# What's your favorite brain teaser question?April 30, 2014 7:19 AM   Subscribe

I'm looking for a really hard "brain teaser" question.

At our staff meetings, we have to play little games (yeah, I know). It's my turn to lead a little game, and what I'm going to do is pass out a sheet of brain teaser questions -- like the ones here. I want most of them to be solvable fairly quickly, and I can find those myself, but I would like to have one really tricky one, and that where you guys come in. Suggestions?
posted by JanetLand to Grab Bag (53 answers total) 71 users marked this as a favorite

You have two US coins. Their total value is thirty cents. One of them is not a nickel. What are they?

A quarter and a nickel. One of them is not a nickel. The other one is.
posted by FAMOUS MONSTER at 7:25 AM on April 30, 2014 [6 favorites]

Here's my favorite. It's not "tricky" in that the solution is simple, but it does require some thought.
You have a string of 100 Christmas lights that work on a toggle system (i.e. you flip the switch, all the lit lights turn off and all the unlit lights turn on). On your first switch, every first light (so, every light) toggles on. On the second switch, every second light toggles. On the third switch, every third light toggles. And so on until you’ve flipped the switch 100 times. At the end of 100 toggles, which lights are lit?
posted by phunniemee at 7:37 AM on April 30, 2014 [1 favorite]

For what it's worth, that one was given to me while I was out at brunch, and I solved it by actually going through and toggling a row of 20 coffee creamers and extrapolating from there. Encourage your coworkers to use props if necessary.
posted by phunniemee at 7:38 AM on April 30, 2014

The Monty Hall Problem.
"No other statistical puzzle comes so close to fooling all the people all the time." -- cognitive psychologist Massimo Piattelli-Palmarini.
Caveat: You'll find different presentations and explanations, some clearer than others. The link above seems good, and it also provides a simple interactive demonstration anyone can do.
posted by LonnieK at 7:48 AM on April 30, 2014 [4 favorites]

From here:
A father and his son were driving to a ball game when their car stalled on the railroad tracks. In the distance a train whistle blew a warning. Frantically, the father tried to start the engine, but in his panic, he couldn’t turn the key, and the car was hit by the onrushing train. An ambulance sped to the scene and picked them up. On the way to the hospital, the father died. The son was still alive but his condition was very serious, and he needed immediate surgery. The moment they arrived at the hospital, he was wheeled into an emergency operating room, and the surgeon came in, expecting a routine case. However, on seeing the boy, the surgeon blanched and muttered, “I can’t operate on this boy — he’s my son.”

What do you make of this grim riddle? How could it be? Was the surgeon lying or mistaken? No. Did the dead father’s soul somehow get reincarnated in the surgeon’s body? No. Was the surgeon the boy’s true father and the dead man the boy’s adopted father? No. What, then, is the explanation? Think it through until you have figured it out on your own — I insist! You’ll know when you’ve got it, don’t worry.
posted by alex1965 at 7:56 AM on April 30, 2014 [4 favorites]

(x-a) * (x-b) * (x-c) * ... * (x-z) = ?

Zero, because (x-x).
posted by Etrigan at 8:01 AM on April 30, 2014 [6 favorites]

The puzzle of 100 hats (solution)
posted by crocomancer at 8:15 AM on April 30, 2014

In a "Knight's Tour", a Knight begins on one square of a chessboard, and, moving as in the normal rules of chess, visits every square on the chessboard exactly once. Is there a possible Knight's tour which begins on one corner of the board, and finishes at the diagonally opposite corner?
posted by thelonius at 8:31 AM on April 30, 2014

A man has two cubes on his desk. every day he arranges both cubes so that the front faces show the current day of the month. what numbers are on the faces of the cubes to allow this? Solution.
posted by mskyle at 8:40 AM on April 30, 2014 [4 favorites]

Argh, phunniemee, I had to make a simulator to try out that toggle problem for myself. Here it is. (I put in 1000 lights, if you're patient enough to click 1000 times.)
posted by moonmilk at 8:48 AM on April 30, 2014 [1 favorite]

Is the Blue Eyes Puzzle too long (or too well known)?
posted by saladin at 8:57 AM on April 30, 2014

Bulgarian Gods should shut up most people for a bit.
posted by themel at 9:02 AM on April 30, 2014 [1 favorite]

It's not a quick puzzle, but the Self Referential Aptitude Test is a classic.
posted by It's Never Lurgi at 9:37 AM on April 30, 2014 [2 favorites]

I've got two.

This brain teaser was presented to my gifted and talented class in grade school many years ago, and I've loved it since.

Every day a person goes in to work in an office building, on the 31st floor (or any high numbered floor of your choosing). Sometimes he (or she, or zie -- any gender pronoun will work) rides the elevator to the 20th floor and walks up the stairs for the remaining 11 stories. Sometimes this person will ride the elevator all the way up to the 31st floor. At the end of the day, this person always rides the elevator all the way down to the first floor and goes home.

Assuming this person is not doing it for the exercise, why (and under what circumstances) will this person only ride the elevator to the 20th floor?

