ID 920

Practical Mathematics K12 John works 4-hour shifts at a call center.
He earns $4 per hour and $4 per call.

How many calls does he need to receive per shift to earn a total of exactly $400 in 4 shifts?

ID 921

Practical Mathematics K12Tom is choosing between two brands of AA batteries for his pocket flashlight. A package of two Brand A-Super batteries costs $4.99, and a package of two Brand B-Cool batteries costs $3.29. The runtime of the A-Super package is 2.5 hours. The runtime of the B-Cool package is 100 minutes.

Help him choose.

ID 945

Practical Mathematics K12A taxi company charges $1.75 for the first kilometer and 25 cents for each additional kilometer.

What is the maximum distance someone could travel with seven dollars?

ID 946

Practical Mathematics K12If 9 workers can build 9 houses in 9 months,
then how many months would it take 11 workers to build 11 houses?

ID 951

Practical Mathematics K12Jim sells 80 percent of pineapples he had and throws away 10 percent of the remainder. On the next day, he sells two-thirds of the remainder and throws away the rest.

What percent of his pineapples does Jim discard?

ID 952

Practical Mathematics K12If eight deciliters of Swiss apple juice, priced at $4.00 per liter, are combined with twelve deciliters of Italian apple juice, priced at $3.00 per liter, what is the price of the resulting mixture?

ID 954

Practical Mathematics K12A space rocket has a critical fuel-control system protected by 4 fuel micro-controllers running together. If all 4 micro-controllers fail during the flight, the rocket will crash. The probability that any one micro-controller will fail is 1/5.

If the rocket has lifted off, what is the probability that it will not crash due to the fuel-control system?

ID 973

Practical Mathematics K12A carnival game offers you the opportunity to bet $1 on a number from 1 through 6 on a single roll of the two dice.
If your number comes up on one die, you win $2 and keep the $1 you bet.
If it appears on both dice, you win $5 and keep the $1 you bet.
Only if the number does not appear on either die do you lose your $1 bet.

Does this game favor you or the carnival?

Source: Mathematics Teacher, NCTM Journal

ID 981

Practical Mathematics K12Jane wants to buy a car.
The fuel efficiency is two times more important to her than the price of the car.
Help her to choose a car.

1 mpg (mile per gallon) = 0.425 kilometers per litre

The photograph courtesy of Roland Sauter

ID 998

Practical Mathematics K129 farmers grow 9 apples trees in 9 years.

How many years would it take for 999 farmers to grow 99 apple trees?

ID 999

Practical Mathematics K12A bicyclist pedals downhill at 20 km/h (kilometers per hour) and uphill at 10 km/h.
It takes 4 hours to travel from a Swiss mountain village to another village.
The return trip takes 5 hours.

Find the distance between the two villages.

ID 1001

Practical Mathematics K12You have eight dimes; seven are real and one is fake.
All the real ones weigh the same, and the fake weighs less than the real ones.

How many times do you use a balance scale to find the fake dime?

ID 1049

Practical Mathematics K12A city hall floor is to be tiled in the following pattern.

The hall measures 121 tiles x 61 tiles.

How many green tiles do we need?

ID 1061

Practical Mathematics K12It costs $24 to paint a cube, the cost being proportional to the surface area.
Before painting, it was cut in two pieces by a plane.

What is maximum possible cost to paint these two pieces?

ID 1506

Practical Mathematics K12The traveling salesman problem: a salesman has to visit 9 towns and return home.

What is the shortest available route between the towns?

Any route chosen must lie on the paths shown. Paths with unmarked distances should be calculated from the geometry of map.

ID 1508

Practical Mathematics K12The Chinese postman problem: a postman wants to travel along each road in his quarter and come back to the Start.

Find the minimal length of his route.

ID 1617

Practical Mathematics K12The diagram illustrates five villages, A, B, C, D, and E, with the distances between them in miles.

A postman must travel from A through each of the other villages exactly once and then back to A.

Identify the shortest possible route.

ID 2100

Practical Mathematics K12The Legend of Carthage: Queen Dido and her followers arrived in North Africa.
The locals told them that they could have the coastal area that an ox hide would cover.
She cut the hide into a series of thin strips, jointed them together, and formed a coastal shape.
The ox-hide enclosed area was known as Carthage.

If you had a 10 km long strip, which shape (rectangle, triangle, semi-circle, or semi-ellipse) would you choose to maximize the enclosed area?

