimum number.
The figure shows a triangle made of discs.
I want to move the discs and turn the triangle upside down.
What is the lowest possible number of moves that I must make?
Two rectangles enclose five regions.
Find 2 figures that can form the largest number of enclosed regions.
You can move and rotate the shapes.
A password consists of five digits, 0-9.
How many passwords are there that read the same backwards as forwards?
Yellow Taxi Service charges $1.20 for the first mile and $.79 for each additional mile.
How far could I go for $20 if I gave the driver a $3 tip?
An integer consists of 2010 digits such that any consecutive 10 digits are different.
What is the sum of all digits?
Twelve couples met at a party.
Each person shook the hand of each of the other people except their beloved spouse.
How many handshakes were there?
There are 24 balls in the box. X of them are white.
When we add 12 white balls, the probability of picking a white ball doubles.
There are four brothers in a family.
The sums of the ages of three of them are 30, 32, 32 and 35.
What is the age of the eldest brother?
Bill buys oranges at five for $1 and sells at one for $5.
How many oranges does he need to sell to make a profit of $96?
I have apples and paper boxes.
If I place 8 apples into each box, I will have one box left over.
If I put 7 apples into each box, I will have one apple left over.
How many paper boxes do I have?
What is the probability that the next person you meet is George Washington, the first president of the United States?
It takes two painters 4 days to paint a house.
The older painter would only take 6 days to do the job on his own.
How many days would the younger painter take to paint the house on his own?
Two apples and two peppers have the same weight as three eggs.
Six eggs and one pepper balance five apples.
How many peppers does it take to balance one apple?
A group of gentlemen visited a produce shop.
Each gentleman bought the same number of apples as the other gentlemen.
Each gentleman bought the same number of tangerines as the other gentlemen.
The price of an apple is $3.
The price of a tangerine is $5.
How many apples did they each buy if together they paid $91?
I must balance any whole number load from 1kg to 40kg using these four weights and a balance.
What is the largest weight?
Based on 20 years per generation, estimate the number of ancestors John has in 200 years, if none of them appears more than once in the list.
A kitten has a 50/50 chance to be male or female.
My cat just delivered two adorable kittens.
My veterinarian said that at least one of them is female.
What is the probability that the other kitten is a boy?
I sold two cars and received sixty thousand dollars for each car.
I received 50% profit on one of the transactions and lost 40% on the other.
What is my net profit on the two transactions?
Every year on my son's birthday, I put multiples of one thousand dollars in his bank account that are equivalent to his age in years.
After his 20th birthday, I stopped the deposits and he started to withdraw money according to the same rule: -$21,000, -$22,000 and so on.
How many years can he withdraw money from the account?
Sixty-five students want to share 15 melons.
They decide that four boys share a melon and five girls share a melon.
How many girls are there?
Bill (B), Cindy (C), and Daniel (D) work on a project.
(1) Together, B and C can complete it in 10 days.
(2) Together, C and D can complete it in 12 days.
(3) Together, D and B can complete it in 15 days.
How many days are needed for Bill to complete the project?
A magician placed 3 bowls of fruit in 3 closed boxes and 10 people tried to guess which fruit was in which box.
One person guessed all 3 fruits correctly, 3 people guessed only 1 fruit correctly.
How many people did not guess any fruit correctly?
It takes exactly 1 hour to burn a rope when I light one of its ends.
The rate of burning is completely random, but the final result is always 1 hour.
How many different periods of time can I measure with 2 such ropes?
Three glasses contain orange juice.
The first one is 15% full, the second is 50% full, and the third is 55% full.
Water is added to fill each glass completely.
All drinks are then poured into a large jar.
Which fraction of the mixture in the jar is orange juice?
Many people stand in a line (queue) to buy tickets to a match.
There are enough tickets for each person to have two tickets.
Instead, every person in the beginning of the line buys three tickets until there are none left so 14 people are left without tickets.
How many people were there in the line to begin with?
In the first week John made $1.
He made 4 times more than the previous week if the week was odd, and 2 times less if the week was even.
How many weeks did he work before becoming a millionaire?
Twenty years ago, Bob was four times as old as Anna.
Today, he is twice as old as Anna.
