Suppose there is some large number of nuts, N, where N is evenly divisible by 6. We arrange the nuts in a neat line and mark nuts to be discarded if their position numbers are divisible by either 2 or 3. For example nuts at positions { 2, 4, 6, 8, 10, ... } are marked to be discarded, and so are nuts at positions {3, 6, 9, 12, 15, ... }.
Having discarded the marked nuts, how many are left?
On a circular road seventeen police officers are on a special mission. Two neighboring policemen are 1 km apart along the road.
They have badges numbered from 1 to 17, and they remain in that order clockwise. Their captain orders them to change their positions so that the order of the badges becomes from 1 to 17 anti-clockwise.
What is the shortest total distance they must walk along the road to do this?
A certain number of students take a test, their mean score being 49. Another group of students take the same test, but there are twice as many students in this second group.
The combined mean score is now 45.
What is the mean test result for the second group on its own?
There are N students in a class.
Can you find at least two students in the class with the same number of friends?
Note: The friendships are symmetric: if Anthony is a friend of Bethany, then Bethany is a friend of Anthony.
Three girls bought an apple tree. Aylin contributed $50, Belin $20, and Cailin $10. They want one of their number to plant the tree in her garden.
They have a fair coin that shows heads 50 percent of the time and tails 50 percent of the time. They want to toss the coin several times to define who wins a tree.
Their chances must be proportional to their contributions.
What is the least number of throws that is needed?
The game is an example of the combinatorial game Nim in which two players take turns removing objects from a pile of objects.
There are 13 coins a pile.
On each turn, Jane and Gerry must take either one or two coins from the pile. They keep all the coins they take. The person who takes the last coin also receives 7 additional coins. The object of the game is to collect as many coins as possible.
If Jane starts first, what is the largest number of coins she can obtain if they both are smart?
80 people live in a village.
80% of them are adults.
40 of the adults are married.
60% of them are brown-eyed.
20 of the married brown-eyed adults are redheaded.
80% of them are tall (taller than 1.8 meters).
What percentage of the village's population are married redheaded brown-eyed tall adults?
The numbers from 1 to 12 are placed clockwise on a circle. We move around the circle clockwise erasing every other number until only one number remains.
If we start by erasing 1, what is the last remaining number on the circle?
On an island a family is considered as lucky if the number of female and male children is the same.
For example, the probability for a two-child family to be lucky is 50%.
What is the probability for a four-child family to be lucky?
The probability that a child is a girl (or a boy) is 50%.
Six people sit at a round table. They swap their places in pairs between two neighbors to change the sitting order from clockwise to the inverse direction (anti-clockwise).
What is the minimum necessary number of pair swaps needed?
A magician put several otherwise identical balls of different colours in a bag.
He said that if we take a ball, there are more chances that it is red.
I asked: "Are there more chances to take a red ball?" The answer was "No".
What is the least possible number of balls in the bag?
The image shows three triangles, two individual small triangles, plus the two triangles together making a larger triangle.
If instead of 3 blue vertexes (vertices) we had 100 blue vertexes all along the dotted line, together with a suitable number of green sides joining the vertexes, how many triangles would there be?
The day of the week in a note book has been recorded with just the first letter of the given day.
What is the probability that the weekday is not clearly stated?
What is the most probable score on two fair standard 6-sided dice?
The score is the sum of the values shown by the dice.
In a fair game using a standard 6-sided die, the square of the value on the top face of the die after being thrown is the amount you get paid in dollars.
If you throw a 3 you get $9.
What is the average win per throw?
The kid's dart board has only two possible scores per dart. Any dart on the edge between the 4-region and the 7-region is not counted.
The dart is removed from the board after each throw, but a running total score is kept.
The dart can be thrown as often as needed.
How many scores above zero are not possible?
At the end of step 1, Giselle has counted to 1.
At the end of step 2, Giselle has counted to 3, which is 2 on from the previous step.
At the end of step 3, Giselle has counted to 7, which is 4 on from the previous step.
At each next step, the count moves on from the previous count by twice the previous move.
What is the count at the end of step 10?
1 house (blue) is protected by 12 units of flood defence (brown).
4 houses are protected by 24 units of flood defence (6 per house).
What is the minimum length of flood defence per house for a very large square grid of houses?
I roll two dice.
What is the probability that the second number will be greater than the first number?
The 3x3x3 cube is made of 26 yellow small cubes and 1 green cube that are glued together.
How many different 3x3x3 cubes of this type are there?
You can rotate the large cubes when comparing them.
Jane draws a pyramid with 6 lines of alternating green and yellow circles.
How many yellow circles would such a pyramid with 2N lines have?
