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Month: Problem
Past Problems Of The Month
January: 2016
In the middle of an otherwise empty field there lies a man wearing a pack. He is dead. There are no other clues visible. How did he die?
Quiz:
Where is the world's largest New Year's party?
a. Times Square, New York
b. Rio de Janeiro, Brazill
c. The Champs Elysees, Paris
d. Sydney, Australia
December: 2015
There are 8 match sticks in the pyramid shown in the figure below. Now move 4 sticks to form 5 equilateral triangles.
Quiz:
Where did the song "Have Yourself a Merry Little Christmas" originally appear?
a. Miracle on 34th Street
b. It's A Wonderful Life
c. Meet me in Saint Louis
November: 2015
Use five 0's and any math operation to get the total of 120.
Quiz:
Though wild turkeys can only fly for short distances, they can sometimes reach speeds of:
a. 7 mph
b. 35 mph
c. 55 mph
d. 72 mph
November: 2015
Consider 17 lines drawn at a tangent to an ellipse. The lines break up the plane into several regions, some bounded (i.e., enclosed) and others unbounded. How many unbounded regions are there?
Quiz:
Which Elton John song did the Beach Boys sing backup vocals on?
a. Candle In The Wind
b. Bennie &the Jets
c. Don't Let The Sun Go Down On Me
d. Yellow Brick Road
March: 2014
Problem:
A cylinder 15 cm high has a circumference of 4 cm. A string makes exactly 5 complete equally spaced turns around the cylinder from top to bottom. How long is the string in cm?
Quiz:
On March 12th, 2009, the U.S. House of Representitives passed a non-binding resolution making March 14 the observance day of what nathematical constant?
February: 2014
Problem:
A metal band circles the earth touching the ground at all locations. The Earths circumference is approximately 40,0000 km. Now add 10 meters to the total length of the band. It now sits magically just above the ground. How far has it risen? Could a flee, a rabbit, or even a man squeeze underneath?
Quiz:
At what stadium was the first Super Bowl played?
a. Louisiana Superdome
b. The Orange Bowl
c. Los Angeles Memorial Coliseum
d. Lambeau Field
January: 2014
Problem:
How many triangles can you find int eh picture below?
Quiz:
What is the name of the main office of Pixar called?
December: 2013
Problem:
Calculate the number of presents in the song "12 days of Christmas".
Quiz:
Which two states in the US have towns called Christmas?
November: 2013
Problem:
Two equal squares are placed side by side. The second square has been cut in half diagonally (see
drawing below). Cut the figure into four identical pieces - the pieces may be flipped over.
Quiz:
Which of the follwing is heavier than a cumulas cloud with a volume of 1 cubic kilometer?
a. 100 blue whales.
b. None of the options.
c. the Eiffel Tower.
d. the largest ship in the world.
October: 2013
Problem:
A goldfish can survive in 1000 cubic inches of water. How many fish can live in a fish bowl that has a diameter of 20 inches?
Quiz:
Why do Sleepy Hollow town historians believe the Headless Horsemean is often near the church?
a. They believe he is trying to atone for his sins and get to heaven.
b. They believe his body is buried in teh churchyard.
c. They believe he died looking for sanctuary.
d. They believe he died while attacking the church.
September: 2013
Problem:
This shape was formed by removing a small cube from a big cube. The side length of the removed cube is two thirds of the side length of the original cube. What is the volume of the new shape compared with the original volume? 
a. 70%
b. 50%
c. 60%
d. 80%
Quiz:
How did September come to be named?
August: 2013
Problem:
Three boys want to equally share three pancakes.
The picture shows the pancakes' diameters.
Which part of the largest pancake will one of the boys receive?. 
Quiz:
What is the highest recorded temperature in the US?
a. 128
b. 154
c. 134
d. 162
July: 2013
Problem:
The the match sticks below show 3 squares and 2 triangles. Rearrange the matches to make 5 squares and 6 triangles. 
Quiz:
What might the estimated number of 4th of July cookouts?
There are four small squares and four small triangles
June: 2013
Problem:
A cloth bag contains a pool ball, which is known to be a solid ball. A second pool ball is chosen at random in such a way that it is equally likely to be a solid or a stripe ball. The ball is added to the bag, the bag is shaken, and a ball is drawn at random. This ball proves to be a solid. What is the probability that the ball remaining in the bag is also a solid?