ID 2168

Practical Mathematics K12Anna can complete a project in 40 days.
Bill can complete the project in 50 days.
Cindy can complete the project in 60 days.
Daniel can complete the project in 120 days.
Their daily wages are proportional to their performance.

Find 3 people who together complete the project in exactly 20 days.

ID 2171

Practical Mathematics K12Choose the best advice for a strategic decision to the top management of a bank.

The profits stated are NET, in other words costs have already been deducted.

ID 2204

Practical Mathematics K12You have 240 golden bricks identical in size and appearance but one is lighter than the others.

How many times do you use a balance scale to find the odd brick?

ID 2214

Practical Mathematics K12I am selling my car. People come to my garage one at a time and make bids to buy it. I make an immediate decision whether to accept or reject an offer after receiving it. I decide to reject the first N offers, mark the highest price P, and accept the first offer that is greater than P.

What number N do you recommend me if I expect that 270 people will make a bid?

If N is small, I can accept a small amount of money.
If N is large, I can reject the best offer.

ID 2297

Practical Mathematics K12A goldfish need 1000 cubic inches of water to live in.
An aquarium is 20 inches in diameter.

How many fish can live in an aquarium?

ID 3178

Practical Mathematics K12John's dad pays him $2 for each correct answer he gives in his math homework and fines him $8 for each incorrect answer.
Today, John received nothing after doing 50 problems.

How many problems did John answer correctly?

ID 3181

Practical Mathematics K12Bob will work 5 days.
Which payment plan should he choose?

ID 3609

Practical Mathematics K12"Letter frequency. Accurate average letter frequencies can only be gleaned by analyzing a large amount of representative text." (source: Wikipedia)

What is the most common letter in the English alphabet?

ID 3645

Practical Mathematics K12I gave $120 to Brett, Cindy, and Daniel.
Brett and Cindy received twice as much as Daniel.
Daniel and Cindy received three times more than Brett.
Who received the most money?

ID 3683

Practical Mathematics K12The diagram shows a road network.
All cars drive in one direction from A to F.
The numbers represent the maximum flow rate in vehicles per hour.

Engineers want to construct a new road with a flow rate of 100 vehicles per hour. Drivers randomly choose the road at crossroads.

What new road decreases the capacity of the network (the number of vehicles at point F)?

ID 3744

Practical Mathematics K12The Lucas problem.

François Édouard Anatole Lucas (1842-1891) was a French mathematician.

Every day at noon, a ship leaves Le Havre for New York and another ship leaves New York for Le Havre. The trip lasts 7 days and 7 nights.

How many ships will a ship leaving Le Havre today meet at sea?

ID 3752

Practical Mathematics K12A red-line subway train arrives at a station every 5 minutes and stays for 30 seconds.
A blue-line train arrives on the other side of the platform every 2.5 minutes and also stays for 30 seconds.
I randomly arrive at the station and always choose the train which arrives first, or any of the two if both trains are present.

What is the largest possible percentage of time that I take the red-line train?

ID 3757

Practical Mathematics K12Four people arrive at a river at night. There is a narrow bridge, but it can only hold two people at a time. They have one torch and, because it is night, the torch has to be used when crossing the bridge.
Person A can cross the bridge in one minute, B in two minutes, C in five minutes, and D in eight minutes.

What is the shortest time they all can get across the bridge?

Source : Wikipedia

ID 3797

Practical Mathematics K12Every year, a man who had a million dollars at the beginning gives away half of his money to his son, and after that gives 20% of what he has left to charity.

How much does he end up with at the end of the 5th year?

ID 3882

Practical Mathematics K12The speed of a bus is 25 miles per hour (mph) including stops and 40 mph excluding the stops.

For how much time does the bus stop in a 48-minute trip?

ID 3889

Practical Mathematics K12Job interview logic puzzle in a bank.

Which of these pieces of information would be most useful for estimating the number of people who travel in a train with 20 passenger coaches?

ID 3895

Practical Mathematics K12Wikipedia says that the equator is about 40,075 kilometers (24,901 miles) long; 78.7% is across water and 21.3% is over land.

A yard was defined as the distance from finger tip to nose with the arms straight out to the sides.
Allowing 5 inches for a palm grip at each side we have 2(36-5) = 62 inches or 1.6m.

Estimate the number of people who holding hands in a human chain cover the length of the equator.

ID 3925

Practical Mathematics K12In a game, Anna and Bill take 1, 2, or 3 coins on each turn.
The player to take the last coin from the pile wins.

If Anna goes first and there are 40 coins on the table, how many coins should she take to guarantee that she would win?