The director of a prison decides to give 4 prisoners a slim chance to leave. He arranges 4 numbered boxes [1 - 4] in a room. Under each box is a random unique ticket in the inclusive range 1 to 4. The 4 prisoners are also numbered 1 to 4, inclusive. The prisoners enter the room one at a time in a random order, then pick two boxes at random to see the hidden ticket numbers. The prisoners leave the room in exactly the same state as they entered it, and by another door, so they do not interact with the other prisoners.
If and only if all four prisoners find their respective numbers do they get early release.
What is the probability of this outcome?
The picture shows 5 blue and 5 yellow circles in a line.
Imagine such a line with 50 blue circles at the left and 50 yellow circles at the right.
We exchange the positions of two neighbouring circles of different colours for one step.
How many steps are needed to move all 50 blue circles to the right and all 50 yellow circles to the left?
If I roll five dice, one at a time, what is the probability that I will get a five on the fifth roll?
Gerry decides to read an 1001-page adventure book One Thousand and One Nights as follows:
On the first day he reads just one page. The second day he reads 2 pages, the third day 3 pages, and so on.
How long does it take to read the whole book?
Three ants begin to crawl when the traffic light becomes green. They crawl only on the red part of the triangular sign. Each of them randomly chooses one of the two possible directions.
What is the probability that two ants don't collide?
The number of girls in a class is greater than 60% and smaller than 65%.
What is the least possible number of students in the class?
At the beginning of a school year a new math teacher asked 25 students of a class "Who loves math?"
Only 20% answered Yes, while others said No.
80% of them answered Yes at the end of the school year.
What is the least possible number of students that started loving math during the year?
We randomly pick two squares on the 2 x 2 grid.
What is the probability that the squares share at least one common vertex?
The probability that a $1 ticket wins $2 is 0.4.
What overall result do you expect (on average) if you buy 5 tickets?
A carpenter wishes to cut a wooden cube, four inches on a side, into 64 one-inch cubes.
He can do this easily by making 12 cuts through the cube, keeping the pieces together in the cube shape.
What is the smallest number of necessary cuts if he rearranges the pieces after each cut?
Three large triangles contain small blue and white triangles.
How many small blue triangles are there in a large triangle that has 10 blue triangles in its base?
A shoe lace is lying on a table, with as many crossing points as shown in the image.
The lace is equally likely to pass over itself or under itself when we move from one end to another.
What is the probability that the shoe lace is knotted after its ends are pulled?
Five friends live in 5 different cities.
The pictures shows the travel time of available routes between the cities in minutes.
In which city should they meet if they want to meet as soon as possible?
The picture shows two sets with 7 and 8 columns.
What would be the number of small squares in two similar sets with 99 and 100 columns?
There are 200 dice in a bag, 99% of them are red and the others are green.
How many red dice are needed to be removed to make the percentage of red dice 98%?
Place numbers 1, 2, 3, 4, and 5 in the arms of a star.
The outside numbers are the results of multiplication of the two numbers in the nearest arms of the star.
The sum of the five outside numbers is 43 in the given example.
What is the largest possible sum of the outside numbers?
Addy laid 2022 nuts in a long line.
When his friends removed nuts, they never considered where nuts used to be.
Bady removed every sixth nut.
Cady removed every fifth nut.
Dady removed every fourth nut.
Eady removed every third nut.
Fady removed every second nut.
Gady took the remaining nuts.
How many nuts did Gady take?
This large cube is made from smaller cubes.
The number of white cubes on each side of the large cube is the same.
There are only small red cubes inside the structure.
What is the percentage of small white cubes in the structure?
In the 1980s, a company tried to compete with the Macdonald's Quarter Pounder by selling a ⅓ pound burger at a lower cost.
The product failed, because most customers thought the ⅓ pound burger was smaller.
How much is ⅓ greater than ¼?
Sixteen boys sit on a bench. The first student tells a number to the second student and he tells another number to the next student.
The first student starts with 17 and each next student either divides the number he received by 2 if it is even or multiplies it by 3 and adds 1 if it is odd.
What is the final result?
This is a standard set of dominoes.
The dominoes have numbers from 0 to 6.
How many dominoes are there in a full set with numbers from 0 to 10?
John must play three singles matches against his parents.
If he wins two matches in a row he gets money for a new computer.
His father is a better player than his mother.
Should he play Mother-Father-Mother (M-F-M) or some other order?
If I roll three dice and multiply the three resulting numbers,
what is the probability that the product will be odd?
Odd positive numbers are 1, 3, 5, …
There are 7 students in a group: 3 girls and 4 boys.
Their teacher randomly chooses two students.
What is the probability that they are a boy and a girl?
