Mathematical Puzzles:
How many of these can you answer?

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      #1.  If a hen and a half can lay an egg and a half in a day and a half,
         A.  How many hens would it take to lay 6 eggs in 3 days?
         B.  How many days will it take 3 hens to lay 9 eggs?
         C.  How many eggs will 6 hens lay in 3 days?
       #2. At 12 noon the hour and the minute hands of a clock coincide exactly.
        A.  How many other times during a 12 hour period do the hands coincide? State the times to the nearest minute.
         B. At 3:00 the hour and minute hands form a 90 degree angle. How many times in a 12 hour period does this occur? What are the times(to the nearest minute) at which this happens?
      #3. Take 1 teaspoon of coffee from a cup of coffee and empty it into a cup of tea. Stir the tea. Take 1 teaspoon of tea from the teacup and empty in into the coffe cup. Stir.
       Is there more coffee in the teacup or tea in the coffee cup?
       #5.  A length of wire completely surrounds the earth at the Equator. Imagine that the wire floats, that it has negligible mass, and that it fits snugly around the earth. Cut the wire and splice in an extra 20 feet of wire. Now the wire will be slightly slack in its fit. Raise the wire equally at all points away from the earth until it is tight again.
       A. How high will the wire be off the earth at all points?
       B. If the wire had been lifted straight upward at one point, how high would you lift it until the wire is snug again?
       #6.  A basket contains 8 eggs, one of them lighter than the rest. Using an equal arm balance devise a method for finding the light egg in at most 2 balancings.
       #7.  Two cars are in a race from Southey to Regina and back. If one car drives 100 kph both ways and the other drives 90 kph to Regina and 110 kph back to Southey, which car wins the race?
       #8.  What 2 numbers formed by using the digits 1,2,3,4,5 only once will yield the largest product?
       #9.  A gardener harvested 100 pounds of potatoes. After some time in the harsh sunlight the water content of the potatoes went from 90% down to 50%. How much do the potatoes weigh now?
       #10.  A 5 mile long column of soldiers march in single file in a straight line at a constant speed. Dan, a mounted courier, leaves the rear of the column and rides for the front of the column at a constant speed. When he reaches the front he instantly reverses his ride to the rear of the column, going at the same speed. When he reaches the rear he discovers that he is at the spot where the front of the column was when he began his ride.
How far had Dan ridden?
       #11.  The hour hand and the minute hand of a clock are superimposed at 12 noon.
a.What is the exact time at which the hands coincide again?
b. What is the exact time of superposition if the hands are nearer to the number 4 than to 3 or 5?
c. At what time will this occur if the hands are closer to 6 than to 5 or 7?
       #12.  In Russian folklore this was a way that a girl of marriageable age could determine her chances of getting married within a year.
She holds six long blades of grass in her hand with the ends protruding at the top and bottom. Another girl then ties the upper six ends in pairs and the lower six ends in pairs also.
If, by following this procedure the blades of grass turn into one big ring, then she will get married within a year.
So what would you say are the chances of this girl of getting married?
       #13.  In a rectangular room with dimensions 30' by 12' by 12', a spider is located in the middle of a 12' by 12' wall one foot away from the ceiling.
A fly is in the middle of the opposite wall one foot away from the floor.
If the fly remains stationary, what is the shortest total distance the spider must crawl along the walls, ceiling, and floor in order to capture the fly?
       #14.  In the Monty Hall Quiz show Monty offers the successful candidate another challenge to determine what prize he/she gets. Monty shows the contestant 3 doors, behind one there is a new car and behind the other two there are goats. The contestant chooses one door and then Monty opens one of the other doors revealing a goat. He then offers the contestant the chance of changing his choice.
Should the contestant switch to the other unopened door?
If you believe that it doesn't matter whether you switch or not check this site
       #15.    3 missionaries were escorting 3 cannibals back to civilization when they came upon a river which was too wide and too deep to ford or to swim.
     They found a small boat which could accomodate only 2 persons at most at a time.
     Can you get them safely across the river?
     Be advised that each of the missionaries plus only one cannibal can row and you cannot allow the cannibals to outnumber the missionaries at any point because of their natural affinity for human flesh particularly of those embodying the spiritual nature.  
       #16.  This was a coded message that James Bond sent to M. Solve the puzzle to find out how much money he was requesting.
    S E N D
+ M O R E
       #17.  I was travelling Northward in my automobile at 100 km/hr. A motorcyclist travelling at 150 km/hr overtook me and immediately cut in front of me.