ID 3993

Practical Mathematics K12John and Mary have square tiles with sizes 2 cm by 2 cm, 4 cm by 4 cm, 6 cm by 6 cm and so on.
Their kitchen is a rectangular room with an 224 cm by 288 cm surface.

What is the minimum number of tiles of the same size required to completely cover the surface without cutting the tiles?

ID 3999

Practical Mathematics K12John and Mary have square tiles with sizes 5 cm by 5 cm, 10 cm by 10 cm, and 15 cm by 15 cm.
Their kitchen floor is a rectangle with an 230 cm by 440 cm surface.

What is the minimum number of tiles required to completely cover the floor surface without cutting the tiles?

ID 4005

Practical Mathematics K12The size of a swimming pool is 25 x 12.5 meters.

How many people must jump into the pool so that the water rises by 1 meter?

ID 4011

Practical Mathematics K12Which point cuts the rope into two equal parts?

ID 4031

Practical Mathematics K12If John walks up an escalator at a rate of one step per second, 12 steps take him to the top.
If John goes up at two steps per second, he reaches the top in 20 steps.

How many steps are there on the escalator?

Inspired by A. Dunn, Mathematical Baffles, Dover Publications, 1980, p 17

ID 4032

Practical Mathematics K12Two proofreading programs, A and B, discovered 30 and 40 errors, respectively.
There are 10 errors in common.
Estimate the number of errors that are still undetected.

ID 4046

Practical Mathematics K12Anna was planning to buy 10 souvenirs from the honesty shop.
She wanted some badges, which cost $5 each, and some Swiss chocolate bars, which cost $4 each.
After checking her wallet she decided to put 20% of the badges back.

How much money did she spend in the shop?

ID 4059

Practical Mathematics K12Water is pumped into an empty swimming pool at a linearly increasing rate, which was zero at the beginning.

If the pool is half full in 10 hours, how much extra time is needed to completely fill it?

ID 4067

Practical Mathematics K12Twenty theater tickets for the first row were randomly distributed among 20 students.

What is the probability that John gets a seat next to his true love Jenny?

ID 4077

Practical Mathematics K12Two years ago, I bought a cottage for $800,000.
I was short of money and borrowed 12.5% of the money from a bank with 10% annual interest.
I sold it after two years and its value increased by 5% in that period.

What is my profit after I paid the bank back?

PS: I did not pay any tax for such a small transaction.

ID 4078

Practical Mathematics K12Mrs. Brown bought 98 boxes of strawberries at $9 per box but 25 % of them were found to be rotten.
She sells the non‐rotten strawberries.

What should the selling price per box be so that her profit is 50%?

ID 4093

Practical Mathematics K12When I put 10 cubes of ice into my glass and they melt, the water doubles its volume and completely fills the 160 ml glass.

Estimate the size of a cube.

1 ml = 10mm x 10 mm x 10 mm

ID 4094

Practical Mathematics K12Estimate how many symbols you can write on your body if one symbol requires one square centimeter.

ID 4120

Practical Mathematics K12A father has left 47 donkeys for you to distribute to his three sons;
1/2 (23.5) should go to his eldest son,
1/3 (15.667) to the middle one, and
1/8 (5.875) to the youngest.

You arrive with your own donkeys.
You can add or take some donkeys from the herd.

How do you divide them so that all sons are happy with your decision?
How many donkeys does the eldest son get?

Inspired by Malba Tahan “The man who counted.”

ID 4122

Practical Mathematics K12Mary and John manage two different projects and they have a common budget.
Mary spent half of the budget, then John spent half of what was left, then Mary spent half of what was left and so on until the last cent.

What proportion of the budget did Mary spend?

ID 4124

Practical Mathematics K12Management support accelerates the execution of a project by 10% during the first year of the project.
The same support delays the project execution by 10% during the second year.

Will the project execution take more or less time with management support?

ID 4126

Practical Mathematics K12There are 190 people in a company including the project managers and CEO.
Project managers successively take out half of the total number of people to start a project until only the CEO is left.

How many project managers are there in the company?

ID 4164

Practical Mathematics K12One by one, 40 cars enter a company parking lot with 40 assigned places.
The first driver forgets his place number and takes a random place.
The remaining drivers take their assigned place, if available, or take a random place.

What’s the probability that the last driver ends up in his original assigned place?

Inspired by Peter Winkler's airplane problem.

ID 4168

Practical Mathematics K12You pay $6 to enter a game.
You roll 2 dice.
You then have two choices: you can cash out and get paid the dollar amount of the roll, or you can pay $1 to roll the dice again.

