The ratio of goats to tigers in a zoo is 3:2.
There are a total of 100 animals in the zoo.
10% of the animals are goats and tigers.
How many goats are in the zoo?
The ratio of goats to tigers in a zoo is 3:2.
There are a total of 100 animals in the zoo.
10% of the animals are goats and tigers.
How many goats are in the zoo?
Anna spent $9.90 on groceries. She bought three liters of milk and 24 cereal bars.
Three cereal bars cost the same as one liter of milk.
How much does one cereal bar cost?
Which statement is INCORRECT?
Here,
'even' is an even number;
'odd' is an odd number;
{Evens} = 2Z = {..., -6, -4, -2, 0, 2, 4, 6, ...},
{Odds} = 2Z + 1 = {..., -5, -3, -1, 1, 3, 5, ...}.
Ten men met at a conference.
Each man shook hands with each of the other men exactly once.
How many handshakes took place?
For every birthday, John's parents put as many dollars in a piggy bank as his age in years.
There is a total of $105 in the piggy bank.
How old is he?
The product of three consecutive whole numbers is 999,900.
What is the smallest of the three numbers?
Three boys, A, B, and C, are at the corners of a rectangular field.
At which point should the boys meet so that the sum of the distances they walk to that point is minimized?
Eugenia, the magician, receives a 50% discount every time she asks for the price.
She bought a $100 puppy for less than $1.
How many times did she ask for the price?
The picture shows two dice with faces numbered 1 through 6.
Six faces are visible.
How many dots are NOT visible in the picture?
Find the average of the numbers
7 77 777 7777 77777 777777 7777777
Which is the best estimate of the average?
A melon slice weighs 5kg, and 95% of the weight is from water.
After lying in the sun, the water makes up 75% of the weight.
Estimate the new weight of the slice slice in kg.
Four friends tried to guess the number of sheep in a flock.
Alex guessed 21,
Bob guessed 26,
Chris guessed 20, and
Daniel guessed 21.
Two were wrong by 2, and two were wrong by 3.
How many sheep were in the flock?
Ninety-nine people stand in a line (queue) to buy tickets to a match.
There are enough tickets for each person to purchase two tickets.
Each person in the beginning of the line buys three tickets until there are none left.
How many people do not receive any tickets?
If nine hens can lay six eggs in two days, how many hens would be needed to lay 24 eggs in three days?
What is the lowest number of chain links that must be opened to join the pieces on the right into a circular chain?
Tree diagrams present the hierarchical structure of schools or companies.
Which diagram has the smallest number of hierarchical levels?
A dragon drank 1/5 of the water in a lake.
After a break, he drank 1/4 of the remaining water.
After another break, he drank 1/3 of the remaining water.
After a final break, he drank 1/2 of the remaining water.
How much water is left in the lake, compared with the initial amount?
A banker forgets which key fits in which of three keyholes.
What is the minimum number of trials to identify which key is meant for each lock?
It usually takes a man several hours to walk from a railway station to his home.
If he traveled 20% faster than normal, he would arrive one hour too early.
How many hours does he normally walk?
Anna ran in the north direction at a speed of 8 km/h, Bobby ran east at a speed of 14 km/h, and their dog, Rex, was running between them at a speed of 20 km/h.
How far did the dog travel in one hour?
After a gun is fired in a saloon, 75% of the cowboys have a wounded ear, 80% have a wounded eye, 85% have a wounded arm, and 90% have a wounded leg.
What is the greatest percentage possible of cowboys who do not have any wounds?
I want to move just one matchstick to make the phrase correct.
From which part will I take the matchstick?
I can buy Swiss cheese in boxes of 250 grams, 450 grams, 650 grams, and 850 grams.
What is the smallest number of boxes I will buy if I want exactly 5 kilograms?
John answers 25 multiple-choice questions and receives a zero score.
Each correct answer is worth 3 points.
Two points are deducted for each incorrect answer.
How many questions does he answer correctly?
Several students want to rent a car for the next weekend.
If each contributes $12, they lack $4.
If each contributes $14, they have an extra $4.
How many students are there?
John can eat a pizza in 4 minutes.