Odd numbers are: 1, 3, 5, 7, . . .
Even numbers are: 2, 4, 6, 8, . . .
Write a positive whole number onto every card in the pyramid, so that every number is equal to the sum of the two numbers on the cards that are directly below.
What is the maximum number of odd numbers you can write on the cards?
Gerry plans to travel across the network from point A to point B, travelling only in the direction of the arrows.
How many routes are possible?
The ball is made by sewing together 12 black pentagons and 20 white hexagons. The area of a black pentagon is approximately ⅔ of the area of a white hexagon.
Gerry kicks the ball and scores a goal.
What is the probability that he kicks the black part of the ball?
Some students in Johnny's class, including him, have a math grade below C.
If he improves his grade to C or higher, the percent of below C students will be 24%.
If Johnny leaves the class, the percent of the below C students will be 25%.
How many students are there in the class?
Martin has 9 reams of copy paper (500 sheets each).
He wants to equally share them into 5 piles.
It takes 1 minute to count 100 sheets.
How much time does it take to do the job?
There are 7 red, 8 yellow, and 9 green balls in the bag. All the balls are the same size and weight. You take each ball without looking.
What is the minimum number of balls you need to take from the bag to be sure that you have three balls of the same color?
In a student hostel, 30 rooms have one occupant, 20 rooms have two occupants, and 10 rooms have three occupants.
What percentage of students have no room-mates?
Jane painted pickets of a fence. The total number of wooden pickets is 77.
On Monday she painted every seventh picket of the fence: number 7, 14, 21, . . .
On Tuesday she painted every sixth picket of the fence.
On Wednesday she painted every fifth picket of the fence.
On Thursday she painted every fourth picket of the fence.
On Friday she painted every third picket of the fence.
On Saturday she painted every second picket of the fence.
On Sunday she went to a local church and did not paint the fence.
If a picket was already painted, then she just added a small decoration element.
How many pickets are not painted yet?
You have a set of five wooden sticks of lengths of 1, 2, 3, 4, and 5 inches.
You can put three of them together tip to tip and form a triangle.
What is the probability that three randomly chosen sticks form a triangle?
A shop suggests that I pay $9.99 or 9% of the smart watch's price monthly during 12 months.
What is the difference of the money I pay during the year and the price that I can pay right now?
Seventy percent of the earth’s surface is covered in water. However, only 3% of the earth’s water is freshwater and two-thirds of freshwater is frozen in ice sheets and glaciers. The rest is found in lakes and rivers.
What part of the earth's surface is unfrozen rivers and lakes?
Our hero has walked into a torch-lit smokey cave where there are three large identical-looking covered magic urns. He is told that each urn contains 3 balls of the same colour. One urn contains only red balls, one contains only blue balls, and the other only green balls. Being magic urns, as soon as a ball is removed, it is magically replaced with another ball of the same colour. Additionally the contents of all three urns also rearrange themselves when the lid is closed so that a new random sequence of colours is achieved. Nevertheless, at any moment in time the three urns together contain all the available colours, and each urn only contains one ball colour.
Given that our hero is maximally unlucky, how many balls does he need to remove from the urns, one at a time, until he has a pair of the same colour?
(The lid must be closed after each ball is withdrawn. Having opened a lid on an urn, a ball must be withdrawn).
The regions A, B, and C on the diagram were intended to represent:
{ girls with blonde hair }, { kids who wear glasses }, and { girls with brown hair}.
Sadly the index has gone missing, so we don't know which label refers to which set.
What set is outside of all three sets?
In this Venn diagram the outer rectangular box contains all integers.
The circle A contains all even counting numbers.
The circle B contains all odd integers.
What is in the white region?
Draw a small circle around each of 5 numbers, one circle per number. The sum of the circled numbers must be 21.
In how many different ways can this be done?
There are five students in a group.
Anna has 4 friends in the group.
Betty has 3 friends in the group.
Craig has 2 friends in the group.
Dianna has 1 friend in the group.
How many friends in the group does Ethan have?
There are ninety students in the Summer Wizard School, including Katie and Harry.
How many students failed the exit exam if ninety percent successfully passed?
All these rubber boots have the same size.
Jane picks a blue boot and asks Gerry to throw her another boot, which he randomly chooses.
What is the chance that it will be a good match for her?
You wish to make a sign using exactly 3 distinct letters from this set, with the total cost of the letters being exactly $10.
In how many ways can this be done?
There are
10 red tokens numbered from 1 to 10 in a red bag,
5 blue tokens numbered from 6 to 10 in a blue bag, and
2 green tokens with numbers 6 and 7 in a green bag.
You blindly select a token from each bag.
