ID 855

A recipe to make a cake for 66 people uses 3333 grams of sugar.

How much sugar would be required to serve 88 people?

ID 860

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.

ID 864

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?

ID 865

Anna's income is seven-eighths that of Beatrice. Anna's expenses are seven-eighths those of Beatrice.

The girls' expenses are less than they earn.

Given that the girls save all that remains from their earnings after their expenses are paid, who saves more?

ID 877

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.

ID 880

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?

ID 881

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?

ID 885

ID 886

ID 887

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?

ID 893

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?

ID 894

The first six numbers in a sequence are shown on the right.

What is the 66th number in the sequence?

ID 901

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?

ID 908

ID 911

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.

ID 912

ID 913

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?

ID 914

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?

ID 917

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.

Find X.

Source: Berrondom, Marie Mathematical Games, 1983

ID 983

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.

ID 984

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?

ID 985

Two rectangles enclose five regions.

Find 2 figures that can form the largest number of enclosed regions.

You can move and rotate the shapes.

ID 1034

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?

ID 1220

An integer consists of 2010 digits such that any consecutive 10 digits are different.

What is the sum of all digits?

ID 1273

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.

Find X.

ID 1355

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?

ID 1368

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?

ID 1376

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?

ID 1377

What is the probability that the next person you meet is George Washington, the first president of the United States?

ID 1378

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?

ID 1392

ID 1430

ID 1440

ID 1469

ID 1553

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?

ID 1561

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?

ID 1698

I must balance any whole number load from 1kg to 40kg using these four weights and a balance.

What is the largest weight?

ID 1778

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.

ID 1833

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?

ID 1928

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?

ID 1944

ID 1945

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?

ID 2000

Sixty-five students want to share 15 melons.

They decide that four boys will share a melon, and five girls will share a melon.

How many girls are there?

ID 2027

ID 2215

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 on his own?

ID 2232

ID 2243

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?

ID 2244

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?

ID 2252

ID 3127

Three identical 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?

ID 3130

ID 3132

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?

ID 3139

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?

ID 3169

ID 3171

Twenty years ago, Bob was four times as old as Anna.

Today, he is twice as old as Anna.

How old is Bob today?

ID 3187

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?

ID 3206

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?

ID 3268

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?

ID 3287

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?

ID 3329

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?

ID 3358

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?

ID 3419

ID 3487

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?

ID 3505

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?

ID 3558

ID 3587

Logic riddle:

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.

ID 3604

ID 3623

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?

ID 3626

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?

ID 3635

At a party 60% of the boys are dancing with 90% of the girls.

How many people are dancing if there are 50 people?

ID 3658

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?

ID 3684

ID 3707

ID 3715

ID 3717

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.

ID 3969

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?

ID 3971

ID 4056

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?

ID 4109

ID 4119

ID 4123

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?

ID 4170

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?

ID 4177

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?

ID 4238

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?

ID 4346

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?

ID 4417

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?

ID 4482

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?

ID 4495

ID 4576

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?

ID 4585

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?

ID 4595

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?

ID 4624

ID 4628

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?

ID 4630

ID 4647

Three positive whole numbers have the same answer added together or when multiplied together.

How many sets of such numbers exist?

ID 4656

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?

ID 4693

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?

ID 4731

ID 4832

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?

ID 4896

ID 4899

ID 4924

ID 4953

ID 4979

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?

ID 5007

ID 5050

In a room, there are 3 bosses, 2 wives, and a plumber.

What is the least possible number of people in there?

ID 5166

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

ID 5218

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)

ID 5223

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

ID 5236

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.

ID 5256

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?

ID 5302

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?

ID 5320

On an European island,

18 are kids, 28 are divorced, 38 are married, and the others are single people.

If there are 55 houses and all single and divorced people live in separate houses how many people live on the island?