Jim can eat a pizza in 5 minutes.
Their grandfather can eat a pizza in 20 minutes.
If two boys and their grandfather all start eating the same pizza at the same time, how many seconds does it take them to finish the pizza?
Construction work commenced on both sides of a 450 meter tunnel.
If a boring machine cuts through chalk marl at a rate of 4 meters per day and another machine cuts through at 5 meters per day, what is the difference between the distances made by the two machines?
Bryan went for a haircut yesterday.
He has 120000 strands of hair and it took 12 minutes to cut all his hairs.
His barber charges $180 per hour.
How much does it cost to cut 1 strand of hair?
Three ducks and four ducklings weigh 3.4kg.
Four ducks and three ducklings weigh 4.3kg.
If all ducks weigh the same and all ducklings weigh the same, what is the weight of a duckling?
The Ancient Olympic Games were held every four years.
They already existed at the time of Homer in 776 BC.
A Roman emperor banned the games in 393 AD.
How many Ancient Olympic Games were held?
[ It should be noted that at the time of Homer they were not using the current Gregorian calendar. Historians have effectively relabelled the old dates to make them easier for us to understand. The Gregorian calendar is widely used, but it can be offensive to non-Christians to use the BC/AD terminology. Hence they are being replaced by BCE and CE, the CE meaning Common Era. Since this change only started happening around 2002, the older system is widely used and you should know both. ] - commented by Leslie Green
Large individual letters are differently priced.
The letters in the word SPRING cost $19.
The letters in the word SUMMER cost $20.
The letters in the word AUTUMN cost $21.
The letters in the word WINTER cost $20.
How much would the letters in the word SEASONS cost?
There is insufficient information to solve this problem.
Use the simplest assumption which exactly matches one of the answers given below.
The figure shows the number of people required for the activities of a project and the number of people available in the company.
When must the project manager hire the largest number of additional personnel?
Logic riddle
This occurs once in every second, once in every hour, and twice in every afternoon.
How often does it occur in every month?
Use all the digits from one to nine and any combination of plus signs and minus signs to obtain 111.
What is the minimum number of plus signs you can use?
Ninety percent of apples in a box and ninety percent of an apple cost the same as all apples in the box.
How many apples are there in the box?
A city hall contains 280 seats. Ninety percent were full and 3/7 of the audience were male.
How many were female?
The mass of Earth is 5.9742 x 1024kg,
the mass of Venus is 4.8685 x 1024kg.
The mass of Mars 6.4185 x 1023kg.
The mass of Moon is 7.3477 x 1022kg
What is the smallest mass from the following?
The total weight of Bob and his sister Anna is 151 kilograms. Bob's weight is 1 kilogram more than twice Anna's weight.
What is Anna's weight?
Alex, Bill, and Craig have a combined weight of 111 kilograms.
Alex weighs 44 kilograms and Bill weighs seven-eighths of Alex's weight.
What is Craig's weight in kilograms?
A letter in the English alphabet has four times as many letters before it as after it.
Find the letter.
The sum of five consecutive numbers is 2010.
What is the sum of all the digits of these five numbers?
14 students are evenly spaced on the circumference of a big circle.
They are numbered from 1 to 14.
Which number is opposite 10?
22 students are evenly spaced on the circumference of a big circle.
They are numbered from 1 to 22.
Which number is opposite 17?
A river boat travels 4 km in 10 minutes with the current and 1 km in 15 minutes against the current.
Determine the speed of the boat.
Three boys put $550, $550, and $555 in a piggy bank.
Bill is 10% taller than Alex.
Craig is 10% taller than Bill.
How should the money be split if it is distributed as a ratio that is proportional to their heights?
Alex paints twice as fast as Bill and three times as fast as Craig.
It takes them 48 minutes to paint a fence.
How long would it take Alex if he works alone?
For every birthday, John's parents put as many dollars in a piggy bank as his age in years.
The total in the piggy bank is $136.
How old is he?
A melon slice weighs 5kg, and 90% of the weight is from water.
After lying in the sun, the water makes up 75% of the weight.
Estimate the new weight of the slice in kg.