What is the probability of getting three 7s?
We wish to navigate in this triangular table from the top box (containing 6) to the bottom right box (containing 46).
Each step can only be down (D) or right (R), and we must stay within the bounds of the table.
Any valid path will be a sequence of D and R steps.
How many letters are in such a sequence?
The first column has 6 boxes in it. Suppose that instead it had N boxes in the first column, with the same type of overall shape.
How many green squares would there be?
Count the numbers of green squares on each side of a Rubik cube.
What is the largest possible product of the six numbers?
A tetrahedron (triangular-based pyramid) has four faces. Dice can be made from regular tetrahedra, with the faces numbered 1 to 4 inclusive.
What is the average (mean) score from one roll of such a die?
Five friends use a coin to fairly decide which one of them goes shopping.
What is the smallest possible number of flips needed to randomly choose a single person?
We wish to form as many distinct (unique) sequences of the letters A, B, and C as possible, given that each sequence uses each letter exactly once.
How many are there?
On a standard die, the sum of the numbers on any pair of opposite faces is 7.
A 3x3x3 cube is formed by gluing together 27 standard dice.
What is the maximum possible sum of all the numbers showing on the surface of the 3x3x3 cube?
The pile contains coins of value 1, 3, and 5 piastras.
With 10 coins, how many distinct combinations of coins can be used to form the sum of 26 piastras?
Define set P as the set of all prime numbers.
Define set E as the set of all even counting numbers.
Define set X as the set containing elements which occur in both set P and set E.
How many elements are in set X?
An inverse operation undoes the first operation. We do a particular operation such as adding a constant. Doing the inverse operation would be subtracting the same constant.
What is the inverse operation to adding 25%?
The Smiths have two children who have the right to sit in the front seat of the car. When they get into their car, two people sit in the front, and the other two sit in the back. Either Mr. Smith or Mrs. Smith drive the car.
How many seating arrangements are possible?
1! + 2! + 3! + . . . + 98! + 99!
What is the last digit of the sum?
3! means 3 factorial : 3! = 1 x 2 x 3 = 6
Gisela and Klaus play a game with three tiles, numbered 1 to 3 respectively.
The first player picks a tile and places it face up on the table.
The second player picks a tile and places it to the left or right of the existing tile.
The first player takes the remaining tile, and places it to the left or right of the previously placed pair of tiles.
Without worrying about the winning positions, how many different game plays are there?
You have a 5 digit number, and you wish to swap the digits around, subject to the constraint that only non-adjacent digits can be swapped.
How many distinct swaps are possible as the first step?
Five numbers have an average (arithmetic mean) that is 10.
The smallest number is 5 and the largest number is 30.
What is the average of the three other numbers?
This is a typical ACT question.
Jane tosses a fair coin three times.
What is the probability that she gets either 3 heads or 3 tails?
Your mission is to plan the transportation of two loads of purified Radioactium from the green squares to the blue squares. At each step, both loads can (and must) be moved exactly one square (left, right, up, down, or diagonally). They must both reach the blue squares after the same number of steps, and each load must not return to a previous square on its path. No step can end on a red no-go square.
Each load of Radioactium is individually subcritical. If two loads end up touching on adjacent sides then that makes a supercritical mass - it is best not to let that happen! Loads can touch on the corners without unpleasant consequences.
How many steps are required to complete the mission?
I have gold coins in denominations of 1, 2, 4, 8, 16 and 30 guilders.
I wish to make a single payment of a whole number of guilders, without requiring change.
Which amount is the smallest payment that cannot be made with the available coins?
We have 3 shapes to be placed along a line.
The order is which they are placed is important.
Each shape can occur any number of times along the line.
We don't care about their color.
How many different arrangements are there?
A company has concrete blocks that weigh 4, 5, 6, 7, 8, 9, 10, and 11 tons.
The capacity of the company truck is 12 tons.
How many trips are necessary to deliver all the blocks to a customer?
1 2 3 4 5 6 7 8 = ?
Put plus (+) or minus (-) signs between the numbers.
Which result cannot be achieved?
Imagine that the numbers in the image are written onto a cylinder so that 1 is next to 5, but also next to 3 -- going the other way.
A swap consists of interchanging the contents of two adjacent boxes. For example 2 and 4 are adjacent, and they could be swapped in one operation.
We want to sort this set of numbers into increasing order, but they are allowed to increase left-to-right or right-to-left. We always check for increasing order starting from 1, but 1 does not have to be in the leftmost position shown.
How many swaps do we need to perform?
You have a sequence of 9 letters.
XXXYYYZZZ
For each move you take a letter out of the sequence, and the sequence closes up so that no gap is left behind. This letter is then placed back into the sequence by creating a new gap between the letters.