Quiz:
What is the name of Jupiter's wife, the patroness of marriage, that the month of June is name after?
May: 2013
Problem:
A person has to visit towns B and C in any order. The roads connecting these towns with their home are shown on the diagram. how many different routes can they take starting from A and returning to A, going through both B and C (but not more than once through each) and not traveling amy road twice on the same trip
A. 10
B. 8
C. 6
D. 4
Quiz:
May is named after the goddess Maia. What is she the goddess of?
April: 2013
Problem:
This months problem is two fold:
1. Find the sum of the interior angles of a heptagon (7 sided polygon).
2. Drawing lines connecting the vertices, how many triangles
can a heptagon be divided into?
Quiz:
In 1993 city officials in Cologne, Germany imposed a new regulation on people jogging through the city park. Runners were required to pace themselves to go no faster than six mph. Any faster, the city officials cautioned, could disturb the squirrels who were in the middle of their mating season.
True or False?
March: 2013
Problem:
Arrange 12 match sticks to make 6 squares with side length of one match stick.
Quiz:
One player had five of the top ten single game scoring outputs in Division I tournament history during the 20th century. Who was he ?
1. Austin Carr of Notre Dame2. Lew Alcindor of UCLA
3. Bill Bradely of Princeton
4. Oscar Robertson of Cincinnati
February: 2013
Problem:
Take the four numbers 2, 9, 10, 14 and use addition, subtraction, multiplication, and division to make them equal 24.
Quiz:
Legend has it that St. Valentine was a Priest during third century Rome. Who was the emperor at that time?
A. CesaerB. Cupid
C. Claudius II
January: 2013
Problem:
In the triangles below, 3(y-x)= ?
A. 15
B. 30
C. 45
D. 60
E. 105
Quiz:
The month of January was named afer?
A. Hindu PrincessB. The Roman God Janus
C. The Greek God Januarius
D. A fromer Roman goddess
November: 2012
Problem:
Mr. Pilgrim needs fencing for his turkey coop. The perimeter is 240 yards. The length is 16 yards longer than the width. What are the dimensions? What is the area?
Quiz:
The Wampanoag Indian tribe was part of the very first thanksgiving. How long had this tribe been living in the Cape Cod area when the English settlers arrived?
A. 100,000B. 12,000
C. 500
D. 10
October: 2012
Problem:
If it takes a marshal 7.5 hours to catch 5 rustlers, how long will it take him to catch 2 rustlers?
Quiz:
September: 2012
Problem:
One snowy night, Sherlock Holmes was in his house sitting by a fire. All of a sudden a snowball came crashing through his window, breaking it. Holmes got up and looked out the window just in time to see three neighborhood kids who were brothers run around a corner. Their names were John Crimson, Mark Crimson and Paul Crimson. The next day Holmes got a note on his door that read "? Crimson. He broke your window." Which of the three Crimson brothers should Sherlock Holmes question about the incident?
Quiz:
August: 2012
Problem:
Choose a number. Triple that number. Add 200. Double the result. Subtract 100. Divide by 4. Subtract 150% of the original number. I am the result no matter what number you started with. What integer am I? For bonus can you explain why I am always the result?
Quiz:
A. Bigger, Better, Best
B. One World United
C. Hold onto your socks
D. Faster, Higher, Stronger
July: 2012
Problem:
Sometimes it is very easy to find in a series what number comes next, but usually it is not! Here is a tough example: try to replace the 'X' in the following sequence with the most appropriate number: 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 18, 5, 19, 10, 20, 3, 21, 11, 22, X, ...
Quiz:
June: 2012
Problem:
The square ABCD touches the circle at 4 points. The length of the side of the square is 2 cm. Find the area of the shaded region.
Quiz:
Which bird is the international symbol of happiness?
May: 2012
Problem:
A computer cable has seven connectors, arranged in a perfect circle -- so by rotating the plug, it can be connected to the outlet in any of seven different ways. Each of the connectors is numbered from one to seven, each number being used exactly once. The same is true for the holes in the outlet. The device that uses this cable only requires that one of the connectors match up to its corresponding hole in order to operate. How should you number the connectors on the plug and the holes in the outlet so that, no matter how the cable is rotated and plugged in, at least one connector matches up?