       A. Assuming that the leading edge of his front tire was 1.0 m away when it was directly west of my front bumper what is the maximum angle from North in which he could safely negotiate this cutoff? (Assume that the length of the motorcycle was 2 m.)

        B. What minimum speed would he require to negotiate this cutoff safely at an angle of 30 degrees?

Diagram to illustrate the problem

        C. Solve A and B if the 1.0 m was the distance of the nearest approach of the leading edge of his front tire from my front bumper.
       #18.   A 2" diameter hole is drilled perpendicularly through one face of a 4" cube and through the opposite face.
        A. What is the volume of the remaining material of the cube?

       B. If this procedure was done on 2 other faces with no intersection with the other holes what is the volume of the remaining material of the cube?

       C. If these 3 holes intersected maximumly with each other, what is the volume of the remaining material of the cube?
       #19.  Problem for a 5th Grader
       #20.  A 1.8 m tall man walks away from a street light at 5 km/hr. His shadow extends before him on the street. What is the speed of the farthest point on the shadow when the man is 50 m. from the light standard and the light is 10 m. above the street?
       #21.  A cylindrical container(similar to a 500 ml. plastic tub for sour cream) is used to store hymn number cards. If the radius of the container is 5 cm. and it is 10 cm. high and each card is 5 cm wide, 10 cm long and 1 mm. thick, what is the maximum number of cards that can be stored in this container?
Here's one format for storing:
       #22.   Wanna Play Nim?
                 or something easier?  
Try this!
       #23. Bridge construction is in progress on Highway #6 in the
Qu' Appelle Valley. There is room for single lane traffic past the construction area. In lieu of human traffic controllers red/green lights have been installed at each end of the area. The distance between the lights is 0.6 km and the speed limit is 60 km/h in this zone.

        A. If the duration of the red lights is 3.0 minutes what is the duration of the green lights?
       #24. Albrecht Durer designed a 4X4 Magic Square in 1514.

The sum of each of the rows, columns, and diagonals equals 34.

Can you change the totals to 36? to 100?
       #25. You meet 3 men, 1 who is an inveterate liar, 1 who always tells the truth, and 1 who answers at random in the veracity sense. Each of them knows the property of the others.
What 3 questions can you formulate, answerable by a Yes or a No, that will enable you to determine who was who?
       #26. Tom travels from his work place in the city by train to his home station. His wife picks him up by car from the station and drives him home.
     One day he took an earlier train. He arrived at the station one hour earlier than usual. Because his wife isn't there to meet him he decides to start walking towards home.
     His wife left home at the usual time and met him on route and drove him home.
     If they arrived home 20 minutes earlier than usual how long did Tom walk?
       #27. Consider the series: -8,-1.5, 1,...
        A.What are the next 3 terms?
        B.What is the sum of 11 terms of this series?
       #28. Car A travelled Southward for 50 km. at 100 km/hr.
During this trip he met 76 vehicles going Northward.
        A.What is the rate of vehicular traffic Northward? (assume that the northbound traffic was also going 100 km/hr)
        B.What is the rate of northbound traffic if Car A travelled at 120 km/hr and all other parameters were the same as in A?
        C.What is the rate of northbound traffic if Car A travelled at 200 km/hr and all other parameters were the same as in A?
        D.What is the rate of northbound traffic if Car A travelled at 50 km/hr and all other parameters were the same as in A?
       #29. Click for larger image
       #30. Click for larger image
       #31. Click for larger image
       #32. Click for larger image
       #33. Click for larger image
       #33B. Click for larger image
       #34. Click for larger image
       #35. You have 100 light bulbs placed in a row, each with an on-off switch.

Step 1: Switch each of them "On".
Step 2: Switch every 2nd bulb.
Step 3: Switch every 3rd bulb.
Step 4: Switch every 4th bulb.
Step 5: Switch every 5th bulb.