What is the minimum number of moves to transform the sequence into XYZXYZXYZ?
On a road, the probability of observing a car during an hour is 0.2.
What is the probability of observing a car in two hours?
Each colored square is only allowed to share a common side with at most two other colored squares. Here we show increasing square grid sizes, packed with as many colored squares as possible (whilst still following the common-side rule).
The sequence of maximum numbers of squares in each grid is: 1, 4, 8, 12, 18, 26, 34.
What is the maximum number of colored squares we can fit in the 8x8 grid whilst still following the maximum common-sides rule?
by Leslie Green
We have 3x3 blue tiles, but to add interest we color exactly 2 of the 9 squares green.
How many distinct tiles can we create?
(A tile is not distinct if another tile can be rotated and then looks the same as this one. Mirror symmetry, on the other hand, is considered as distinct.)
Gerry knows nothing and Jane knows all the correct answers on a SAT test.
Gerry managed to see Jane's answers to half of the 44 multiple-choice math questions on the SAT. He answered the remaining questions by guessing between one of five answer choices for each multiple-choice question. He answered all the questions.
Calculate his expected fractional score, expressed as a percentage, for the mathematical part of the test.
Evguenia's teacher assigns 10 math problems to solve. She sorts them from the simplest to the hardest. She can solve the simplest problem in 1 minute. Each following problem requires 30 seconds more than the previous one.
How many problems would Evguenia solve in 20 minutes, given that the sorting operation took a negligible amount of time?
The Arecibo message was a short radio message sent into space to celebrate the remodeling of the Arecibo radio telescope in Puerto Rico in 1974. It will take 25,000 years for the message to reach the stars, and at least another 25,000 years to get any reply.
The first part of the message (the picture at the right) shows the numbers one (1) to ten (10).
What fraction of the messages is white squares?
The Happy Town Council decides not to use unhappy numbers (4 and 13) and their multiples.
If there are 77 houses in Happy End Street, what is the number of the last house?
On an island, everybody owns only one car. Every car's license plate contains only 2 characters: digits or capital English letters.
Estimate the maximum possible number of people on the island.
Gerry opens every single locker. Then he closes every second locker. Then he goes to every third locker, closing it if it is open, or opening it if it is closed.
Then he does the same with every fourth locker and so on. The process is completed with the twelfth locker.
How many lockers are open at the end?
In a group of five students, Ann has one real friend among them, Betty has two, Craig has three, and Dianna has two.
How many real friends does Edgar have in the group?
Three boys decided to give a rare coin to one them. They want to randomly choose the person. They want that Gerry who is sick today has twice as many chances as another boy.
What is the minimum number of times they flip the coin to define the winner?
What value of H is not possible according to the pattern of the equation?
(In this context the three dots, an ellipsis, means that terms have been omitted, but the pattern continues unchanged throughout.)
In a basketball tournament each team plays one match against each of the other teams. There can be no draws.
If 12.5% of the teams do not win any of their matches, how many teams are there?
The positive integers m and n satisfy the equation
20m + 19n = 2019
How many possible values of n are there?
At a meeting, everyone shakes hands with everyone else.
Altogether there were 36 handshakes.
How many people were there in the meeting?
Ten consecutive integers have a sum of 155.
What is the sum of the least and the greatest of the ten integers?
What part of the first 10 natural numbers are prime numbers?
A prime number is a positive integer that has no positive divisors other than 1 and itself.
The managing director of a company decides to dismiss 50% of the company employees and to increase the wages of the others by 50%.
What is the company spending on the people compared to the initial situation?
Swiss public schools usually use a 6-point grading scale, where 6 represents the highest grade and 1 the lowest possible one.
6 (excellent) is the best possible grade. (100%)
5.5 (very good) (90%)
5 (good)(80%)
4.5 (satisfactory)(70%)
4 (sufficient) (60%)
3.5 (insufficient) (below 50%)
3 (poor) (40%)
2.5 (very poor) (30%)
2 (very poor) (20%)
1.5 (very poor) (10%)
1 (very poor) (0%)
If Hans got 3 fives, 2 fours and 1 one, what is his average score?
Betty collected 20% more marbles than Alice, but 20% less than Cindy.
How many more marbles does Cindy have compared to Alice?
A broken calculator does not display the digit 0.
For example, if Gerry keys in the number 2020, only the number 22 is displayed, with no spaces.
He keyed in a 7-digit number, but only 12345 appeared on the display.
How many different numbers could Gerry have entered?
There were 2048 books in a school library.
The parents' donation helped to increase the number of books by 25% every year for 4 years.
What is the number of books now?