What is your final gain per game if you play many times and choose the strategy to stop once you get more than 6 on two dice?

ID 4241

Practical Mathematics K12I see the reflection of the mountain peak 10 meters from me.
I know that the difference between the height of the lake and that of the peak is 1,800 meters.

How far from me is the mountain if I am 1.5 meters tall?

ID 4278

Practical Mathematics K12An entrepreneur sells 1,250 tickets for a show, with 20% of them sold with 20% off.

How much does a normal ticket cost if the total income must be $120,000?

ID 4308

Practical Mathematics K12A pirate boat is floating on a lake.
The pirates throw a heavy chest with gold coins overboard.

What happens with the water in the lake with respect to the shore?

ID 4345

Practical Mathematics K12A space rocket with 4 engines blew off one of them after one-month of flight.
It continued the flight at three-quarters of its former speed, which brought it to the destination two months late.

How long did the trip last?

ID 4358

Practical Mathematics K12What is the minimum monthly salary you negotiate with your boss if you need

$1,800 per month to pay your house loan and its expenses,
$200 per week for yourself, and
$18,000 per year for leisure and saving?

PS: You pay 20% tax.

ID 4420

Practical Mathematics K12What is the total surface area of 100 identical cubes which together have a volume of 51,200 cubic units?

This is a typical SAT question.

ID 4428

Practical Mathematics K12You have a large supply of 5kg and 12kg weights.
Six 5kg weights and one 12kg weight have an average weight of 6kg.

What is the minimum number of weights that have an average weight of 7kg?

ID 4470

Practical Mathematics K12Gerry plans to swim a total of at least 1000 laps in January.
He swims every day except weekends (Saturday and Sunday).
He wants to increase the number of laps each day by one.

What is the least number of laps he must complete on the first weekday if January 1st is Saturday?

ID 4471

Practical Mathematics K12Texas experiences wide temperature fluctuations within a single day.
On January 1st, the temperature drops from 62° to 30° in Austin, and from 24° to 13° in New York.

What is the range within which the temperature difference between these two cities must be?

ID 4478

Practical Mathematics K12James bought a new car for $30,000.
Each year it depreciates (loses value) at a rate of 20%. The maintenance costs $3,000 the first year and it increases by 20% each year.

When does the maintenance cost exceed the value of the car?

ID 4489

Practical Mathematics K12While eating out Gerry and Jim together tipped their server $7 in total.
Gerry tipped 20% of his bill and Jim 15% of his bill.
Jim's bill was twice as much as Gerry's one.

They don't remember how much they paid.

Can you find the total including the tip?

ID 4564

Practical Mathematics K12The water from an open swimming pool evaporates at a rate of 5 gallons per hour in the shade and 15 gallons per hour in the sun.

If the pool loses 8,400 gallons in June and there were no clouds, what is the average duration of night during that month?

ID 4577

Practical Mathematics K12The limousine service makes 100 trips Center-Aeroport every day, each of which costs $50.

The company estimates that the number of trips decreases by 5 trips per day for each $5 increase in the fare and vice versa.

What fare is the most profitable for the company?

ID 4591

Practical Mathematics K12I decided to use a password that includes 4 different numbers, with each number smaller than the previous one.

How many options do I have?

ID 4650

Practical Mathematics K12Gerry drives from his home to Jane's house at 50 mph.

How fast must he make the return trip via the same route such that the average speed of the entire trip becomes 40 mph?

ID 4660

Practical Mathematics K12Gerry gave half of his money to Jane.
Next day, she gave half of all her wealth to Gerry.
After the last exchange they each have exactly as much as they originally started with.

Who is richer?

ID 4733

Practical Mathematics K12A district sends, on average, a total of 205 million gallons of water each month to its 20,000 residential customers.
In the winter months, it sends an average of 100 million gallons per month.

Assuming the winter period lasts three months, what is the average number of gallons sent to each person in each nonwinter month?

ID 4883

Practical Mathematics K12The manager of a company planned to distribute a $101 bonus to each employee from the company fund, but the fund contained $1 less than what was needed.
The manager gave each employee a $100 bonus and kept the remaining $199 in the company fund.

What was the amount of money in the company fund before any bonuses were paid?

ID 4900

Practical Mathematics K12If you have a piece of paper that is 0.1mm = 0.01cm thick, how many times will you have to fold it in half in order for it to become as tall as me?

I am 163cm tall.

ID 4910

Practical Mathematics K12What is missing?

