Puzzles

FUNDRUM MY CONUNDRUM

The answers are given below the puzzle but are in white color font. Change font color tosee the answer after u try.

Here are the hard puzzles: (easy | medium | home)

68. 8 BBs look alike but one is slightly heavier than the others. How can you identify theheavy BB in only two weighings on a balance scale?Keep 2 –weigh 3-3; Then keep 1 and 1-1;

69. A man has an office north of his home and a factory south of his home. Every day hegoes to the train platform at completely random, different times. There is a train goingnorth, stopping on one side of the platform, every ten minutes. There is a train goingsouth, stopping on the other side of the same platform, every ten minutes. He alwaystakes the first train that comes along after his arrival on the platform. Nine days out of tenhe goes to his office. Why?

70. A man leaves home, makes three left turns and comes home to find two masked menthere. What is this all about?

71. A man drives 10,000 miles in his car. He changes his tires around so that all 5(including the spare) get an equal number of miles of wear. How many miles does eachtire get?8000

72. After a number of tests three final applicants for a job are placed in a room andblindfolded. They are told that a mark, either black or white is being placed on eachforehead. They are told to raise their hand if, after the blindfolds have been removed, theysee a black mark on either of the other two applicants. Black marks are placed on all threeforeheads and, of course, when the blindfolds are removed they all raise their hands.They are told that whoever first figures out what is on his own forehead will get the job.After a little while one announces that he has a black mark. How did he tell?

simple

73. A square window, 4 feet by 4 feet, is to have half its surface painted black but stillleave a square measuring 4 feet in both directions. How can this be done?

There are two surfaces. Paint only one surface

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74. A man enters a town having only two barber shops and wants a haircut. He sees thatin one shop it is neat and clean and the barber has a very nice haircut. In the other theshop is messy and the barber has a bad haircut. He chooses to go to the messy one. Why?

The barber’s take each other’s help for cutting their own hair

75. Quickly give 100 words with no "a" in them.One to hundred in words

76. You have two hourglasses - one measures 7 minutes and one measures 4 minutes.How can you time 9 minutes?simple

77. Mr. A lies on Mondays, Tuesdays and Wednesdays; Mr. B lies on Thursdays, Fridaysand Saturdays. One day Mr. A said "Yesterday was one of my lying days." Mr. B said"Yesterday was one of my lying days too." What day of the week was it?Thursday ??

78. A twine is tied connecting your two wrists. Another twine is tied connecting the twowrists of your friend. The twines are crossed so that you cannot get apart. Withoutuntying, how can you separate yourselves?

79. We meet three people and don't know if they are good guys or villains. #1 says "Allof us are villains." #2 says "Exactly one of us is a good guy." What are each of the three?#2 good guy and #1 and #3 are villians

80. The length of a certain fish is equal to 20 plus 1/2 its length. The head of the fish is 9inches; the body is equal to the head plus the tail. How long is the body? The tail?40,11

81. A man can perform a certain task in thee days working alone. He has a helper whotakes two days to do what the man can do in one. How long will it take to get the taskdone if they both do it together?2

82. Can you name ten body parts of three letters each?Eye,ear,leg,hip,lip,

83. A town has 20,000 people in it. 5% of them are one- legged and one half the balancego barefoot. How many shoes are needed?20,000, be quick here

84. The Smiths have a number of birdhouses in their yard and all are occupied. Sincethere are more birdhouses than there are birds in any one house, at least two of thebirdhouses must contain the same number of birds.



True prov by induction

85. The following diagram shows a railroad switch. A and B are boxcars and E is anengine which is larger than the boxcars. The piece of track from X to Y is long enough toaccept a boxcar but not long enough for the engine. How can you push and pull to switchthe two boxcars?

86. How can you throw a ball and make it stop and come back to you without it touchinganything or having anything attached to it?Throw up !!

87. A group of airplanes is based on a small island. The tank of each plane holds justenough fuel to take it half way around the world. Fuel can be transferred from the tank ofone plane to the tank of another while in flight. The only source of fuel is on the islandand we will assume there is no time lost in refueling either in the air or on the ground.What is the smallest number of planes that will ensure the flight of one plane all the wayaround the world (on a great circle) assuming that all planes have the same constantground speed and rate of fuel consumption and that all planes return safely to the island?