Quiz:
1. And now for something completely different...
2. I love it when a plan comes together.
3. The world is your lobster.
April: 2012
Problem:
Each of three successive months has four Sundays. Prove that one of these months is February.
Quiz:
March: 2012
Problem:
A cloth bag contains a pool ball, which is known to be a solid ball. A second pool ball is chosen at random in such a way that it is equally likely to be a solid or a stripe ball. The ball is added to the bag, the bag is shaken, and a ball is drawn at random. This ball proves to be a solid. What is the probability that the ball remaining in the bag is also a solid?
Quiz:
Covered with a sweet fragrance,
Guarded by five guardsmen,
Two of them clean-shaven,
Two of them unshaven,
And the last one half-shaven.
What am I?
February: 2012
Problem:
Once upon a time, Mars, the God of war, intended to test the IQ of the goddess Minerva. So, showing his shield, he told her: "Darling, on my shield, there are 3 equal circles which represent the qualities of the warrior: strength, flexibility, and decisiveness. As you can see, one of the circles has been scratched by a sword, and the resulting score is three inches long (line AB in the illustration). Can you then tell me what is the area of my shield?".
Find the very shortest way to solve this puzzle and use only basic geometry, trigonometry is not allowed!
Quiz:
How can you take 9 toothpicks and make ten without breaking the toothpicks?
January: 2012
Problem:
There are three switches downstairs. Each corresponds to one of the three light bulbs in the attic. You can turn the switches on and off and leave them in any position. How would you identify which switch corresponds to which light bulb, if you are only allowed one trip upstairs?
Quiz:
A farmer has seventeen sheep. All but nine of them die. How many sheep does he have left?
November: 2011
Problem:
Every year the President of the US pardons a turkey and it goes to a public farm called Frying Pan Park, Herndon, VA. Which President is believed to be the first to pardon a turkey and start his annual tradition?
A. President Andrew Jackson
B. President Millard Fillmore
C. President Harry Truman
D. President Warren Harding
October: 2011
Problem:
At the Halloween Ball, every wizard brought at least one black cat. The organizers want to know how many cats and wizards attended. Unfortunately, the only record they have is a group photo taken as the photographer tripped, and all it shows is feet and paws. A ghost flying over the Ball also snapped a photo but it was midnight and all he captured was the total number of eyes, glowing in the dark. If the photographer counted 196 feet and paws and the ghost tallied 126 eyes, how many wizards and how many black cats were at the Ball?
Brain Teaser:
'Children Of The Corn' is yet another of King's
short stories that was made into a movie. What was the name of the
character that organized the children and spoke for the never seen,
'He who walks behind the rows?'
a. Malachi
b. Jeremiah
c. Isaac
d. Elijah
September: 2011
Problem:
Triange DEC is inscribed in rectangle ABCD. If side AB=30 units, side EC=17 units, and side AE=side EB, what is the area of triangle DEC?
a. 60 square units
b. 120 square units
c. 136 square units
d. 240 square units
e. 255 square units
Brain Teaser:
I herald the darkness which descends on all creatures; You will know my approach by moans and wracked features. I visit the hippo, hyena, and horse, But never go near snails and spiders, of course. I would circle the glove, leaping one to the other, Should all the world's people ever clasp hands together. What am I?
August: 2011
If ABCD (shown below) is a parallelogram, what is the measure of angle ABC?
a. 7 Degrees
b. 68 Degrees
c. 78 Degrees
d. 102 Degrees
e. 112 Degrees
July: 2011
A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
A. 48
B. 32
C. 24
D. 18
E. 12
June: 2011
With Just 3 straight lines through the zed below, form the largest possible number of triangles.
-
May: 2011
The square ABCD touches the circle at 4 points. The length of the side of the square is 2 cm. Find the area of the shaded region.
April: 2011
A circular swimming pool with a diameter of 28 feet has a deck of uniform width built around it. If the area of the deck is 60(pi) square feet, find its width.
March: 2011
Cut a perfect hexagon into 5 peices that fill / fit together to form a square.