You have 243 gold coins, exactly one of which is fake, and therefore significantly lighter than the rest. You have a pair of balance scales which will balance for any equal number of true gold coins on both sides.
What is the least number of balance operations required in order to guarantee finding the fake coin in the case that the person choosing the coins is infeasibly lucky?
by Leslie Green
Tom goes to the shop and buys a carton of 6 eggs. He fails to check for cracks in the eggs until he gets home. He then finds one egg is broken, a total loss.
What is the effective cost increase per egg?
Gerry has 400 coins, 4% are gold coins and the rest are copper. He removes one copper coin every day until the pile contains 40% gold coins.
Estimate how much time it takes.
When a boy joins the group of five students, the average (mean) age of the group decreases from 11 to 10 years.
What is his age?
I have a very poor memory for numbers, so I like to write down PIN numbers in a little grid (in a fairly secure location), as shown. Each letter represents a digit in the PIN number.
What I do remember is a little picture of the sequence in which the digits were written down. Maybe clockwise, maybe anti-clockwise, maybe diagonal, and of course starting with any digit.
How many such little pictures are possible?
A letter costs the exact number of dollars as its position in the alphabet.
For example letter A costs $1, letter B costs $2, . . ., and letter Z costs $26.
What is the average cost of the letters?
The term "per cent" is derived from the Latin per centum, meaning "by the hundred".
According to the Royal Statistical Society, 10% of the UK adult population does not understand percentages.
Which example confirms this?
Only Gerry and Jane correctly solved a math puzzle.
If the teacher said that 95% failed to solve the puzzle, how many students tried to solve it?
The image shows Stirling's Triangle. Each element in a row is generated from just the two elements above it.
In Pascal's Triangle we generate an element E from the left value above, L, and the right value above, R, as E = L + R.
If either L or R does not exist (outside the triangle) we give it a value of 0.
Stirling's Triangle uses a different rule.
What is the missing value?
by Leslie Green
John's monthly electric bill was $40 in January.
The bill was increased by 2.5% from April, and by $4 from September.
How much more does John pay in December compared to January?
In a class survey, 7 children walk to school, 8 come on a bike and 9 come by car.
What fraction (expressed as a percentage) come by car?
According to the wise old saying,
"There are old soldiers, and there are bold soldiers, but there are no old bold soldiers".
Supposing this statement to be true, which region(s) on the Venn diagram represent this empty set.
by Leslie Green
The human skeleton is composed of 270 bones at birth. This total decreases to 206 bones by adulthood after some bones have fused together.
Bones of the arm include those in the wrist and hand. There are a total of 64 bones in the arms of an adult (32 on each side).
Approximately what percentage of bones in the human body are found in the arms of an adult?
Gerry shuffled a standard deck with 26 red and 26 black cards and started looking at the colors of the cards.
What is the probability that the top card is the same color as the bottom card?
Mr Greed's 5929 gold ingots can be separated into equal piles, where a "pile" is more than one ingot.
What is the smallest possible number of the ingots in a pile?
Gerry had $7, Jane $18, and Kate as much as Gerry and Jane together.
They gave all their money to a Children Charity Foundation.
What was Gerry's contribution in percent?
A genie has rewarded Gerry with four wishes to be executed on Gerry's money:
A: Add $1
D: Divide by 2
M: Multiply by 3
S: Subtract $4
Gerry must take all four wishes.
In which order do you advise Gerry to use these wishes?
When the genie does calculations
it effectively presses "equals" after each step.
Thus "add one, multiply by 3" does not appear as X + 1 x 3
it is evaluated as (X + 1) x 3.
The genie is using a running total, not rules of precedence.
Bob is currently paid $99 for working a day.
His hourly wage is to be increased by 10% but his hours are to be reduced by 10%.
What is his new daily salary?
In a school, the size of a class is between 20 and 30 students.
If 48% of the students in a class are girls, how many boys are there in the class?
Evguenia had a mean score of 80 points on five tests. One test was scored incorrectly, and its score was later raised by ten points.
What is the new mean score?
The Funny Pins bowling club consists of five married couples.
The club has decided to create a mixed (man-woman) team for the next tournament by randomly selecting partners. They don't want spouses to play in the team.
How many different teams are possible?
In the diagram on the right, certain paths correctly spell the word PUZZLE.
What is the total number of different paths for PUZZLE in the diagram?
A small unmanned rocket program is having budget difficulties so the project director wants at least a 1% cut in the parts cost. The parts are roughly broken down as follows:
$9M Rocket Engines
$900k Avionics
$90k super-structure
$10k miscellaneous items
Which change best meets the project director’s requirements?