88. During a certain baseball season Babe Ruth had a higher batting average than LouGehrig for the first half of the season - and again for the second half of the season.However, Lou Gehrig had a better batting average than Babe Ruth did for that season.How come?

89. You encounter a man at a fork in the road. One fork leads to Chicago and you want toknow which one it is. What question can you ask so that you will be certain how to get toChicago regardless of whether the man is a good guy who always tells the truth or avillain who always lies?

90. A man buys a pair of shoes for $10 dollars and gives the owner a $20 bill. Having nochange the owner goes to the barber next door, gets change and gives the customer $10and the shoes. Later the barber tells him the $20 was counterfeit so the shoe man giveshim $20. If the shoes actually cost him $5 how much did the shoe store owner lose on thewhole affair?

91. Fill in the squares in the following diagram with numbers from 1 to 8 so that nonumber is adjacent to one that is in sequence with it either horizontally, vertically ordiagonally.



92. Jones sold his house for $4,000 and bought it back for $3,500 and sold it again for$4,500. How much did he gain?

93. We have three caskets - a gold, a silver and a lead. There is a prize in one of them.They have statements written on them as follows: On the gold - "The prize is in thiscasket." On the silver - "The prize is not in this casket." On the lead - "The prize is not inthe gold casket." At most, only one statement is true. Where is the prize?

94. 12 BBs look alike but one is different - either slightly heavier or slightly lighter. Howcan you identify the odd BB and tell if it is heavier or lighter in just 3 weighings on abalance scale?

95. An arab sheik died leaving 17 horses to his three sons. His will gave 1/2 to his oldestson, 1/3 to the middle son and 1/9 to the youngest son. The sons saw the impossibility ofdoing this, but their uncle came along and suggested a solution. What was it?

96. Here are the clues to a mathematical crossword puzzle:ACROSS DOWN1. Half of 6 across 1. 1rst two digits of 1 across, times the last two digits5. 3 times 10 across 2. Same as 7 down6. See 1 across 3. Reverse the first two digits of 1 down and multiply by 210. See 5 across 4. Reverse the 1rst two digits of 1 across7. Same as 2 down8. 2 times a perfect square9. A perfect square

97. How many mugs balance a flower pot in the picture below?

98. Who goes with whom? Where did they meet? How old is each of my kids?

One of my daughters met her boyfriend Alex at a disco, but he seems quite nice.Another is very serious about George, she's over 15. The didn't meet at a party.My eldest child, Betty, didn't meet her guy on a plane.My 14 year old met someone at a school; Peter is over 15.One of the boys brought home a girl called Molly the other day, but he hadn't met her atschool or on the plane.



Ray is dating my 16 year old daughter, that's not Rachel.

George Molly Alex Ray Michele Disco School Plane Holiday Party 12 14 16 18 20BettyRachelPeterMaxClare1214161820DiscoSchoolPlaneHolidayParty

99. Suppose a 24 foot long wire were added to a band tightly encircling the globe at theequator. Approximately how much space would there be between the band and theequator everywhere in the world?

100. Here are clues to a mathematical crossword puzzle:ACROSS DOWN2. See 6 down 1. Clue 5 + clue 8 +2005. Square of 4 down 2. Twice 4 down7. Twice 5 across 4. See 5 across9. Same as 6 down 6. 3 times 2 across

8. See 1 down

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Three Dots(John Banks)You are travelling in a deep, dark forest when, suddenly, on a dark and stormy night, youare captured by the kind-but-not-so-bright forest people. They keep looking at you andsaying to each other, "It be a smart person!"

You are marched to their village and seated in the square. Before you are blindfolded,you notice two other lucky souls seated in chairs facing you. Then you are told that theforest people king is about to die. He previously sent messengers throughout the land



seeking the 3 smartest people. You are one, and two others have also been found. He nowgives you all a task to see which one is the wisest.

