ID 587

ID 591

Americans measure the temperature in ^{o}F.

Europeans measure the temperature in ^{o}C.

The formula to convert Fahrenheit to Celsius is:

c = 5 (f - 32) / 9

where / is the symbol for division, f represents the temperature in ^{o}F and c represents the temperature in ^{o}C.

What is the temperature in ^{o}F when it is 20^{o}C?

ID 600

Jim bought a laptop at 25% off the regular price of $500.00.

He also bought a printer at 50% off the regular price of $250.00.

Find the amount of his discount.

ID 605

A new road is being constructed to re-route its flow around the exterior of a wildlife preserve.

The figure shows the original straight road (S_{1}) and the new road (S_{2}).

How many extra kilometers will people have to drive once the new road is constructed?

ID 610

The drama club is selling tickets to a play for $8 per ticket.

The cost to rent the theater and costumes is $500.

In addition, the printers are charging $1 per ticket to print the tickets.

What is the minimum number of tickets the drama club must sell to make a profit?

ID 615

Jack went for a drive. Before he left, he noticed that the gas tank was 3/4 full. When he returned home, the gas tank was 1/6 full. The gas tank holds 60 liters.

How many liters of gas did the car use on his drive?

ID 617

ID 620

John wants to build a wooden fence around his garden.

He is considering four different designs for the garden.

Which design shows the longest fence?

ID 621

A city of 1,111,000 residents had a total of 111 car accidents in 1999.

There are 111,000 cars in the city.

There were no accidents the following year.

How would you describe the percent change in car accidents?

ID 622

A particular stock is valued at $40 per share.

The value increases by 25% and then decreases by 20%.

What is the value of the stock per share?

ID 625

ID 628

Three friends visited a restaurant where everything costs $0.50.

They ordered two teas, three cakes, and a coffee.

They gave the waiter 15% of the sum of the bill as a tip.

They paid with a $10 note.

What was the change?

ID 657

A stadium security system consists of two stages.

In the first stage, 60% of the spectators are inspected.

In the second stage, 80% of the people undergo an inspection.

Estimate the percentage of the spectators who do not undergo any inspection.

ID 658

Sixty carpenters and forty plumbers work together.

The average daily rate of a carpenter is $300 while the average daily rate of a plumber is $400.

What is the average daily rate of all those involved in the project?

ID 661

ID 664

There are 140 cars in a village of 30 families.

Each family has either 4 or 5 cars.

How many families have 5 cars?

ID 665

Apples are sold in bags of four that cost $5 per bag, or bags of six that cost $6 per bag.

What is the smallest cost at which you can buy 74 apples?

ID 666

John buys shares in the stock market for $1000.

He sells the shares when the value of the shares increases by 20%.

He pays a 5% transaction fee on both his purchase price and sale price.

How much proﬁt does John make?

NOTE: When a transaction fee is paid for a stock purchase, the amount of stock purchased is reduced by that commission.

ID 667

A girl drives from home to her school at an average speed of 90 kilometers per hour, and she drives back at an average speed of 110 kilometers per hour.

What is her average speed for the whole journey?

ID 668

A 1-meter tall fence is parallel to a very high wall 1 meter away.

What is the length of the shortest ladder that will reach from the ground over the fence to the wall?

ID 669

A 100-liter vessel is full of a mixture of juice concentrate and water, in which there is 40% concentrate.

50 liters are sold, and the vessel is filled up with water.

What is the new fraction of the juice concentrate?

ID 675

A stadium contains 20,000 seats. At a match, 25% of the seats remain empty.

One ticket costs $20.

Find the cost of the total tickets sold.

ID 676

Normal milk has 35 grams of fat per liter.

Fat free milk has 5 grams of fat per liter.

Estimate the approximate percentage of fat that is removed from normal milk to produce 'fat free' milk.

ID 683

A car that originally sold for $40,000 depreciates at a rate of 50% per year.

What is the value of the car after ten years?

ID 1120

A class picnic is estimated to cost $212.

The boys agreed to contribute $1 more than the girls.

If there are 12 boys and 8 girls in the class, how much money should each boy contribute?

ID 1364

ID 1371

Four children Addy, Brady, Cady and Dendy started at the same point S and walked to point F at the same speed.