Tim is building two hamster cages in the shape of rectangular prisms. The first cage is 44 cm long, 33 cm wide and 33 cm high. The second cage has the same width, but is 20% longer and higher.
What is the difference between the volumes of the cages?
Pipe 1 can empty a full tank in 1 hour. Pipe 2 can empty the tank in 2 hours.
If both pipes are used to empty the tank, how long will it takes to empty the tank?
The number of strawberry cones sold at an ice cream store was 1 more than 3 times the number of vanilla cones sold.
A total of 301 cones were sold.
How many vanilla cones were sold?
Alex needs six tacks to fix two rectangular pictures because he can overlap the pictures.
What is the least number of tacks he needs to tack 120 pictures?
Water flows through two pipes from F to G.
As shown, there are four taps, A, B, C, and D, which can be opened or closed.
What is the most probable outcome if we randomly set all taps?
There is a set of 10 numbers. Five numbers are selected from the set and multiplied together.
The remaining five numbers are also multiplied together. These two numbers are then added.
Find the maximum possible result.
John's dad pays him 70 cents for each correct answer he provides in his math homework and fines him 30 cents for each incorrect answer.
Today, John received $15 after completing 50 problems.
How many problems did John answer correctly?
It takes 2 cards to build a single-storey card house.
It takes 7 cards to build a 2-storey card house.
It takes 15 cards to build a 3-storey card house.
How many stories can you build with 80 cards?
It takes Alex 40 minutes to paint a fence while it takes Bill 1 hour to paint the same fence.
How long would it have taken if they worked together?
There are 30 boys and 60 girls in Funnytown.
There are 70 men and 40 women in Funnytown.
What is the percentage of boys in the town?
Six post office employees are working today.
It takes one employee one minute to serve one person.
How long would you have to wait in the line if you hold number 201?
Anna had an average score of 90 on her first nine tests.
Her average after all ten tests was 88.
What was the score on her last test?
There are 100 rabbits in Funnytown.
The population of rabbits in Funnytown doubles every 8 months.
How long ago was the population of rabbits less than ten?
Each child in a family has at least 1 brother and 3 sisters.
What is the smallest number of children their parents might have?
The time on a digital clock reads 9:43.
What is the shortest length of time, in minutes, until all of these digits appear again?
Juice is poured from a full 1 L bottle into an empty glass until both the glass and the bottle are 90% full.
What is the volume of the glass?
Mrs. Smith has 80 birds: geese, hens and ducks.
The ratio of geese to hens is 1:3.
60% of the birds are ducks.
How many geese does Mrs. Smith have?
It takes six people 36 hours to paint a house.
How long would it take to paint the house if three people were added in the middle of the project?
Swiss trains leave from Zurich for Geneva every hour.
The trip takes three hours.
Each train returns back without any delay.
How many trains are needed to cover a period of twenty-four hours if there are no trains between 1:00 am and 4:00 am?
A cube consists of small black and white cubes.
Two small cubes of the same color never share a common face.
How many more black cubes are there?
A number is said to be perfect if it is equal to the sum of its proper divisors, that is all divisors excepting the number itself.
For example, 28 is a perfect number:
1 + 2 + 4 + 7 + 14 = 28
What is the perfect number that is smaller than 28?
Nine students travel in a car.
They speak English, French and Spanish.
Everybody speaks two languages.
Four students speak French.
Five students speak Spanish.
How many students speak English?
Two hundred employees work for company XYZ, where the ratio of men to women is 11 to 9.
If 60 men leave the company and 10 women are hired, what is the new ratio of men to women?
Four sisters are all 3 years apart in age.
The total of their ages is equal to 30 years.
How old is the eldest sister?
A flower shopkeeper works 6 days per week and sells four times more flowers on Friday and Saturday than the other days. How much does she sell on Friday if she earns $6,000 in flower sales every week.
Eight people pay $7.50 each for a meal in a restaurant.
They leave a 10% tip for the waiter.
How much change do they receive from 4 $20 notes?
The photograph courtesy of Roland Sauter
A non-stop train leaves Zurich for Bern at 58 miles per hour and another non-stop train leaves Bern for Zurich at 62 miles per hour.