Author: Leslie Green
In a competition "The Best Smile of the Year", twenty participants successfully failed to pass to the final stage of the competition.
This is 40% of the total number of participants.
Of course, handsome Johnny passed to the final.
How many participants passed to the final stage of the competition?
The surface area of the Earth is 510 million km2. About 71 percent of the Earth's surface is water-covered.
An expert estimates that the area of the Bermuda triangle is about 2.55 million km2.
What percent of the Earth's water surface is the Bermuda triangle?
There are four people in a line.
If only the order of men and women matters, how many ways can they line up?
People used to work shifts lasting up to 14 hours per day, 6 days per week in the 1800's.
In 2002, the average working week was 41.5 hours in Swiss companies.
Estimate the percentage of the working time now compared to the age of the Industrial Revolution (the nineteenth century).
The History of Art in the Dark Ages is an epically boring subject and too many students pass by simply answering the 100 multiple choice exam questions randomly. This year the marking scheme has been changed so that of the 4 possible answers, the correct answer scores one point, two wrong answers score 0, but the remaining stupid answer scores minus two points.
What is the expected score for a student who guesses randomly?
Ten-dollar hammers are on sale in the Cheat-Mart today.
Buy two for the price of three and get 60% off!
What is the final hammer price for me if I really need only one hammer?
What is the largest number of X's you can place on the 4x4 board without making four-in-a-line in any direction?
Gerry's rich uncle gave him $2 on his first birthday. On each birthday after that he doubled his previous gift.
How much did the uncle give on Gerry's tenth birthday?
Jane buys a chair during the sale. If the original price was $40, how much does Jane pay if it is written “Sale : 40% OFF”?
At a school, there were forty-five ninth graders who received a mom's kiss in the morning and thirty who did not.
What percentage of the ninth graders received a mom's kiss?
Today is Monday.
If a fortune teller correctly predicts that you will become an Olympic Champion in 1000 days, what day of the week will it be?
Gerry used a calculator to find the difference of two positive integers, but instead of pressing the minus key (-) he pressed the plus key (+).
The answer was 9.
What should the answer have been?
Gerry rolled three standard cubical dice and added up the numbers showing on the top faces.
How many different sums are possible?
Jane has forgotten the address of her friend’s house, but knows it contains the numbers 7 or 9.
She wants to choose one of the directions, and then recognize the house, which she visited a couple of years ago.
Which direction has more mathematical chances?
Three brothers share their father's sheep.
Father said that the second son gets 20% less sheep than the eldest son, and the youngest son gets 20% less than the second son.
How many sheep does the eldest son get if there are 488 sheep in total?
Martin saves $8 on March 1st.
Each day after that he saves $2 more than he saved the day before.
How much would he have saved by April 1st?
What is the sum of dots that are not visible from the current direction, but would be visible if the tower were looked at from the other side?
The opposite sides of a standard die have numbers that add up to seven.
The letters A, E, I, O, and U are vowels.
What percent of the letters in the word FACEBOOK are vowels?
A bus can hold 66 students.
The bus starts out empty and picks up 1 student at the first stop, 2 students at the second stop, 3 students at the third stop, and so forth.
After how many stops will the bus be full?
Nine people stand in a queue.
The first person takes 9 apples, and each next person takes one apple less than the person before them.
The last person takes the last apple.
What percentage of the total number of apples does the first person take?
The symbol N! denotes the product of the first N positive integers.
Find the value of N for which
(3!)(4!)(7!) = 2(N!)
Maria answered 22 of the 25 questions on her test.
Half of them, she did correctly.
What is her score on the test?
Anna needs $250 to buy a music box. In January, she saved $4. She saved twice as much in February as she saved in January.
If she continues to save twice as much each month as she saved the previous month, in what month will her total savings be enough to purchase the device?
What is the average of the first 2016 counting numbers?
Counting numbers (1, 2, 3, . . .) are whole numbers (0, 1, 2, . . .), but without the zero, because you don't "count" zero.
Arrange nine numbers in a circle so that the difference between neighboring numbers is always less than 3.
Which of the following pairs cannot be neighbors?
A surgeon has two pairs of surgical gloves.
What is the maximum number of people on which he is able to operate?
NOTE:
1)There is no blood contact between the people including the surgeon.
2) The surgeon needs to use both hands for each operation.
John owns 3/4 of a timber business and sells 2/9 of his share for $600,000.
What is the value of the business?
A palindrome is a word, phrase, or sequence that reads the same backwards as forwards.
For example, 123454321 is a nine-digit palindrome.
What is the minimal difference between two nine-digit palindromes?
Bob shaves himself for 3 minutes every day, including the weekends.