ID 4986

Practical Mathematics K12There are 17 parallels and 12 meridians on a globe.

Into how many areas is the surface of the globe divided?

ID 4989

Practical Mathematics K12When 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 100 cm long in the evening.

What is the least possible number of times he opened his mouth today?

ID 5038

Practical Mathematics K12What is average diameter of the logs if the height of the pile is 5.33m?

ID 5059

Practical Mathematics K12The 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 strongest opponents left to play?

ID 5068

Practical Mathematics K12I add blue blocks one by one on the top.
Does the structure fail?

ID 5094

Practical Mathematics K12A worker prepared a block for a pyramid in a day.

If every day the number of workers doubled, how many days did they need to prepare 1000 blocks?

ID 5137

Practical Mathematics K12A girl walked along a level road and up a hill from home and back.
Her pace on the level is 4 km an hour, uphill 3 km, and downhill 6 km.

How much time does it take if the total distance is 20 km?

Inspired by Lewis Carroll's Tangled Tale

ID 5139

Practical Mathematics K12Eugenia wants to make a simple bridge for her dog. Currently he has to run through a tiny stream in the back garden and then walks mud into the house. Since Eugenia’s dad owns and runs a machine shop, she can easily get a single sheet of steel, aluminum or wood to bridge the stream.

The length suits the size of the stream, the width suits the size of the dog, and the weight will be as much as she can carry.
The strength of a plain sheet is proportional to the relative strength of the material, its width and the cube of its thickness.

Which of the available materials makes the strongest bridge?

Suggested by Leslie Green

ID 5143

Practical Mathematics K12Now that I have made a vast fortune from my patented premium dog biscuits, I can afford to build the luxury mansion of my dreams.

I thought my design requirement was very clear: The water for the walk-through shower can be turned ON and OFF from both ends of the room.

The plumber doesn't understand so I have drawn him a plan. I had a few attempts before I got it right!

Which is the correct drawing?

The problem was suggested by Leslie Green

ID 5145

Practical Mathematics K12There are 10 coins and 5 of them are fake.
The real gold coins have the same weight, while all fake coins have different weights and each fake coin is lighter than a real one.

How many times do you use a balance to find all real coins?

Find the best strategy and the least possible number of weighings in the worst case.

ID 5155

Practical Mathematics K12A train runs from Lausanne to Zurich at 100 km/hour without any stops and another one from Zurich to Lausanne at 80 km/hour.

What is the distance between the trains 15 minutes after they meet each other.

ID 5213

Practical Mathematics K12Shops have sales all the time to attract your business. Let the buyer beware! Not all sales are as good as others.

Given the same branded goods being sold, and the same quality of after-sales service, which shop offers the best value, given that two weeks ago all had the same price.

The problem was suggested by Leslie Green

ID 5221

Practical Mathematics K12Leslie Green asks:

My neighbor John has invented a perpetual motion machine. It pumps water with no apparent power input and can even pump water up over a 2m fence.

How would you categorise this invention?

ID 5238

Practical Mathematics K12Leslie Green asks

"Suppose a particular nuclear waste material has a half-life of 100 years.

What could you do to reduce the radioactivity of the material itself to less than 7% of its current value?

(The half-life of a radioactive material is the time it takes, on average, for half of it to change into something else by spontaneous radioactive decay.)"

ID 5259

Practical Mathematics K12Jane and Gerry compete in a best-of-three match.

If Gerry plays so that his girl-friend has a 75% chance of winning any particular game, what is the likelihood that she will win the match?

ID 5274

Practical Mathematics K12 There is a fault with the cruise control on Hank's car such that the speed continuously and linearly increases with time.

When he starts off the speed is set to exactly 60 mph. He is driving on a long straight route with the radio on at full blast and he is not paying any attention to his speed. After 3 hours he notices that his speed has now reached 80 mph.

For how many miles did he drive above the state speed limit of 70 mph?

Author: Leslie Green

ID 5279

Practical Mathematics K12Before the death, a rich man signed his will.

"If my wife gives a birth to a boy, she will get a third of $42,000,000 and my son will get two thirds of the money.
If my wife gives a birth to a girl my wife will get two thirds of the money and my daughter will get one third."

The rich man has successfully died and his beloved wife gave birth to twins: a boy and a girl.

What is the fair share of the money for the lady?

ID 5284

Practical Mathematics K12Gerry promises to be at Jane's house at 19:00.
If he bikes at 15mph, he arrives 1 hour earlier.
If Gerry bikes at 10mph, he is 1 hour late.
What is the speed to be exactly on time?