The picture shows the streets and square city blocks.

Who finished last?

ID 1468

The space between these green square tiles is filled by grout.

Its width is about 1% of the tile width.

The pattern is extended to cover a large surface.

Estimate the proportion of the surface that is covered by grout.

ID 1486

January 1st, 2012 was a Sunday.

2012 is a leap year and therefore contains one extra day.

Which days of the week occured more frequently in 2012?

ID 1621

Enclosed is a lamb using a 4-crosspiece log fence.

What is the smallest number of crosspieces I needed to separately enclose four lambs?

ID 1723

John is making a rectangular ﬂower box. He is using wood that is 10 centimeters wide to make the ﬂower box.

Which design gives the smallest area for the flowers?

ID 1771

Four towns are situated at the corners of a square.

The government decided to build a new road linking all four towns together.

Engineers suggested four different designs.

Which design illustrates the longest road?

ID 1899

I have eight bills consisting of $5 and $10 bills.

The total amount of money is $60.

How many $10 bills do I have?

ID 1996

John deposited 400 dollars at 40% interest compounded annually.

Estimate his fortune after four years?

ID 2007

What is the total worth of the $1 bills which are consecutively numbered from AB01234567 to AB11111111?

ID 2045

ID 2068

A man and his equipment weigh 180kg on Earth.

If he takes the same set of scales to the moon and weighs himself there, the scales would read 30kg.

If the wrought iron structure of the Eiffel Tower weighs about 7,200 tons, what would be its weight on the moon?

ID 2147

A gardener increased the length of his rectangle-shaped garden by 10% and kept the garden perimeter unchanged.

How did the width change?

ID 2293

A race car is constructed from ultra-lightweight materials.

The car weighs 640kg (1,411 lb) including the driver and a full fuel tank.

The fuel is 25% of the total weight.

What will the car weigh with 10% of the maximum fuel?

ID 2295

I bought a 20'' laptop with the ratio of the screen width to the height 4 : 3.

What is the screen's width?

ID 2298

152 Garfield Show episodes were produced in 2009 - 2012.

Each episode is 22 minutes.

How many days (twenty-four hours) would I spend watching all these episodes without breaks?

ID 2936

John paid $90 for 8 CDs.

All CDs cost the same price, but 2 of them were on sale for 25% off.

How much did each CD cost?

ID 2945

John is making a rectangular flower box.

He is using wood that is 10 centimeters wide to make the flower box.

Which design gives the largest external perimeter?

ID 2951

ID 2954

Tim placed an order for a book.

If the order is below $40, then the minimum shipping and handling charge of $5.99 will apply.

If the order is higher, then the charge is 15% of the total order price.

Tim's order price is $40.00.

What is the total cost of the order including shipping and handling?

ID 2955

ID 2977

The total price of an apple and a tangerine is 39 cents.

The total price of 2 apples and 3 tangerines is 99 cents.

What is the price of one tangerine?

ID 2978

A hockey team lost every fifth game and won 3 more than it lost.

There are no draws.

How many games did the team win?

ID 2979

If six people can stand on a square meter of carpet, how many of them can stand in an elevator cab that is 2.1 meters by 1.2 meters and 2.2 meters high?

ID 2982

The left clock runs slower at a rate of 5 minutes per hour.

The second clock runs faster at a rate of 5 minutes per hour.

Both clocks start at the same time.

When will they be one hour apart?

ID 2984

There are 15 men on a basketball team, and in a game 5 of them play at any one time.

If the game is 48 minutes long and if each man plays exactly the same amount of time, how many minutes does each man play?

ID 2985

There are 16 men on a basketball team, and in a game 5 of them play at any one time.

If the game is 48 minutes long and if each man plays exactly the same amount of time, how many minutes does each man play?

ID 2986

Anna earned $72.

She gives her mother 1/4 of this amount and spends 1/5 of the money on going out.

What fraction of the $72 is left?

ID 2987

Anna earned $72.

She gives her mother 2/15 of this amount and spends 1/6 of the money on going out.

What fraction of the $72 is left?

ID 2991

John started a business in which he earned $1 on the first day, $4 on the second day, $7 on the third day, $10 on the fourth day, and so on.