He tells you, "I have seated you in an equilateral triangle so that each of you faces theother two. While you are blindfolded I will paint a dot on each of your foreheads. Eachdot will be red or green so that there can be any combination of red and green dots, forexample, 1 red and 2 greens, or all red, etc. When I remove the blindfolds each of youmust raise your hand if you see _any_ green dots, i.e. 1 or 2 dots. As soon as you havefigured out what color your own dot is, tell me how you knew."

So he paints a green dot on all three foreheads. When the blindfolds are removed, allthree hands go up. After a long pause, the wisest person, (that's you!) say, "Yourhighness, I have a green dot. The reason I know this is that..."

How did you know?

Extra credit: assume there are 4 people and all have green dots... can our hero figure it outnow?

Note: please don't write,

"I knew because I saw that two other hands were up!" (Like DUH!) or"I guessed!" or"I saw the reflection in their eyes!" or"I recognized the smell of the paint!" or"The other people's eyes were looking at me when they raised their hands!" or"The paint dripped!""3 green dots are the only fair test!" or"Paint flakes off!" or"The forest is green!" or"They have no red paint!""There were mirrors in the room!""There was a 50% chance!"...or any other such drivel! If any of those kinds of answers were correct, it would be aterrible riddle!Sadly, every one of the above sentences was sent to me as a possible solution!

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Three's a Crowd(Clayton Lewis)After solving the riddle of the three wise folks, three scoundrels claim to be the smartestin the country. So you decide to give them a challenge. Suspecting that the thing theycare about most is money, you give them $100 and tell them they are to divide this



money observing the following rule: they are to discuss offers and counter-offers fromeach other and then take a vote. Majority vote wins.Sounds easy enough... now the question is, assuming each person is motivated to take thelargest amount possible, what will the outcome be?

Note: careful... if the answer were that they split it 50% / 50% / 0%, or 1/3 / 1/3 / 1/3, itwouldn't be a riddle!

Note: careful... 96.6523544 % of people who send answers to this have not thought aboutit for even 1 minute. I guarantee you won't solve it in a minute. (96.6523544% of the timethis guarantee is correct.)

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Lying Defeeted(John Banks)After being the ruler of the forest people for a while, you get bored. So you visit an islandon which two tribes of natives live. One tribe has purple soles and always lies; the othertribe has green soles and always tells the truth. There are three natives standing near you.You can't see the bottoms of their feet, and indeed you find out it is rude to look atanother's soles, but you are curious so you ask the first man,

"Sir, what color are your soles?" Now he happens to understand English, but he can'tspeak it, so he replies in his native tongue, "Glub Glub". Though you don't speak thelanguage, you know that "Glub Glub" either means purple or green.

You turn to the second man and ask, "Sir, what did he say?" The second man replies, "Hesaid he has green soles."

Now to be sure, you turn to the third and ask, "Sir, what color of soles does this secondman have?" The third man replies, "Sir, he has purple soles."

Now the question is, what color of soles does the third native have?

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Open Door Policy(John Banks)On your trip back from the Island people to the deep dark forest, you get lost. A trap doorsuddenly opens and you fall down into a dark chamber.



You hear a voice, "You are trespassing and the penalty is death. In five minutes you willbe buried alive. However due to our exceeding kindness and mercy, and because youwere once ruler of the forest people, we will allow you to earn your life back. In this darkchamber there are two doors. You may choose to open either one - if you choosecorrectly, you will go free. If you choose incorrectly, well, instead of just being buriedalive, you will be eaten alive by army ants.

To help you choose a door, you may ask a question. However, you should know that twopeople will hear you and one of them always lies and the other one always tells the truth.One of them will answer your question, but you will not know which one. Each of themknows which door leads to freedom.

Good Luck, you have four and a half minutes left."

What question do you ask to win your freedom? (At least two solutions.)

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Trouble in River City(John Banks)After asking which door he would send his Mother-In-Law through and choosing theother one (Open Door Policy), you are allowed to walk through the Door of Freedom.After taking a few deep breaths of fresh air, you set out to escape this deep dark forest.As fate would have it, you feel a thud on your noggin and wake up in a dimly lit roomwith a pool table. You are about to be challenged to a game of 9-ball when the wickedforest people notice chalk on your hand. Wary of the possibility of you turning out to be apool shark, they give you this challenge instead.

