Medium difficulty puzzles, riddles and brainteasers
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THERE ARE THREE KINDS OF PEOPLE IN THE WORLD,
THOSE WHO ARE SKILLED IN MATHEMATICS
AND THOSE WHO ARE NOT.


Use the email link at the bottom of this page to send your answers to any of the riddles.
We will let you know if your answers are correct.
We will post the names of anyone who solves the puzzles marked *


Memory Test - Part A
       This is a memory test. Study this information for 60 seconds, then scroll down to Part B for the question.
       You are driving the Foodletown bus down Portmanteau Ave. At Maple St. 3 Iranian summer students get on. At Hawthorn St. a priest and a nun climb aboard. At Windsor Ln. 3 farmers in bib overalls get on. At Downing St. a British banker gets on. At School Rd. the 3 students get off. At Sheep Meadow 2 farmers get off and a policewoman gets on. At Clock Tower Square the priest gets off and a drug dealer gets on. At Merkle Circle the policewoman drags the drug dealer off in handcuffs.
       Click here for Part B.   Do not look at this part again.


10 People
       There are 10 people in a room. One is a nurse, one is a Socialist, one sings in a choir, one smokes cigars, one collects stamps, one has lived in China, one wears a wig, one likes Cajun food, one plays the flute, and one of them speaks fluent Arabic.
       One of them is called Bob. Which one?


* Brothers
       Charles and William are two men in their forties who live in the same house. Charles is William's brother, but William is not Charles's brother.
       How is this possible?

Solved by:   Delmar Fenn, Kaustuv Sengupta


Beer (contributed by Pete Wiedman)
       Dale and Dana go on a picnic. Dale brings 5 cans of beer, and Dana brings 7 cans. Before they start drinking, Lee comes along and asks to share the beer. Lee sees that they are not too happy about this, and offers to pay for the beer. They share the beer equally, and then Lee leaves, giving them $6 for the beer.
       How should Dana and Dale fairly split the $6?


Eggs (contributed by Jerry Russo)
       A farmer has some eggs for sale. The first customer buys half the eggs plus half an egg. The second customer buys half the remaining eggs plus half an egg. The third customer buys half the remaining eggs plus half an egg.
       At this point there are no eggs left. How many eggs were there at the start?


Detective
       The famous Cohen-Ur diamond has been stolen. Detective Foodlemyer brings in 3 suspects, Abe, Bert and Costello. One of them is the thief, and will lie. The other 2 are innocent and truthful. The detective gets the following statements.

First Suspect
   Costello is a liar.   I am not the thief.
Second Suspect
   I am not Bert.   I am not the thief.
Third Suspect
   The other suspects are liars.   I am not the thief.

       The detective, who knows each suspect's name, now knows who is the thief. Who is the thief, and what are the three suspects' names?


Lug Nuts
       Joanie Foodlemyer is driving her Cooper Mini on a rural road late one night. She gets a flat, and steps out to fix it in the wan moonlight. To make sure she can find the lugnuts, she places them in the hubcap, which she sets off to one side. Unfortunately, she later steps on the rim of the hubcap, and the four lugnuts catapult into the deep boggy weeds. After 10 minutes of careful searching she decides they cannot be found.
       What should she do?


The Underground
       Every day Derek goes to the Underground and takes either the northbound train to his girlfriend Honoria, or the southbound train to his girlfriend Prudence. He goes straight to the station after work, any time from 5 to 6:30 PM, and he always takes whichever train arrives first. There is a train every 10 minutes going north, and a train every 10 minutes going south, yet he finds that he goes north 4 times as often as he goes south.
       Why?


Nine Dots
       Everyone knows how to connect the 9 dots below with 4 continuous straight lines. How do you do it with just 3 continuous straight lines? (You are not allowed to fold or roll the paper.)

⚫   ⚫   ⚫

⚫   ⚫   ⚫

⚫   ⚫   ⚫



Army Column
       An army column one mile long is moving along a straight road. Major Blunder at the rear of the column sends a messenger to General Mayhem at the head of the column. At the same moment, the General sends a messenger to the Major. The column and the messengers move at constant speeds. As soon as each message is delivered, the messenger returns with the answer. When the messengers deliver the replies, the end of the column is where the start of the column was when the message was sent.
       The two messengers pass each other twice. How far apart are the points where they meet? [No algebra is required, only logic.]


Six Sheep
       A farmer has six sheep which she wants to put in separate pens. She has 12 identical sections of fence which can be joined only at their ends. Show how she can build the pens.


Place Eight
       Write the numbers from 1 to 8 into the 8 boxes in the diagram below so that no number is adjacent to the next successive number, either along an edge or at a corner.
 