How old is Bob today?
Twelve European teams enter a football tournament.
Each team plays one match against each of the other teams, with three points for a win, one point for a draw and none for a defeat.
The probability of a draw is 0.2.
What is the most likely score of a team?
Anna traveled 3600 miles in a car.
She had five tires and changed them such that each tire was used over the same distance.
For how many miles was each tire used?
On January 1st, Anna and Bill have $55 each.
Each month Anna saves $5 more than she spends while Bill spends $5 more than he saves.
At the beginning of what month is Anna 10 times richer than Bill?
Anna bought 1 slice of mushroom pizza and 2 slices of cheese pizza for a total of $4.
Bill bought 2 slices of mushroom pizza and 3 slices of cheese pizza for a total of $7.
What is the cost of one slice of mushroom pizza?
There are a number of apples, all of different weights.
The 10 lightest apples weigh 30% of the total weight.
The 10 heaviest apples weigh 35% of the total weight.
How many apples are there?
John has just had a 1% pay rise.
He used to earn $5000 a month.
He told his wife that the rise was a half of a percent.
How much more money does he keep for personal spending this year?
Logic puzzle: a secret door.
A man approached the door of a secret laboratory and the door robot said "SIX." The man replied, "THREE" and was let in.
Another day, the robot said, "TWELVE."
The man replied, "SIX" and was let in.
Today, the robot said, "TWENTY."
What should the man say?
The figure shows a triangle made of discs.
I want to move two discs and turn the triangle upside down.
How many different ways can I do this if a disc moves less than its three-diameter distance?
In a house, there are three switches on the ground floor and a light bulb in the cellar. I cannot see the light from the ground floor.
What is the minimum number of trips to the cellar I need to make to identify which switch corresponds to the light bulb?
We assume that the bulb in the cellar works, that there is power to the house, and that one of these three switches will switch on the cellar light.
Anna, Beatrice, and Cindy run a 1000-meter race.
All of them run at a constant speed.
Anna beats Beatrice by 100 meters.
Beatrice beats Cindy by 100 meters.
By how many meters does Anna beat Cindy?
Brett, Cindy, and Daniel each launch a 100-day project.
On day 100, Brett completed his project, at which point Cindy had completed 90% of her project.
When Cindy completed her project, Daniel had completed 90% of his project.
What part of the project was completed by Daniel on day 100?
At a party 60% of the boys are dancing with 90% of the girls.
How many people are dancing if there are 50 people?
There were nine knights in a kingdom and enough hay to feed their horses for three winter months.
The winter lasts five months.
Five knights were killed and their horses were sold after the first month of the winter.
Will there be enough hay to feed the horses that remain?
I want to measure exactly six minutes using only a five-minute hourglass and a four-minute hourglass.
How many times do I flip over an hourglass?
Count the initial flip(s) and find the minimum possible number.
A series of 10 books were published at one-year intervals.
The sum of the publication years was 20,005.
When was the first book published?
Five pirates capture some treasure.
They divide the coins and find that there are 2 coins left over.
They throw one pirate overboard and split the coins again: there are 3 coins left over.
They throw another pirate over. This time, two coins are left over.
They throw another pirate over. This time, one coin is left over.
What is the fewest number of coins there could have been?
There are four new projects in a company.
The sums of the budgets of three of them are 30, 32, 32, and 35 million dollars.
What is the budget of the largest project?
A rich man is saving for a new car.
He sets up an automatic transfer of $1000 that posts every January 1st to a special no-interest account. At the end of every month, he withdraws $50 for leisure.
The car costs $25,000.
How many years will it take him to save up for the car?
Three years ago there were 32 people in our company, and the ratio of men to women was 5 to 3.
Since then, the same number of men and women have joined so that the ratio is 7 to 6 now.
How many people are there in the company now?
A 40-month long project is divided into three consecutive activities.
The duration of the middle activity is 10 months.
What is the time between the midpoints of the other two activities?
A leading supplier left a solar plant project seven months after the project started.
It decreased the productivity of the project team by 25%. The duration is inversely proportional to the productivity.
How much longer does the project last if its initial planned duration was 19 months?