...Continue in similar fashion until

Step 100: Switch every 100th bulb.

    A. How many light bulbs are on?
    B. Which light bulbs are on?

       #37. One hundred prisoners are lined up, one behind the other, all facing forward. On each prisoner's head is a hat, either red or black. Each prisoner can see the hats of all the people in front of him, but he cannot see his own hat and he cannot see the hats of the people behind him.
Starting with the prisoner in the back of the line (the one that can see all 99 other prisoners), the prison warden asks the prisoner what color hat he is wearing. Each prisoner can hear the guesses of all of the prisoners behind him. If a prisoner correctly guesses his hat color, he is set free. If he guesses wrong, he is executed.

The prisoners are allowed to agree in advance on an algorithm to use, and you can assume that they all agree to follow the agreed-upon algorithm.
The prisoners are NOT allowed to provide each other with any additional clues once the hats are placed on their heads. (For example, tapping shoulders or modulating their voices are not allowed.) The only information each prisoner has is the guesses for the prisoners behind them, and the hats on the prisoners in front of them.
Design an algorithm for the prisoners to follow that saves the most prisoners from execution.

What is the maximum number of prisoners you can guarantee to save?
       #38.  A train and a morning walker leave their respective places at the same time and travel in opposite directions. They meet each other at a fixed place and fixed time. The speed of the train is 60 km/h and the speed of the morning walker is 5 km/h One day, the train is late. The morning walker has to travel 5 km extra to meet the train. By how many minutes is the train late ?
       #39. Click for larger image
       #40. Click for larger image
       #41. Click for larger image
State the sum of the coordinates
of A to nearest 3 decimals.
       #42. Click for larger image
State the length of the side
of the square to nearest 3 decimals
when the intersection with the circle
is 1/2 of the area of the square..
       #43. Click for larger image
Find the area of the rectangle correct to 3 decimal places.
Hint: The length of SR varies from 2 to 0.
At 2, B = 0 and A is maximum, thus B/A = 0.
As SR decreases from 2 to 0, B increases and
A decreases and B/A increases.
You're to find SR and thereby the area of PQRS
when B/A = 1/2
       #44. Click for larger image
       #45. Click for larger image
How much empty space is in the box?
       #46. Click for larger image
What is the sum of the 2 radii?
       #47. Click for larger image
State the area to nearest 2 decimal places.
       #48. Click for larger image
State the area to nearest 1 decimal place.
       #49. Click for larger image
Two pyramids with 3 cm. square bases intersect.
Their bases have the coordinates of (0,0,0), (3,0,0), (3,3,0) and (0,3,0).
The pinnacle of one is at (1,1,3) and of the other is (2,2,4).
The highest point of intersection is P(x,y,z).
Calculate x + y + z to nearest 3 decimals
       #50. Click for larger image
What is the value of ?
       #51. Click for larger image
Tom is sitting on a blanket in a park enjoying a folk festival performer. Bill wanders into the standing area and blocks some of Tom's view of the stage. If Tom's eye level is 2.5' above the ground and his distances from the stage and to Bill is 47' and 22' respectively, Bill is 6' tall, and the stage is 4' 3" high, how many inches in the height of the performer is blocked from Tom's view? Assume the ground is level. State answer to nearest inch.
       #52. Click for larger image
Five people come to a river at nighttime. There is a narrow bridge, it can only hold two people at a time. They have one torch and, because it's 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 four minutes, D in seven minutes, and E in eleven minutes. When two people cross the bridge together, they must move at the slower person's pace. What is the minimum time for them to cross the bridge (in minutes)?
       #53. Click for larger image
In the above diagram, how many red squares should go in the ? to make it balance? Note: Assume the hangers and wire are all weightless and each hanger is symmetric.
       #54. Click for larger image
       #55. Click for larger image
A cone contains an amount of water. When placed in configuration "A" the distance from the the surface of the water to the top of the cone is 8 cm. When placed in configuration "B" the distance from the the surface of the water to the top of the cone is 2 cm. Find the height of the cone.
        There's 55! If you're done with these you can get to more of my problems on   Search for Guiseppi Butel and click on Problems.

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