How far apart are the trains three minutes before they pass each other?
I ride along a long valley by bus and walk back.
The bus speed is 10 miles per hour and I walk at 4 miles per hour.
If I limit the entire trip to seven hours, how far can I ride by bus?
A shopkeeper buys two kinds of cacao beans at $64 and $96 a bag.
He mixes the beans and sells at $96 a bag, making a profit of 20% on the cost.
What is proportion of the different beans in the mix?
You multiply two consecutive integers and the result is 80 greater than one of them.
What is the smallest of these two integers?
Logic puzzle.
A word for a family member is the same spelled forward and backwards.
How many letters does the word have?
Can you predict the score of any match before it begins?
What is the score of England against France tomorrow?
An Honesty shop sells the first candy for 1 Swiss franc and each next candy for 10% less than the previous one.
Which candy costs nothing?
My father was 27 years old and 9 times as old I was many years ago.
Now he is twice as old as I am.
How old is he now?
At a flower shop, a bouquet of five roses costs $5 and a bouquet of nine roses costs $8.
How much money do I need to buy 77 roses?
A truck can transport either 9 bags or 7 wooden boxes.
Yesterday, the truck transferred 74 items and it was full each time.
How many of them were cacao bags?
A car weighs 988kg when empty and 1224kg when John, his sister Jane, and their two parents are inside.
What is the average weight of a member of the family in kg?
Anna has 7 biscuits, Bill has 4, and Cindy has 1.
They share them out equally.
Cindy pays for her biscuits by leaving 9 wafers.
What is the fairest way for Anna and Bill to share out their wafers?
If the green, yellow, and red regions have areas of 12, 9, and 7 square meters, what is the area of the blue region?
Metro Card prices: a single ride is $2.50 and a 7-day Metro Card costs $29.
How many rides per week makes the 7-day Metro Card profitable?
In a remote county, 40 villages are connected by roads in such a way that three roads lead in and out of each village. There is only one road in and out of the county.
How many roads are there in the county?
When two non-zero integers are added, multiplied, divided, or subtracted, I can always arrange them such that I get one of the numbers or 3.
What is the largest number?
How many pages do I turn over to go from page 33 to page 222?
(The convention is to number page 1 as the right hand page in a book.)
Alex is twice as old as Bill was when he weighed 10kg more than Cindy.
How much did Alex weigh at that time if Cindy weighed 25kg and the sum of their three weights was 100kg then and it was 6 years ago?
What is the largest result that can be achieved if different letters in the expression
AB6 + BC1
are replaced with different numbers from 0 to 9?
The question is typical for PISA Test.
PISA stands for Programme for International Student Assessment.
Three couples have 81 coins to share equally between them.
How many coins will each husband get if his wife always gets twice as many as he receives?
A class was given a math problem with four options as the answer.
Ten students chose option A,
six students chose option B, and
two students chose option C.
Gerry Geek chose option D.
Five students didn’t answer.
Which option is correct if the teacher said that one twelfth of the class gave the correct answer?
Once upon a time, there were three little pigs - ages 2, 4, and 6 months.
If one was born in January, when was one of his brothers born?
I multiply the ages of three kids and get 48.
If I add their ages, what is the smallest possible sum I might get?
A car traveling with speed 12 meters per second decelerates uniformly until it comes to rest for 4 seconds.
What is the total distance the car travels as it decelerates?
A car traveling with speed 12 meters per second decelerates uniformly until it comes to rest.
It takes 30 meters to stop.
How much time does it take?
Gerry had 24 LEGO bricks and Jane had 6 bricks.
Gerry gave some of his bricks to Jane so that she ended with twice as many bricks as Gerry.
How many bricks did Gerry give to Jane?
It takes 30 seconds to cut the woodblock into three pieces.
How much time does it takes to cut the same block into four pieces?
Gerry and Jane race on a velodrome.
Gerry can ride 11 miles for every 9 miles that Jane rides.
If Jane rode 54 miles today, how far did Gerry ride?
According to research, an average waist circumference of American men is greater than 40 inches (1 meter).
A $1 bill measures 156 mm long and weighs approximately 1 gram.