February: 2011
It took Marie 10 minutes to saw a board into 2 pieces. If she works jst as fast, how long will it take her to saw another board into 3 pieces?
January: 2011
Find the angle " a " in the diagram below (solve this puzzle using just basic geometry, no sines or cosines allowed).
December: 2010
The circle is tangent to all three sides of the right triangle. Solve for " r " and no trig required.
November: 2010
A small boat is floating in a swimming pool. You have a rock which you will throw into the pool or put into the boat. Which is true?
a) The water in the pool rises higher when the rock is put in the boat
b) The water in the pool rises higher when the rock is put into the pool
c) The level would rise the same either way
October: 2010
Find the hidden nine letter word in the grid below. You may move adjacently in any direction including diagonally.
September: 2010
What letter is next in this sequence?
O, T, T, F, F, S, S, E, ___
August: 2010
Using four different colors, shade this map so that no adjacent borders have the same color.
July: 2010
What English word is nine letters long, and can remain an English word at each step as you remove one letter at a time, right down to a single letter?
June: 2010
What is the next number in the sequence: 32 - 35 - 40 - 44 - 52 - 112 - ? (Hint: there are only nine numbers in this sequence, you have ben given the first 6).
May: 2010
Complete the series. 9 = 4, 21 = 9, 22 = 9, 25 = 10, 8 = 5, 7 = 5, 99 = 10, 100 = 7, 16 = ?, 17 = ?
April: 2010
A fishing boat is docked in the harbor. There is a rope ladder hanging over the side with its end touching the water. The rungs of the ladder are 1 meter apart and the tide is rising at 50 centimetres an hour.
At the end of 6 hours, how many of the rungs will be covered?
March: 2010
Why are some letter above the line, and the rest below the line?
February: 2010
John had a bag of oranges to share with two friends. To the first of his friends, he gave half of the oranges plus one more. To his second friend he gave half of the remaining oranges plus one more. By this time, John had one orange left. How many did he start with?
January: 2010
Problem:A rectangle with sides of the ratio phi is called a golden rectangle. If you make such a rectangle smaller by removing a square formed by the smallest side, the sides of the remaining smaller rectangle have the same ratio of phi and so on. What is the value of phi?
December: 2009
Using four unique integer values from 0 thru 9 and any combination of the operators x / + - , create two different equations which = 44
November: 2009
A perfect cube that measured one foot on a side has been expanded such that the cube now has twice the surface area that it originally had. Find the volume of this larger cube.
October: 2009
Determine A, B, C, D so that the following equation works:
ABCD * 4 = DCBA
September 2009
A car travels at 60 miles per hour over a certain distance. The car makes the return trip over the exact same distance at 30 miles per hour. What is the average speed of the car?
August: 2009
If a chicken and a half can lay an egg an a half in a week and a half, how many eggs would this chicken lay in a month and a half (6 weeks)?
July: 2009
How many R's?
Complete the sentences written below.
Do not use numbers like 1, 2, 3, and so
on ...
In the sentence below are .............. R's.
In the upper sentence there are ............. .
R's.
June: 2009
Problem:Take a pencil and draw lines to join each white letter to its black counterpart (m to m, a to a, etc.), without any line crossing another line.
Download printable verions by clicking here.
May: 2009
Problem: Use 5 0's and any mathematical operators to get 120?
April: 2009
Problem: "How much will one cost?" "25 cents"
"How much will fifteen cost?" "50 cents"
"OK then, I'll take one hundred and sixteen"
"Thank you, that will be 75 cents please"
Explain.
March: 2009
Problem: Using the document that you can download by clicking Here. Arrange 7 equilateral pentagons such that each pentagon is touching 3 or more of its neighbors without overlapping any surfaces. (Contact by point or line only)
February: 2009
Problem: Four identical balls on four different tracks are released simultaneously. Which of the tracks (bent, straight, circular, or cyloidal) will deliverthe ball to the end of the slope fastest?
January: 2009
Problem: Two semicircles are inscribed in a square with side 8 m, as shown. Approximate the area of the shaded region to the nearest tenth of a sq cm. Use the approximation 3.14 for p.
December: 2008
Problem: How many 3 digit numbers have different digits in descending order such as 73 or 960?