On the pool table are 12 balls of identical size. And all are of identical weight exceptpossibly one, which is either slightly heavier or slightly lighter than all the others, but notenough for you to be able to tell just by holding it. So you don't know whether they allweigh the same, or whether there is one odd one. And if there is an odd one, you don'tknow whether it's light or heavy.

Now the evil forest people bring a balance scale so that you may compare objects againsteach other. "No problem" you're thinking. "I'll just compare them to each other to find theexception." However, you are then informed that you may only use the scale three times.

How do you use the balance scales so that in just three comparisons, you determine theyall weight the same, or find the one suspicious ball and know whether it is heavier orlighter?

Hints:



If you think you are looking for a heavier ball, please re-read the riddle.If you think you are looking for a lighter ball, and have read the previous hint,immediately box up your computer and ship it back to the manufacturer, because you aretoo stupid to own a computer.If you have no life and are interested in solving this riddle :-) then use this answer format(and a perl script that checks your answer for you) because if you don't understand theanswer format, you don't understand the riddle! Thanks to Paul & Michael for writing theperl script.and... if you have sent me your answer in the correct format and I haven't gotten back toyou... send me a reminder to check it. I promise to deal with your reminder at a pace atleast equal to the original mail :-)

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Asphynxiation(Eddie Gioia)After figuring out how to use the scales just three times to find the odd ball, you arereleased back into the forest. You are walking along minding your business when a snaresuddenly grabs your foot and yanks you upside down 30 feet off the ground. When youstop swinging you realize you won't be able to just climb up the rope, because you areright beneath a large platform with no holds on the bottom. You examine the rope and seethat there is no way to untie it.

"If only I had a knife..." Then you notice slight movement at the underneath edges of theplatform and see that the movement is actually thousands of army ants beginning to movedown over the platform to the underside and towards you. They look exceedingly hungry.They don't look like vegetarians.

When things look hopeless, you notice a sphynx couple sitting on a huge branch. One ofthem throws a knife into the air and when it comes back down, they both reach for it. Youcannot tell which one actually grabbed it. All you know is that you need that knife to cutyourself down.

The husband says "The sphynx with the knife always tells the truth." But the wifecounters, "He's wrong, the sphynx with the knife always lies." As luck would have it, oneof them always lies and one of them always tells the truth. Using only these twostatements as data, you get one chance to guess who has the knife.

The ants are approaching, who has the knife?

Note: please don't just say, "The Wife/Husband has it!". Say _why_.

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Hat-Trick(Bobby Dragon2)After calmly figuring out who had the knife, you cut the rope just as an army ant reachesit. You are lucky and fall into a pile of leaves, bounce up and land in a chair. As you startto look around you hear a stearn voice say, "Eyes forward!" (some of you have heard thatvoice!)

There are two people sitting behind you, so there are three people facing the samedirection. The other two are the two smartest people in the forest (a scary thought). Thereare five hats: three are red and two are purple.

While all of your eyes are closed, a hat is placed on each person's head and the twounused hats are hidden. Then all are allowed to look only forward so that each of you canonly see the people in front of you (the person in the back can see the hats of the twopeople in front; the middle person can see your hat; you can't see any hats at all; so youmight as well keep your eyes closed!)

When someone figures out what color hat they are wearing, they must call out. No onehas called out yet. What color hat are you wearing and how do you know?

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Light Bridge(various - most recently James Spell)After you figure out that you were wearing a Cowboy hat all along, (Hat-Trick) youdecide to go home. Unfortunately you must take an old, old bridge across a deep, darkchasm. It is dark and there are so many steps missing that you ask to borrow a flashlight.Three forest people approach and offer you a flashlight in return for helping them acrossthe bridge. Now the bridge allows a maximum of 2 people at once and for safety, theremust always be someone on the bridge holding a flashlight (of which there is only 1). Inaddition, the three forest people take 2, 5, and 10 minutes respectively to cross the bridge.You, being highly motivated, need only 1 minute.

No problem, you think, we'll just take turns walking folks back and forth with the lightuntil we're all across. But the bridge is enchanted and every million years, it vanishes fora century and that will happen in exactly 17 minutes.

How will all four of you make it to the other side of the bridge in 17 minutes?