What is his earning in day 1001?

ID 3021

ID 3022

ID 3064

ID 3080

The original price of an umbrella was $15.

What was the price of the umbrella after two 10% markdowns?

ID 3082

A food stand buys ice cream cones in packages of 28 and cartons of 12.

What is the least number of packages and cartons of ice cream that need to be bought to have an equal number of ice cream cones from each source?

ID 3089

600 employees work for company XYZ, where the ratio of men to women is 7 to 5.

If 50 men leave the company and 50 women are hired, what is the new ratio of men to women?

ID 3090

Anna is a member of Greenland Velo's race team.

This summer, she has won only 6 out of 16 races.

How many races must she now win in a row to achieve a winning record of exactly 50%?

ID 3099

A lottery has one $8000 prize, four $2000 prizes, and eight $500 prizes.

The organizers retain 20% of the ticket price.

Two thousand tickets are sold.

What is a ticket price?

ID 3201

The desired tip is 15% and you have no change.

Without using a calculator, how much money should you give the waiter if the bill is $120?

ID 3349

ID 3532

You participate in the 191-km stage of the Tour de France.

One second before the finish line you overtake the cyclist in the third place.

In which position are you now?

ID 3596

How many minutes before midnight does a 24-hour digital clock show the same time upside down and the right way up?

ID 3737

I place 11 chairs along the walls in an empty rectangular room.

The number of chairs along each wall is the same.

Find the number.

ID 3775

A piece of wood is to be sawed into 3 smaller similar pieces.

If a cut eliminates 2% of the wood as sawdust, what is the volume of a small piece related to the volume of the original piece?

ID 3975

Seven apricots were dried and no longer contain water.

If the fruits initially weighted 400 grams and now 50 grams, what percentage of an apricot was water?

ID 3979

How high is a $50,000 stack of $1 bills, given that the thickness of 100 bills is about 1 centimeter (0.033 feet)?

ID 4010

ID 4062

I saved $5 on buying coconuts on sale.

If I spent $20 on the coconuts, what is the percentage I saved?

ID 4072

I want to rearrange the logs in the following manner: 8 logs on the bottom row, one less on the next row, and so on.

How many logs are on the top row?

ID 4117

I paid $50 when I filled the tank of my car, at which stage the odometer said 78737.

Now, I am filling up at 78987 and pay $50 again.

How much does the gas cost me?

ID 4142

ID 4152

Mary puts $800 in a bank account.

Each year the account earns 1% simple interest.

How much interest will be earned in five years?

ID 4292

The Tsar Bell weighed 202 tons (like three battle tanks) before a huge slab (12 tons) cracked off during a fire in 1737.

What part of the bell was cracked off?

ID 4347

John plans to go by bus and to walk back, so if the bus goes at the rate of twenty miles an hour and he can walk at the rate of four miles an hour, how far could he ride if he must be back in nine hours?

ID 4381

What is the minimum number of pizzas that a class of 21 students should buy if they would like 3/8 of a pizza each?

ID 4435

Two trains are 1 kilometer apart on a single track railway line. They set off towards one another at 1 meter/second.

A bee sitting on the front of one of the trains sets off and starts to fly along the railway line at 3 meters/second.

When the bee meets the other train it immediately turns around and flies towards the first train and so on . . .

How far does the bee fly?

ID 4437

John's tent is 1.5 m high, 2 m long, and 1.5 m wide.

How much water will fall on the tent tomorrow if a forecast website declares that there will be 4 liters per square meter per day?

ID 4439

The diagram shows the lowest point and the highest point of our planet.

What is the difference between the points?

Source: Nelson Thornes New Maths in Action. 2004

ID 4523

The knights gallop 100 m in 10 seconds.

There are 1000 m in 1 km.

Would the knights get a fine if the speed limit is 40 km per hour?

ID 4531

Jim's route must start and end at his home.

He wants to visit at least 3 places.

Find the shortest route.

ID 4556

Bob's age is between 40 and 60 and it is a multiple of 5.

Next year, his age will be multiple of 7.

How old will Bob be next year?

ID 4590

Gerry drove a total of 420 miles in 6 hours.

How many hours did he drive above the state limit of 70 mph if he accelerated each hour, covering an extra 2 miles compared to the previous hour?