If he starts shaving at the age of 20 and lives 70 years, what is the total amount of time spent shaving?
Bob the plumber has 8 pockets and 40 nuts.
He wants to put the nuts in all of his pockets so that no two pockets have the same number of nuts.
What is the largest number of nuts that a pocket can possess?
The table shows the results of a competition among 5 teams.
How many teams received less points than the average?
Anna recorded the temperature every day for a week (7 days).
It was 22° on Monday.
The temperature decreased by 3° every day.
What was the average temperature for the week?
On the chessboard, what is the probability that a randomly chosen square is dark and it touches the outer edge of the board?
John earned an average of 90% on his five exams.
What is the lowest possible percentage score he could have received in any one of the exams, given that each exam counts equally towards the final result?
In a class, 95% of the students earned A grades on the first test, 90% earned A grades on the second test, 85% on the third test, and 80% on the fourth test.
What is the smallest possible percentage of students who earned A grades on all the tests?
The slice that has been eaten had 7 mushrooms on it.
What is the estimated number of mushrooms on the entire pizza?
A bag contains six green, five gray, and four violet disks.
If two disks are drawn at random from the bag, what is the probability that they are both green?
In a survey of students, 2/3 of the girls and 1/2 of the boys preferred using pens over pencils.
Girls make up 75% of the students in the school.
What percent of the students prefer using pens?
The base of the pyramid is a square.
How many layers are there in such a pyramid, composed of 140 balls?
Three apples were weighed in pairs and the weights were 200, 204, and 208 grams.
What is the weight of the lightest apple?
There are five traffic lights on River Avenue, each traffic light being a block of three lights showing exactly one color at a time.
In how many different ways can the lights be set so that no neighboring traffic lights have the same color?
(We assume a traffic light sequence where only one colour is lit at a time. This would not be the case for traffic lights in the United Kingdom and some other countries.)
I have six poles with the length of 1, 2, 3, 4, 5 and 6 meters.
How many different ways are there to make a triangle by choosing three appropriate poles?
I placed 6 cards in a box.
Two cards are blue on both sides, two cards are green on both sides, and two cards are green on one side and blue on the other.
If the first randomly chosen card is green on one side, what is the probability that the other side is also green?
The average of a set of 12 numbers is 12.
If 1, 2 and 3 are added to the set, what is the new average?
Eugenia earned 60, 65, 71, 79, 85 and 90 on her mathematics examinations.
If she receives a score of 82 on the seventh exam, then the average will . . .
John chooses one tile without looking. He counts the number of spots.
What is the most likely number of spots on his tile?
One person is chosen at random from the list.
What is the probability that his/her name includes the letter e?
A catering company places 14 people around six tables.
What is the minimum and maximum number of people sitting around 15 tables that are all linked together on at least one side? (There must only be one group; they can't be linked in pairs, for example.)
A week ago, Anna's jar was filled with 100 jellybeans.
She always took an equal number of green and red jellybeans from the jar.
Today, there are 11 green and 9 red.
Estimate the number of red jellybeans she has eaten.
Tim received the following scores in the online math tests:
80%, 81%, 82%, 83%, 84%, 85%, 86%, 87%, 88%, and 89%
What was his average (mean) score?
How is the decimal number 111 represented in the binary number system?
Randomly pick two natural numbers. 
How many different ways are there from A to B if we move along the arrows?
Find the sum of the one hundred numbers.
Which of the four squares has the biggest proportion of black area?
What is the next number in this integer sequence?
0.777. . . 
What is the average number of circles of the same colour in the set?
For the set { 12, 22, 32, 42, ... 102 }, what is the average (mean) value?
If you randomly choose a natural number, what is the probability that it will be divisible by 7?
$300 is 500% more than Kevin's hourly wage. 
Which safe lock is better?
In how many ways can four horses with knights cross the finishing line? 
How many different ways are there from the top to the bottom?
A download is 90% complete after 3 minutes. 
The price of a roller was reduced from $640 to $480. 
The picture shows a decision die in three different positions. 
How many squares will be in row 2020?
How many zeros are there in the end of the product of all these numbers?
How many minutes have already passed today?
Would you rather sit in a traffic jam for . . . 
What is the average number of letters in the words of the text?
On average, how many times must you throw a die until you roll a six?
What is the difference between the sums of numbers in the seventh and third columns? 
Thirty-three apples, or 66% of the total, were not sold. 
Which number when it is added to 22/17 gives the same result as when it is multiplied by 22/17 ?
How many diagonals does a regular octagon have?
Which scatter plot best shows the relationship between the time that a bamboo grows and its height?
How many different ways can $100 be made using only $5 and $10 bills?
One person is chosen at random.