ID 5357

Leslie Green asks:

Peter changes his old fashioned single 100W incandescent light bulb to a super efficient 4 LED bulb system which gives the same light output, but only consumes 20W in total.

Estimate the electrical energy saving per year if the bulbs are switched on for 8 hours every day of the year.

(1 kWh is 1000 Watts for 1 hour)

ID 5364

A shopkeeper purchased 300 bulbs for $0.95 each.

However, every 25^{th} bulb was damaged and had to be recycled.

The remaining bulbs were sold at $1.25 each.

What will be the profit percentage?

[Don't count the labor, tax and other expenses.]

ID 5372

Leslie Green asks: "My neighbor Timmy has developed a complicated set of rules for choosing girlfriends.

He likes: all girls with long hair; all girls who are not tall; tall girls who wear glasses; short-haired girls who don't wear glasses.

Can you simplify the rules without changing the requirements?"

ID 5473

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 computer scientist. His tests played an important role in the disciplines of cognitive psychology and cognitive science.

ID 5480

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.

ID 5536

ID 5614

Alec, Beatrice, Crystal and Douglas opened their Christmas presents.

Alec opened 3 presents.

Beatrice opened 5 presents.

Crystal opened 12 presents.

How many presents were opened by Douglas?

ID 5680

ID 5686

The knight jumps either 2 squares vertically and 1 horizontally, or 2 squares horizontally and 1 vertically, as shown in the picture.

What is the total number of squares that can be attacked by the knight from the current position in 2 moves?

ID 5730

Mark, who has been a digital design engineer for many years, is celebrating his 55^{th} birthday. Since the use of 55 candles for a birthday cake seems excessive, he arranges 7 candles in a line and lights the appropriate candles to represent his age in binary, a lit candle representing a “1” state for that bit.

How many candles does he light?

Author: Leslie Green

ID 5754

The typical human blink is 200 milliseconds.

Generally, between each blink is an interval of 2–10 seconds.

Estimate the percent of our daytime we blink.

ID 5797

A teacher set a strange rule for a concert visit of his class.

What is the maximum number of boys that can sit in a row of 35 chairs, if seated boys must be separated by at least two girls?

ID 5839

Eleven players are standing in a soccer pitch such that the distance between each pair is distinct. Each player has a ball, and when the trainer blows a whistle, each player kicks his ball to the nearest player.

Which is true?

ID 5841

There are 100 prisoners in a city prison.

Every week a new prisoner comes in and half or less of them leave the prison.

How much time passes till the moment when there are no prisoners in the prison?

ID 5845

Three cantons are being allocated 22 seats in a Parliament. Canton A has 27% of the population, canton B has 33%, and canton C has 40%. The seats are counted by rounding to the nearest integer.

How many seats does canton C get?

ID 5862

Achilles and the Tortoise

The Paradox of Achilles and the Tortoise was described by the Greek philosopher Zeno of Elea in the 5th century BC. The great hero Achilles challenges a tortoise to a footrace. He agrees to give the tortoise a head start of 100m. When the race begins, Achilles starts running, so that by the time he has reached the 100m mark, the tortoise has only walked 10m. But by the time Achilles has reached the 110m mark, the tortoise has walked another 1m. By the time he has reached the 111m mark, the tortoise has walked another 0.1m, then 0.01m, then 0.001m, and so on. The tortoise always moves forwards while Achilles always plays catch up.

Why is Achilles always behind the tortoise?

ID 5940

The **contrapositive** of a logical statement is formed by negating both the test and the result and then changing their order. For example:

If [this is my house ] then [the door is black].

Becomes

If [the door is not black] then [this is not my house].

Which is a correct contrapositive of

If [this is a fish] then [it cannot live out of the water for very long].

Author: Leslie Green

ID 5990

Barber paradox

In a city, the barber is the 'one who shaves all those, and those only, who do not shave themselves.'

Who shaves the barber?

A barber (from the Latin barba, 'beard') cuts, dresses, grooms, styles and shaves men's and boys' hair.