(Note: Call these people #1 #2 #5 and #10. If you and #10 go across and you return, thattakes 11 minutes. Then you and #5 could go across and you return; we are now up to 17minutes... *poof* - bridge is gone.



The light carrier doesn't have to be you. If the light carrier is accompanied by anyone,they must stay together the whole way across - you cannot have one person stand in themiddle and shine the light. No piggy-backs, no simultaneous-2-way-crossings, etc.)

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Apairantly Not(Caroline Koo)After barely making it across the bridge, you hear two of the forest people arguing. Itseems that just before they crossed the bridge, they each bought 10 pair of socks, and infact, as far as color and size go, they each bought the same exact 10 pairs. Each personhas 1 pair of green, 1 pair of blue, etc. etc... But now they have accidentally dropped alltheir socks and the socks are all mixed up in a pile on the ground.

Because it is pitch-black, they can't see what colors the socks are, but want to divide themup so that they each have the same colors that they bought, i.e. identical sets of green,blue, etc. Luckily the socks are all still in pairs, so they only have to pick up 20 pairs, not40 individual socks.

The light used in crossing the bridge fell into a bottomless forest pit, so even though it ispitch-black, how can you help the two forest people get one pair each of every color, justlike they had before they dropped them?

(Note: no lights, moon, cigarette lighter, etc...)

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Tractor Beam(Frederic H McFarland)You watch the sock-hoppers amble off toward a pier and notice a small island about amile away from shore. Due to your excellent forest vision, you see a Forest personplowing a field with a large tractor. There are no bridges or tunnels to the island and youwonder how the tractor got out to the island.

"That's a good question," says a nearby forest person, reading your mind. "I have the onlyboat around here and it's not big enough to carry that tractor over. I didn't drop off anyparts either so he couldn't have built it there. No one has an airplane or helicopter to dropit off either."

So how did the tractor get on the island?

(Notes:1. the tractor was not built on the island2. even with tides, the water is too deep to drive across



3. it was not driven across the bottom of the ocean or under water4. it was not disassembled)

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Auction Action(Clayton Lewis)After using the same method that the tractor took to get to the Island, you drop in on aparty of the forest people and notice Prof. Chaos with an evil look in her eye. Folks lookbored, so she decides to engage in a little mischief. "I will give this $100 bill to thehighest bidder. The only rule is that the person who bids the second highest amount willalso have to pay me that bid. The highest bidder pays the high bid and takes the bill, evenif the highest bid is only 5 cents."

People start to murmur. Then you hear "A nickel!". "A Dime!". "Two Dollars!"...

Question: what is Prof. Chaos up to?

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No Vacancy(Brady Smith)In the forest, a hotel has an infinite number of rooms. An infinite number of forest peoplearrive and each takes a room. So far so good. Now you would like a room.

Can the hotel accomodate you? If so, how?

(Please enjoy this riddle instead of writing that infinity is the same as infinity plus 1 orsome such gibberish! Folks who send me stupid definitions ("Infinity is, you know, likenever ending, so, like, sure, they'd all have rooms, you know, like duh.") are almostwithout exception the least knowledgeable about infinity! So have fun with it; askyourself what you'd do if you were the inn-keeper. However, you must find _rooms_ foreverybody, no doubling up, sleeping in the kitchen etc.)

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No Vacancies(Brady Smith)



The hotel has an infinite number of rooms. An infinite number of forest people arrive andeach takes a room. So far so good. Now another infinite number of guests arrive.

Can the hotel accomodate them all? If so, how?

(see the note above on "No Vacancy")

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Timing is Everything(Riki Maicas)A Beanie Baby named Joe comes home from work by train every day. He gets to the trainstation at 5 pm and from there his dog picks him up in the car. One day Joe arrived at thestation at 4 pm and decided to start walking and meet his dog somewhere between thetrain station and home. His dog drove the car as usual; met him on the road beforereaching the station, and took him home.That day, they got home 20 minutes earlier.

Question: How long had Joe been walking?(Tips: not 20 minutes; not 40 minutes; of course beany babies can drive; and if beanybabies can drive, well, then so can their dogs.)