In a test of 50 questions, the final score is calculated by subtracting three times the number of wrong answers from the number of correct answers.
If Gerry attempted all questions and received a final score of 22, how many correct answers did he give?
Greg takes 100-point tests.
He wants to achieve an average grade of at least 90 on three tests.
What is the lowest possible score he could have made on the third test if his first two test scores were 82 and 92?
The theory of relativity connects the mass at high speed with initial mass, the velocity of the object v, and the speed of light c.
How much heavier is a bullet that navigates at 60% of the speed of light?
Gerry lives 50 miles away from Jane.
He drives to Jane's house at 60 miles per hour and comes back at 40 miles per hour.
What is his average speed for the entire trip?
A math test has 40 questions worth 100 points.
The test consists of multiple-choice questions worth 3 points each and True/False questions worth 2 points each.
How many points does Gerry get if he answered correctly on all multiple-choice questions and incorrectly on half of the other questions?
Gerry bought 3 oranges and 8 apples for $5.
The next week he bought 8 oranges and 3 apples for $10.
What is the most expensive fruit and by how much?
Three positive whole numbers have the same answer added together or when multiplied together.
How many sets of such numbers exist?
In a village, there are 100 families with either one child or none. This is a traditional old village with only man/woman families.
A wealthy man decided to donate $10 to men, $20 to women, and $100 to children.
How much money does he need to prepare if 20% of the families have no children?
We need 200 tons of such stones to pave a city square.
How much stone do we need if each dimension of the stone doubles?
A grocery store lowered the price of coconuts from 49 cents to 48 cents.
For $100, how many more coconuts could I buy now than before?
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 times he could have opened his mouth today?
In a room, there are 3 bosses, 2 wives, and a plumber.
What is the least possible number of people in there?
Sammy the sea lion has spotted a gorgeous Lady sea lion before anyone else. She is in the sea and he is on the beach. The picture shows the distances in hundreds meters. He needs to get to her as soon as possible to avoid any potential rivals getting to her first.
He can travel three times faster in the sea compared to on the sandy beach over the distances involved.
Which route should he use?
The problem was suggested by Leslie Green
A certain Professor of Statistics is trying to explain to his grandson that once an event has happened its probability of happening is 1 because it is certain that it happened. The grandson disagrees.
The grandson throws a pair of dice and as they are about to settle puts a bowl over them, preventing the Professor from seeing the result. The grandson then peeks at the dice, knowing the value. He then explains that he could now show these dice to an infinite number of people, other than the professor, and yet the professor still could not declare with certainty what the result was, despite the fact that on average, everybody knew!
What can we say with certainty about this situation?
Author: Leslie Green (Leslie is not a Professor of Statistics)
Three observers, not more than 1km apart on flat windless terrain, report the same event quite differently.
They meet up later. Amy says the low frequency sound occurred first, followed by the high frequency sound about 1 second later. John says she is an idiot and claims the high frequency sound happened first, followed by the low frequency sound. Their teacher recorded the event and can prove that both sounds occurred within 0.01 seconds of each other, but being a kind teacher doesn’t actually tell them they are both stupid.
Which possible true statement demonstrates the least incompetence in the observers. . .
(HINT: the speed of sound does not change significantly for the frequencies heard, and there are no temperature gradients or fog to consider.)
Author : Leslie Green
There are three goddesses named Mendax, Fidelis and Furtibus; one on your left, one on your right, and one in front. You do not know which is which. Fidelis always answers correctly. Mendax only answers falsely. Furtibus always answers in a way intended to best hide its identity.
You must determine which goddess is which using the minimum number of YES/NO questions. Each question is heard and answered by all three goddesses. That counts as one question.
How many questions do you need to ask in order to be certain?
[You should ideally think up actual questions before answering!]
Author : Leslie Green
Inspired by G. Boolos. 'The hardest logic puzzle ever', The Harvard Review of Philosophy (6), 1996.
One invention saves 20% on fuel; a second, 30%; and a third, 50%. If the carmaker uses all three inventions at once how much does the car save?
The ratio of women to men at a 100-employee company is 1 : 4.
The company wants to change the proportion to 1 : 2.
How many women must be hired to reach the goal?