ID 4778

ID 4798

The community library fines 20 cents per overdue day of the first week and 50 cents per overdue day thereafter.

If Gerry kept a book for two weeks, how much money does he have to prepare?

ID 4810

ID 4870

ID 4892

ID 4918

ID 4976

Gerry arrived in the Murtenhof Hotel on January 28th in the afternoon and left the hotel on February 2nd in the morning.

How much did he pay if the rate was $49 per night?

ID 5018

A pedestrian crosswalk consists of black and white stripes each 0.4 m wide.

The crosswalk begins and ends with a white stripe, and there are 8 white stripes in all.

How wide is the crosswalk?

ID 5171

Leslie Green asks:

A road traffic junction has no provision for pedestrians. The traffic lights are just changing to stop the RED and ORANGE cars. The GREEN and BLUE cars are next to go. Pedestrians A and B will only start to cross once all cars are stationary.

Compare the crossings for A and B.

(NOTE: Some jurisidictions allow drivers to pass red lights when turning, but that is not allowed at this crossing.)

ID 5178

The King of a far off land has just had the ballroom lights in his palace rewired by probably the most illogical and incompetent electrician in the land. Instead of each of the 8 up/down switch positions turning on one of the banks of lights in the ballroom, each switch has to be in exactly the correct up/down state in order to make all the lights come on at once. In every other switch position all the lights are turned off.

Needless to say the incompetence of the electrician enraged the King so much that the electrician was executed in a gruesome way the same day.

Unfortunately, for some inexplicable reason, electricians seem reluctant to come and fix the problem. The Chief Steward needs to devise a plan to turn the lights on and off every evening so the King isn’t made to look foolish in front of his important guests over the coming weeks.

How many switch positions need to be changed every night to meet the requirements?

Changing any switch lever from down to up, for example, counts as one position change.

The problem was suggested by Leslie Green

ID 5229

Leslie Green asks:

"You accidentally knock an almost full opened can of soft drink over onto a carpeted floor.

Roughly how long have you got to make the can upright before over half of the contents are spilled?"

ID 5757

One teaspoon of honey weighs about 7 grams.

Gerry eats a teaspoon of honey everyday.

How long will a 500 gram jar of honey last at this rate of consumption?

ID 5923

The tires of my car wear out after 40,000 miles.

A garage offers me a set of 5 tires.

Estimate how many miles I can drive if I change the tires at the best moment.

ID 6027

If a shaft rotates through 100 degrees in one second, how many revolutions does it make in one hour?

ID 6070

The Canadian Red Cross advises that the safe thickness of ice on a lake or a river should be 15 cm for skating alone, 20 cm for games, and 25 cm for snowmobiles.

What is the least safe thickness of ice for playing hockey if one inch is 2.54 cm?

The picture shows the mountain lake Champex, Switzerland.

ID 6126

Roman numerals are a numeral system of Ancient Rome based on letters of the alphabet.

For example, CVII is 107 (100 + 7).

What number **cannot** be represented in Roman numerals?

ID 6141

The distance from the heel print of one foot to the heel print of the other foot is the distance traveled forward by a single leg / step.

An average step is 2.2 feet (0.67 meters) for women and 2.5 feet (0.762 meters) for men, but it depends very much on height.

John starts walking to the north. Mary follows him from the same point and in the same direction.

In how many steps does she put her heel exactly in the same point with John?

ID 6154

Evguenia catches fish at a rate of fourteen fish per hour. Her father catches fish at a rate of ten fish per hour.

If they both fish for one and a half hours, how many fish will they catch altogether?

ID 6157

ID 6158

An average American child consumes 32 teaspoons of sugar daily, mostly through soda drinks, multi-component products, and cookies.

The World Health Organization (WHO) recommends just six teaspoons daily.

By how many times does an average American child exceed the recommended daily limit?

(To be clear, we are saying that double the recommended limit exceeds the recommendation by 2 times.)

Info source: Waking Science

ID 6161

There were 4 parrots in a shop. Their average price was $5,000. One day a parrot chose freedom and flew away. The average price of the remaining three parrots was $4,000.

What was the price of the parrot that escaped?