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Enlightenment(various)Strolling through the forest, you hear a muffled shout. Investigating further, you come toa closed, solid, light-proof door. "... need Light! Light!..." you can barely make outcoming through the door.

"Use the switches to know which one controls the Light!" you hear the voice say as younotice three on/off switches beside the door.

Inside the cave is an incandescant lamp which is now off. Next to the door are threeswitches. One of these three switches turns the lamp in the room on and off.

Your job is to figure out which switch controls the lamp. However, you can't just openthe door and look. In fact, you can only enter the cave one time and then you have to saywhich switch controls the lamp. There are no windows, holes, cracks, leaks, bleeding-heart-liberals, etc. You are allowed to set any switches on or off and then enter the cave.That's it.



What will you do to know with certainty which switch controls the lamp?

Extra credit: what if there are 4 switches?

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Ties that Bind(various)After discovering it was the third switch which controlled the light (wasn't it just soobvious), you see a forest person carrying a sign which reads, "The Time has Come!""What time?" you ask."The time to tell you about the String Problem," he answers and then starts to shout, "45!45! 45!"You reply, "Caliber?""No... Minutes! You need 45 minutes! and all we have are these two strings!"

You have 2 long strings which burn at random rates at different positions on their length.Though they are not identical, they do burn exactly 1 hour each. A string might burn 99%of it's length in 1 minute, then take 59 minutes to burn the rest of the way.

You have no way of telling time; clock, watch, sunset, etc. but need to measure 45minutes.

Using these string and a lighter, how can you measure 45 minutes?

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Flight Plight(various)On Tractor Island, there is an airport. The airport is the homebase of an unlimited numberof identical airplanes. Each airplane has a fuel capacity to allow it to fly exactly 1/2 wayaround the world, along a great circle. The planes have the ability to refuel in flightwithout loss of speed or spillage of fuel. Though the fuel is unlimited, the island is theonly source of fuel.

What is the fewest number of aircraft necessary to get one plane all the way around theworld assuming that all of the aircraft must return safely to the airport?

Notes:

ignore extra fuel consumption as a result of acceleration, evaporation of fuel, bleeding-heart-liberal fiscal policies, etc.



All the planes have to make it back safely, so you can't give all your fuel away to anotherplane.

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Heads Up(Ram)After flying around the world and touching down on Tractor Island, you're thirsty fromthe long flight. You walk over to the pop machine and realize you have no quarters.

Then you notice a line of quarters right there on the ground. The line goes on and on,clear into the forest. "There must be thousands of them!" you exclaim.

"Infinite, to be exact." says the voice of an evil forest person. "And you can have them allif you divide them into two piles which have the same number of heads.""How much time do I have?""1 day. You can pick up as many quarters as you want and even flip them over, just aslong as you wind up with two piles that have the same number of heads. I happen toknow that there are 20 heads, the rest are all tails.""Do the piles need to have the same total number of quarters?" you ask observantly."No, just the same number of heads. If you're ready to begin, here's the blindfold.""What blindfold?""The one you have to wear while solving this riddle!"

Question: Given infinte coins,

only 20 of which are heads, andwearing a blindfold,flipping however many you want ...how can you divide the coins into two piles, each with the same number of heads?Notes:

You can pick up, flip, etc. as many coins as you want.You can't remove any coins.You must make 2 piles of coins.No peeking allowed.It's not a probababalistical problem.If you solve this... write me whether you think it is a "logic" or "creative" riddle.

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Sailor's Delight(various)



10 pirates are ranked in order, first to last. After finding a treasure chest of 100 goldcoins, they are discussing how to divide up the booty. They allow the lowest rankedsailor to divide up the coins and then vote on his idea. If the number of pirates who likethe division is equal to or greater than the others who don't like it, then the boss will say,"Make it So." (The proposer of the idea also has a vote.)

Otherwise... well, being pirates their simple solution is to dump the unfortunate sailorinto the deep blue sea and let the next pirate in line decide how to divide up the spoils.

Question: How many pirates will be thrown into the sea?

Notes:

Pirates are smart, want money, and love life, especially their own.This one is harder than average. If you are stuck, think of fewer pirates...Why would #1 ever vote for any schemes?Why would #2 ever vote for any schemes?... hmmmm

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