       
       
       



Light #1 (contributed by Gilles Ravat)
       The Foodlemyer law firm has an inner and an outer office. On the wall of the outer office are three switches. One of them controls the desk light in the inner office. The other two are not yet connected to anything. You are waiting in the outer office for an appointment with the head of the firm, who is still in court. You would like to know which switch controls the light inside. You can easily reach the switches, and can flip any of them without the secretary noticing, but you dare not do anything more, like unscrew the switchplates and look inside. You cannot see into the inner office. Once the boss returns you will be taken inside, and will have no further chance to flip any of the switches.
       How can you determine which switch controls the light?


Light #2
       The Poodlemyer law firm has an inner and an outer office. On the wall of the outer office are four switches. One of them controls the ceiling light in the inner office. The other three are not yet connected to anything. You are waiting in the outer office for an appointment with the head of the firm, who is still in court. You would like to know which switch controls the light inside. You can easily reach the switches. When the secretary looks down for a moment you have the opportunity to flip any combination or sequence of switches you wish, but you know that you will have only this one chance before the boss arrives.
       When you first arrived, the office door was open, and you could see that the inner office was dark, but the secretary has closed the office door, and there is no longer any way to see whether the light is on. Once the boss returns you will be taken inside, and will have no further chance to flip any of the switches.
       How can you determine which switch controls the light?


Light #3
       The Noodlemyer law firm has an inner and an outer office. On the wall of the outer office is a row of five switches. I know that one of them controls the ceiling light in the inner office, and the other four are not yet connected to anything. I am waiting in the outer office for an appointment with the head of the firm, who is still in court. The inner office is closed and locked. I would like to know which switch controls the light inside. I can easily reach the switches. When the secretary looks down for a moment I start flipping the switches. After just 3 flips I determine that the middle switch controls the light.
       How did I figure it out?


11 Horses
       How can you have 11 horses in 10 stalls, if each stall can hold only one horse? You are not allowed to change the walls, partitions, doors, etc., or to have one horse partly in one stall and partly in another, or partly outside the stable.


Frederick
       In the Gilbert and Sullivan operetta "The Pirates of Penzance" Frederick has been indentured to serve the pirates until he reaches his 21st birthday. He turns 21 as the operetta starts, however, since was born in leap year on February 29, he would not reach his 21st true birthday until 1940.
       In what year is the operetta set?


Kronocords (contributed by Cynthia Rudin)
       On the island of Dortn they tell time by the use of Kronocords. These are cords which burn for exactly one hour; however they do not burn evenly, so that a quarter of a Kronocord would not necessarily burn for a quarter of an hour.
       How can you use Kronocords to accurately time an hour and a quarter?


* Hotel Keys
       At beautiful Hotel Foodlemyer the room keys are square plastic cards with an imbedded magnetic code. The keys all look identical to a person, and are completely symmetric, except for a small hole at the center of one edge, which allows them to be put on a keyring. Sherlock Foodlemyer, the hotel detective, has a ring of these keys, which come in just 2 colors. The ring is circular, and the keys slide freely around it. How many keys can Sherlock have and be able to tell the correct room that each key fits?

Solved by:   Toby Gottfried, P.M.A. Hakeem


Groggen
       Two Vishnaks were discussing a recent Groggen match. Dalpu, who had seen the match, reported that the final score was 14 to 10. Lepnor, who had missed it, noted that the winning team must have scored two chaggles and a slortch, while the losers had to have scored a grand boppel.
       How many different ways are there to reach a 20-point total? (Assume that there are no other types of scores, beyond the three mentioned.)


Memory Test - Part B
       What is the name of the bus driver's mother?


Iron Ore (contributed by Don Doyle)
       A ship loaded with iron ore is in a canal lock, with the gates closed at both ends. Suddenly the ship dumps its entire load of ore into the lock. Does the water level rise, stay the same, or drop?


Zorg (contributed by Ken Duisenberg)
       In the game of Zorg, each player draws a numbered disk from a bag containing one each of the numbers 0 to 9. The player then places that disk on any empty box among the 7 boxes labeled A through G on the playing board, shown below. A player who completes a line of 3, as shown in light blue, scores the product of the 3 disks in that row. For example, a line containing 4, 5, 3 would score 60.
       Today I saw a game in which 3 players each completed one of the 3 lines and had tied scores. What number was in box D?
A   B
     
C   D   E
     
F   G



Place 9 (contributed by Ken Duisenberg)
       The 9 numbers from 1 to 9 are placed at the 9 question marks so that the sum of the 3 numbers along any of the 6 lines is always 18. What number must go in the center box? 

 
?---?---?
|\     /|
| \   / |
|  \ /  |
?   ?   ?
|  / \  |
| /   \ |
|/     \|
?---?---?