ID 6207

I can exchange 100 Euros to 110 US dollars (USD) for free. My uncle wants to give me some money. He suggests that I choose among the four options.

Which amount did I choose?

ID 6247

Rather than write the specifications on the side of the packet, manufacturers now use symbols to avoid having to print the specifications in 7 or more different languages.

Sometimes these symbols can be difficult to understand immediately.

Can you decode what this (actual) label tells you about the environmental rating?

Author: Leslie Green

ID 6360

ID 6372

A particular carnival game involves throwing a soft ball at stacks of bottles, with each knocked over bottle contributing to a prize. The stallholder demonstrates how easy it is, and yet you just can’t seem to do it, despite hitting the bottles in the same place that the stallholder did.

Can you guess why this might be?

Author: Leslie Green

ID 6448

Jane, the undercover operative, is in a strange far-away city at night. The sky is overcast and moonless so she can’t get a bearing from it. She has no phone or compass to assist her. She knows that the city streets are drawn on a neat rectangular grid, so in order to keep a note of her direction she adds 1 for a left turn, 2 for a 180° turn, and 3 for a right turn, all relative to the direction she is travelling in before each turn.

She starts off looking directly at the clock in the city square. The rest of the city seems featureless to her foreign eyes.

After an hour of following her suspect, with him deliberately making unnecessary turns to throw off anyone following, she has reached a count of 401.

If facing the clock was looking north, in which direction is she now facing?

Author: Leslie Green

ID 6519

A carpenter had 0.5m-wide planks with lengths of 2m and 1.5m.

He covered a square table with sides of 2.5 meters without using a saw.

How many 2m planks did he use?

ID 6629

The price of a soccer ball was $11 in 2011.

A financial analyst predicted that the price would rise $0.25/year for the next 50 years.

In what year will the price be $21?

ID 6646

Jane and Gerry planned a 6,666-mile trip in a simple car with seven tires, of which four are in use at any time.

They interchange them so that each tire is used for the same distance.

Estimate the distance for which each tire will be used.

ID 6659

Gerry washes his hands ten times per day, each time taking about 6 seconds. He started to wash his hands at the age of 4, and his life expectancy is 94 years.

During his lifetime, how much time will have been spent washing his hands?

ID 6663

Open Eyes Theatre bought a movie license for $1,500 per week.

The cost of keeping the stuff and the hall is $20,000 per month.

If they charge $10 per seat, how many people would have to see the movie in the first four weeks in order for them to recoup the costs?

ID 6669

The picture shows the network of the Swiss Intercity railway network.

What is the least number of lines that must be closed to prevent any traffic from Lausanne to Zurich, routes passing outside of Switzerland not being considered?

ID 6715

Leslie Green asks:

John finds a box of similar looking books in a box in the attic. The books are labelled with large letters: V, X, II, I, IX, and VI.

How many books can he be confident are missing from this collection?

ID 6723

On the chessboard, the number of points in each cell is given. Gerry starts in the bottom-left square and moves to the top-right square, moving only up and to the right.

What is the maximum number of points he can collect?

ID 6735

Leslie Green asks:

In a remote African village it is traditional for the women to set off early in the morning to walk through the desert to fetch water. This is a long and arduous journey. There are three water containers available in adequate quantities, but each woman can only carry one of them.

The measure of water is unique to this tribe and we will just call it a unit.

A large container carries 4 units of water, but its design is so poor that on the trip back, half will be lost by leakage and splashing.

A medium container carries 3 units of water, and has a better design, so only one third is lost on the return journey.

The small container is only slightly smaller than the medium container, carrying 2 and 2/3rds units of water. However, it only leaks one quarter of its original content.

We are told that the container itself weighs half as much as the maximum content it can carry.

Which container should the tribal elders instruct the women to take?

ID 6742

Gerry works 5 days per week. He drives 36 miles round trip per day.

If gas is $3.5 per gallon and his car gets 30 miles to the gallon, how much would he have spent on gasoline in February 2017 getting back and forth to work?

ID 6749

Mary works as a baby sitter.

If she charges $8 an hour plus $2 for each child, what is the most profitable work for her?

ID 6810

Leslie Green asks:

It was announced on the UK news that birds were flying backwards in a certain location at a certain time.

Suggest the most plausible explanation for this report.