How many $1 bills are needed to cover the waist?
If you make one word using each letter below only once, what place does the letter e take?
e r t s s s
Gerry and Jane are flipping dimes.
Each time, they bet $0.10.
At the end, Jane won 30 cents and Gerry won 2 times.
How many games did they play?
Inflation is where the cost of food, goods, and services rises with time.
Governments are happy with a figure in the range of 1 to 4 percent per year.
If there is a 500% inflation in a country how much will a 2-dollar telephone cost in one year?
Today Jane worked 3 hours at the rate of $9.90 per hour.
How much did she earn today if she spent $2 for transport?
Andrew called all the girls in his class.
He called three of them twice, and two of them 3 times.
Each call cost $0.50. His father, being a fair man, insists that Andrew pays the $10 total cost himself.
How many girls are there in Andrew's class?
Two American coins add up to 35 cents but one of them is not a dime.
What is the coin?
Penny = 1 cent.
Nickel = 5 cents.
Dime = 10 cents.
Quarter = 25 cents.
I choose a cube, which is third from the left, fourth from the right, fifth from the bottom, and sixth from the top.
How many cubes are there?
On the train to New York, Jane sat in the second carriage from the front, and Gerry sat in the third carriage from the back.
They saw each other in the windows and noted that there were 4 carriages between them.
How many carriages were there in the train?
Four sisters are all 2 years apart in age and the youngest is 4 years old.
In how many years will the four daughters together be as old as their father, who is 46 now?
Gerry and Jane are on opposite sides of the fountain.
They then start to run round the fountain.
Gerry's speed is 5/4 of Jane's speed.
How many circuits has Gerry completed when he catches up with Jane for the first time?
Jane and Kate are ski racing. They both start at the same place, at the same time, and follow the same path. Jane is traveling at 5 m/s and Kate is traveling at 8 m/s.
How many meters ahead is Kate after a minute?
If we define the 6 letters in the middle of the alphabet as middle letters, what part of the word 'MIDDLE' are middle letters?
Leslie Green asks:
My Interocitor is broken. Fortunately I have replacements for every single part and each part takes the same time to fit as any other. I also know that the designers were so unbelievably clever that it is inconceivable that one faulty part would cause other parts to fail.
The Interocitor has 60 parts, all of which are different, and I can change from one part to another in 10 seconds without even turning the power off (hot-swappable parts). I will know that it is working immediately.
What is the minimum time in which I can guarantee to have fixed it?
An interocitor is a fictional multi-functional device that first appeared in the 1949 story "The Alien Machine".
Leslie Green asks:
"Consider which would hurt less if it was accidentally dropped on your foot, a 30kg bag of cacao beans or a 30kg bag of feathers."
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.
How far did he travel in the first 3 hours?
Author: Leslie Green
What is the main difference between the pictures on the left page and on the right page?
The problem is similar to 100 Bongard Problems on visual pattern recognition.
M. Bongard (1924 – 1971) was a Russian computer scientist. His tests played an important role in the disciplines of cognitive psychology and cognitive science.
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.
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.
An empty truck weighs 5,600 kg. When the truck is loaded with 24 identical crates, the total weight is 20,000 kg.
What is the weight of one crate?
Anna, Betty, and Cindy are playing tennis.
The winner of a set stays on, and the loser waits her turn again.
Anna played 4 sets,
Betty played 6 sets, Cindy played 4 sets.
What is the largest number of sets a girl could have won?
I weigh my three parrots in pairs because my balance only shows the correct weight if the mass is greater than 2 kg.
Buddy and Kiwi weigh 2.8 kg altogether.
Kiwi and Tiki weigh 2.4 kg altogether.
Tiki and Buddy weigh 3.2 kg altogether.
Who has the largest weight?
In order to disguise their ages, four women will only admit that the sum of the (integer) ages of Anna, Belinda, and Christina is 105. They will also admit that the sum of the (integer) ages of Daisy, Belinda, and Christina is 89.
What can you say with certainty?
Author: Leslie Green
John the miller has more flour bags than you see in the picture.
He counted his bags in fours: he had 1 left over.
He counted his bags in threes: he had 1 left over.