* Ten Lines
       Here are 9 dots arranged so that there are 8 lines of 3 dots each (and no lines of 4 or more dots).

⚫   ⚫   ⚫

⚫   ⚫   ⚫

⚫   ⚫   ⚫

How can 9 dots be arranged so that there are 10 lines of 3 dots each (and no lines of more than 3 dots)?

Solved by:   Christian Leger, Ariel and Yvonne Cohen, Hareendra Yalamanchili, Nigel Clark, Marina Plaksina, Paul Leahy, David Newell, Rakesh Kumar Banka, Andreas Abraham, S. Preethi Sudharsha, Vivek Narayanan, Scott Weiss, Arijit Bhattacharyya, Jeremy Pancoast, Nishanthi Sivanandanayagam, Peter Bauer, Bradley Wild, S. Janaki, Susil Kumar Jena, P.M.A. Hakeem, Kevin Moore, Naim Uygun


Eight Triangles
       Arrange 6 toothpicks so that they form 8 equilateral triangles (triangles where all 3 sides are the same length). The toothpicks should meet evenly at the corners, with no "extra bits" extending past.


Number Names
       If you wrote down the names of the numbers in order, ONE, TWO, THREE, etc., the first letter that appears is O, then N, E, T, etc. The letter A does not appear until ONE THOUSAND. What would be the last letter to appear in the list?


Swimmers (contributed by Pete Wiedman)
       Two swimmers start at each end of a pool and swim toward the opposite ends. When they first meet they are 50 yards from the east end. The swimmers pass each other and turn around when they reach their respective ends and swim back toward each other. When they meet the second time, they are 20 yards from the west end. Assuming each swims at a constant speed, how long is the pool?


The Foodlemyer Method
       The Foodlemyer method of copying films is fast and cheap, but it has one drawback. After the film has been copied, both the original and the copy are degraded 1% in quality. For example, if a film is 3% degraded, after copying the film and copy both will be 4% degraded. A film is considered usable if it is no more than 10% degraded.
       How many usable copies can be obtained from one original print?


Perro
       Esteban is walking home with his dog Perro when he sees his sister Luz 10 blocks away coming to meet him. Perro starts to run towards Luz, but as soon as he reaches her, he turns around and runs back to Esteban. He continues to run back and forth this way until the two children meet.
       If Esteban walks 2 miles per hour, Luz walks 3 miles per hour and Perro runs 10 miles per hour, how far does Perro run altogether?


Foodlemyer Fever
       Three patients have just walked into your clinic with advanced cases of Foodlemyer Fever, a disease which is always fatal if left untreated. Any contact with an infected person or surface will spread the disease.
       There is a simple operation you can perform to cure the disease, but you have discovered that you have only 2 pairs of surgical gloves left. It is possible to take off or put on infected gloves without becoming infected yourself by handling only the top edge. How can you perform the 3 operations without contracting the disease or reinfecting one of the patients?
       [Isaac Asimov, the science fiction writer, gave a version of this problem under the name Barzoomian Flu, but Asimov's solution did not protect against transmission from one object to another.]


Holidays
       On the nearby planet of Rien the two principal holidays in the nation of Zip are Nichi Vaw, falling on the 16th of Nada, and Nirgends, falling on the 25th of Nada. What is the probability that at least one of these holidays will fall on Niente, the first day of the week, in any given year?
       The Zippers have a 9-day week, and a month of either 40 or 41 days. There are 14 months in each year, and no leap years.


* Alphabetic Order
       Imagine that all the names of the integers were written down on a huge list and alphabetized. (Assume that hyphens and blanks are ignored in alphabetizing, so that FOUR THOUSAND would come later than FOURTEEN.) What would be the first 5 numbers and the last 5 numbers on the list?

Solved by:   Toby Gottfried, Kevin Moore


The Station
       Every weekday at 6 PM sharp Sir Wolcroft Fotheringstone arrives by rail at the Tushington station, and every weekday at the dot of 6 his manservant Eames arrives to drive him home in the Bentley. One day his last appointment cancels and he takes an earlier train, arriving at the station a full hour early. As the day is fair, he elects to take the air and walk home. His manservant picks him up en route, and drives him the rest of the way, arriving 20 minutes earlier than usual.
       How long had he been walking?


* Bowling
       What is the largest number of strikes you can get in bowling, yet still lose to someone who gets no strikes, and only that same number of spares?

Solved by:   Christo M. D., Toby Gottfried, Craig Shetterly, Jeremy Pancoast, Steven Hugh Edwards, Bradley Wild, P.M.A. Hakeem, Kevin Moore, Kaustuv Sengupta



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