ID 6816

A table with four legs is resting on an uneven floor. Even if the floor were level, the table would still have been wobbly as the legs are not exactly equal.

You have available a set of wedges to place under the legs to make the table secure.

What is the minimum number of wedges required to secure the table in the worst case of mismatched legs and floor?

Author: Leslie Green

ID 6890

ID 6944

The sweets in the bag can be divided equally among 2, 3, 4, 5, or 6 children with no remainder.

What is the smallest possible number of sweets in the bag?

ID 6958

Dates can be represented as DD.MM.YYYY.

For example, January the fifteenth 2018 can be written as 15.01.2018.

What is the largest possible sum of the digits in the 21st century (2000 - 2099)?

ID 6973

Jane has a dozen hens. Half of them lay an egg every day. The other hens each lay an egg every second day.

How many eggs do the hens lay in four weeks?

ID 6998

**A counting-out game**

People are standing in a circle.

Counting begins at a person in the circle and proceeds around clockwise. The player who is selected at the conclusion of the rhyme is out.

The count starts with the next person.

Four children stand in a circle in the following order: Alex, Betty, Craig, and Diana.

If the count-out game starts from Alex, who will win the game?

They use the most common English rhyme:

Tinker, Tailor,

Soldier, Sailor,

Rich Man, Poor Man,

Beggar Man, Thief.

ID 7076

Two coins have the diameters of 30mm and 15mm.

The small coin rolls around the fixed big coin until it returns to its starting position.

How many revolutions of the small coin are there in total?

ID 7163

The Mars Tourist Agency sells places for the Mars Tour at $10 million each or $50 million for a group of 6 people.

There is a fifty-fifty chance of returning safely to Earth.

If a class of 25 brave students wants to make the trip to Mars, what is the minimum possible cost?

ID 7164

In a class, 1/8 only have dogs, 1/4 only have cats, 1/2 have both, and the rest have pocket money of more than $100.

How many children have more than $100 if there are 24 students in the class?

ID 7165

Jason has just realised that playing *Total Death & Destruction XVIII* every night is not going to help him in adult life. Instead he has resolved to spend 20 minutes a night on A+ click, working through all the problems starting from those for 6 year olds, and working his way up. He has realised, somewhat belatedly, that by practicing problems he will get better at solving problems. For the kiddy problems, the game is to solve the problems as quickly as possible whilst still getting the correct answer.

Given that the A+ click problems are supposed to take one minute or less to solve, how long will it take him to solve the first 6000 problems.

by *Leslie Green*

ID 7170

Jane folds a piece of paper in half, creating two layers of paper. She folds the paper in half again, creating a total of four layers of paper.

If she continues to fold the paper in half, which of the following is a possible number of layers that could be obtained?

ID 7189

The size of the side of the square is 60cm.

What rectangular surface can NOT be completely covered by such planks without gaps or cutting planks?

ID 7196

When the car wheels make one full rotation the car moves forward by about 1.5m.

How many times do the wheels rotate annually if the red car drives 24,000 km per year?

1km = 1,000m

ID 7208

If each building in a city block is 16m wide and the gap between buildings is 4m, how wide is the city block?

ID 7243

ID 7248

The flashing light on the lighthouse blinks 15 times a minute.

How many times does it blink in a day?

ID 7326

Sound goes 1 mile in 5 seconds, while light goes 186 thousand miles in 1 second.

How much faster than sound is light?

ID 7346

The field goal percentage is 100x the ratio of the number of made field goal baskets and the number of total attempts.

Jane made 21 out of 30 field goal attempts in her last game.

What was Jane’s field goal percentage?

ID 7348

It takes Gerry 1 hour to make a cherry pie, half an hour to cook it, and 15 minutes to cool and decorate it.

If he starts at a quarter to noon when is the pie ready?

ID 7357

Gerry has a 6-cm ruler that is missing the second mark. However, he can still measure all integer lengths from 1 to 6.

What is the minimum possible number of marks that allow him to measure all integer lengths from 1 to 6 ?

ID 7363

A great grandfather is counting up all of his children and their descendants. They are all still living and he includes married partners in his count. In each generation there are two children.

The great grandchildren are not yet adults.

What is the count?

ID 7385