He counted his bags in twos: he had 1 left over.
What is the minimum possible number of bags John can have?
If it were four hours earlier, it would be twice as long until midnight as it would be if it were four hours later.
What time is it now?
Mr. and Mrs. Smith borrow $54,000 to buy a new car for their son Gerry.
The loan is to be paid off in three years without interest.
Gerry promises to pay 20% of the monthly payment to his parents.
How much is Gerry's monthly payment?
You are on a critical mission. You reach the shore of a lake where 60 similar tiny motor boats are moored. None of the boats have any fuel on board. There are 52 full cans of fuel available, with each can being the same capacity as the on-board fuel tanks of the boats.
There are plenty of volunteers on hand to help you.
The boats use fuel at a steady rate, regardless of the amount of fuel on board. One tank of fuel lasts for 1 hour. Each boat can only hold 3 spare fuel cans, and a fuel can, once opened, has to be completely emptied into the fuel tank of the boat it is on. Fuel in the onboard tanks cannot be shared.
You need to get away as far as possible from this place by boat. How many boats should start the journey?
Author: Leslie Green
A boy, a girl and a dog are walking on a 10-mile circular route.
Simultaneously, the boy starts his journey clockwise and the girl and the dog starts walking in opposite direction: the boy at 4 mph, the girl at 2 mph, and the dog runs back and forth between them at 6 mph.
When do all three meet?
Leslie Green asks:
99 spheres with the same diameter (2cm), weight, and surface texture are put into a black bag. These spheres are coloured red, green, blue, white, pink, fushia, magenta, indigo, cyan, azure, gray, jade, plum, ruby, salmon, and viridian in some undefined way. A single silver sphere is added to the bag. It is double the diameter of the rest, but has the same texture.
You are blindfolded and allowed to pick one (and only one) sphere from the bag. If you pick a vaguely red sphere you get $10. If you pick the special silver sphere you get $1000. If you pick anything else you get nothing.
What is the probability of your getting more than $10?
Gerry has 32 pounds of gold in small pieces.
What is the minimum number of times he uses the balance scale with two pans to measure out 12 pounds of the gold?
If Jane ate 1 blue berry from each row, and then Gerry ate 1 blue berry from each line, how many berries had been left?
Gerry has an 11-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?
There are two elves in front of an elf, two elves behind an elf and an elf in the middle.
How many elves are there?
Planets orbit around the Sun:
Mercury 3 Earth months;
Venus 7 Earth months;
Earth 1 Earth year;
Mars 23 Earth months;
Jupiter 12 Earth years;
Saturn 30 Earth years;
Uranus 84 Earth years;
Neptune 165 Earth years;
Pluto 248 Earth years;
John and Jim are twins.
John flew to Mars 20 years ago and happily lived there all the time, while Jim lives on the Earth.
Who is younger now?
April is 10 years old. If June were half as old as she is now, she would still be twice as old as April.
How old is June?
Gerry has $8, Jane $30, and Kate as much as Gerry and Jane together.
What are the proportions of the money they have?
A brick weighs 777 grams plus half a brick. 
How many whole numbers between 222 and 444 include the number 3?
How many circles can be placed inside the rectangle without intersection?
What do the snowflakes have in common?
What number should replace the question mark?
How many ways can one travel from point H to point F if moving north and west are not permitted?
Find the sum of these 100 numbers.
Find the next letter in the sequence.
What is the largest product of positive integers that add up to 15?
Which is the single discount that is the same as three successive discounts of 20% ?
If I fold this net, which cube will I get?
John has two parents and four grandparents. 
Which statement is NOT correct?
An apple costs $1 and one third of the price of the apple. 
Which direction is the London coach going?
What is half of 8? 
If I place a pair of brackets in to this number expression, what result can be obtained?
Using eight eights and addition only, make 1000. 
How many ways can you rearrange the letters in "DAD" to produce a word?
If Evguenia was exactly 9 years old on the 183rd day of 2007, in what month was she born? 
Leslie Green asks: 
If John earns $19.96 per hour, how much will he get for a 40-hour week?
Which is certainly a fake coin?
Never judge by appearances