ID 6071

ID 6132

ID 6228

Old 20th Century Liar Riddle:

Alex says that Beth tells lies.

Beth says that Craig tells lies.

Craig says that both Alex and Beth tell lies.

Who is telling the truth?

ID 6261

Four teams are in group A of a soccer (football) tournament for young girls.

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.

If the two teams that pass to the next stage get 5 and 4 points and there were only two draws in the group, how many points do the two other team obtain together?

ID 6275

John is on a fixed income. His monthly budget is spent as follows:

Food 10%

Rent 50%

Entertainment 10%

Savings - anything left over.

Suddenly the cost of food rises by 10%. The rent is increased by 5%.

By how much does his monthly savings decrease?

Author: Leslie Green

ID 6296

Logic Puzzle.

A European country has the lowest birth rate in the world.

What is the first letter of the country name?

ID 6348

Susan is walking down the road in a northerly direction at 3 mph. There is a crosswind of 4 mph.

What is her resultant speed?

Author: Leslie Green

ID 6368

Leslie Green asks a logic question:

John has 1/2 of an apple.

Jane has 1/3 of an orange.

Between them they have ...

ID 6447

Leslie Green asks:

A boy throws a very bouncy rubber ball directly down onto a hard concrete floor from a height of 1.5 m.

To what height does the ball bounce?

ID 6563

There are 12 words in the question below.

How many letters are there in the word which is spelt differently?

ID 6636

Big Deal Store bought tin soldiers, five for $160, and sold them four for $200.

They made $360 profit yesterday. How many tin soldiers did they sell?

ID 6721

Leslie Green asks:

Here is a number sequence with a definite mathematical rule to move from one digit to the next.

8, 1, 7, 0, 3, 6, . . .

The tricky thing is that one digit (not necessarily at the end) has been deleted from the sequence, but which digit?

(*Hint: This is just mathematics. It works in any language, not just English.*)

ID 6722

The figure shows a triangle made of 4 rows of coins.

We move three coins and turn the triangle upside down.

What is the lowest possible number of coins that I must move to turn a triangle with 7 rows?

ID 6737

Leslie Green asks:

A shop is offering a luxury food item at half price. It is not close to its "sell by" date.

How is this economically viable?

ID 7036

A mule travels along a special path 500 times today.

Two of his legs travel 1 kilometer more than two others.

What is the shape of the path?

ID 7044

A mule travels along a special circular path 500 times today.

Two of his legs travel 1 kilometer (1000 meters) more than two others.

What is the width between the mule's left and right legs?

ID 7065

A rich father gave the eldest son half of his gold ingots plus an extra ingot.

Then he gave the second son half of what was left plus an extra ingot.

Finally he gave the youngest son half of what was left plus an extra ingot.

He then had no gold left.

How many ingots did the rich man have?

ID 7180

*Leslie Green* asks:

Since we don't actually speak Greek, putting the Greek letters in the correct order can be problematic.

The intention was to write: alpha, beta, gamma, delta, epsilon, from left to right.

Did we succeed?

ID 7267

ID 7270

Gerry said that the pin-code of his phone is the last four digits of the number *&π*.

What is his pin-code?

ID 7280

Gerry has a 100-digit secret number.

The first digit is 9, and the following numbers are formed as double the last known digit.

What is the last digit of the number?

ID 7294

Twenty knights have a dinner. Each knight says a statement.

First knight says: At least one of the statements is false.

Second knight says: At least two of the statements are false.

Third knight says: At least three of the statements are false.

. . .

Twentieth knight says: At least twenty of the statements are false.

How many statements are true?

ID 7298

Gerry has quarters (25-cent coins), dimes (10-cent coins) and pennies (1-cent coins).

What is the largest amount of money that he can choose from the pile and still won't be able to give you exactly $1 (100 cents) from the money?

ID 7305