---

Here's a personal favorite of mine, which was asked of me during a job interview. I got the job. I no longer work there, but I've taken the question and like to ask it at my current employer whenever I'm interviewing job candidates:

You've just been hired to work as an engineer at our company. Our CEO drives one of these expensive luxury cars with heated seats. The switch for the heated seats has two positions, H for High and L for low. If the heater is off, pushing H or L will switch it on to the high or low setting, respectively. If the heater is on, pushing the same setting it's on will switch it off, but pushing the other setting will switch it to that setting.

Our CEO asks you, in casual conversation, if there is a way to guarantee, without feeling the seat, and without knowing the current setting, that the heater is off. What do you tell them?
posted by tckma at 9:47 AM on April 30, 2014 [2 favorites]

There are two possible correct answers to the second problem. It's quick to work out, but the answer's not intuitive. Encourage your co-workers to work it out on paper or a whiteboard if they want to, but only if they ask to.
posted by tckma at 10:08 AM on April 30, 2014 [1 favorite]

Four men want to cross a bridge. They all begin on the same side. It is night, and they have only one flashlight with them. At most two men can cross the bridge at a time, and any party who crosses, either one or two people, must have the flashlight with them.
The flashlight must be walked back and forth: it cannot be thrown, etc. Each man walks at a different speed. A pair must walk together at the speed of the slower man.
Man A needs 1 minute to cross the bridge.
Man B needs 2 minutes.
Man C needs 5 minutes.
Man D needs 10 minutes.
For example, if man A and man C walk across together, they need 5 minutes.

What is the shortest amount of time the four men can cross the bridge?

Hint #1: It is under 20 minutes.
Hint #2: It is under 18 minutes.
posted by ObscureReferenceMan at 10:20 AM on April 30, 2014

One day, a father went to his three sons and told them that he would die soon and he needed to decide which one of them to give his property to. He decided to give them all a test. He said, “Go to the market my sons, and purchase something that is large enough to fill my bedroom, but small enough to fit in your pocket. From this I will decide which of you is the wisest and worthy enough to inherit my land.” So they all went to the market and bought something that they thought would fill the room, yet was still small enough that they could fit into their pockets. Each son came back with a different item. The father told his sons to come into his bedroom one at a time and try to fill up his bedroom with whatever they had purchased. The first son came in and put some pieces of cloth that he had bought and laid them end to end across the room, but it barely covered any of the floor. Then the second son came in and laid some hay, that he had purchased, on the floor but there was only enough to cover half of the floor. The third son came in and showed his father what he had purchased and how it could fill the entire room yet still fit into his pocket. The father replied, “You are truly the wisest of all and you shall receive my property.” What was it that the son had showed to his father?
posted by ObscureReferenceMan at 10:42 AM on April 30, 2014

Here's one I like:

You've got 24 coins on the table in front of you. 10 of them are showing heads, 14 are showing tails, but you're blindfolded and can't tell which is which (neither can you feel for George Washington's face, or any other such funny business).

How can you split the 24 coins into two groups which have the same number of heads showing?
posted by So You're Saying These Are Pants? at 10:43 AM on April 30, 2014

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?
posted by ObscureReferenceMan at 10:45 AM on April 30, 2014 [1 favorite]

A man walks into his back yard in the middle of the night and fires a gun. Due to his strange behavior he never sees another sunrise. (No, he didn’t kill himself.) Can you explain this odd occurrence?
posted by ObscureReferenceMan at 10:47 AM on April 30, 2014

I think I should have asked for answers as well as questions . . . .
posted by JanetLand at 10:47 AM on April 30, 2014 [14 favorites]

I think I should have asked for answers as well as questions

What was it that the son had showed to his father?

Pretty sure this one is a music box. Or for the not-ancient, an ipod.
posted by cashman at 10:51 AM on April 30, 2014

Love the Crimson one, it's funny.

As for the purchase for the boys' father, were these the same four people who needed to cross the bridge, and was the purchase the flashlight? ;)
posted by tckma at 10:51 AM on April 30, 2014

Haha, fair enough. The real "trickiness" comes through when you've spent 15 minutes trying to work out a solution though :)

How can you split the 24 coins into two groups which have the same number of heads showing?

Pick 10 coins at random. These contain x heads and 10-x tails.

The other 14 coins contain 10-x heads. Now flip your group of 10 over and you've got 10-x heads in that group as well. Done.

You can switch up the 14/10 numbers used as you wish.
posted by So You're Saying These Are Pants? at 10:52 AM on April 30, 2014 [1 favorite]

For the elevator, the person is a Little Person and can only reach up to the 20 button on his or her own, but sometimes there's another person in the elevator who can press 31.

For the seat heater, the answer is "Press either H or L, then press the other one twice."

The canonical answer for the three sons is "A match" (fills the room with light). I prefer "Smoke grenade." I also like cashman's answer.
posted by Etrigan at 10:54 AM on April 30, 2014 [3 favorites]

I was figuring the boy had bought a small bottle of a foul-smelling gas.
posted by Hactar at 10:55 AM on April 30, 2014 [3 favorites]

I think I should have asked for answers as well as questions . . . .

The man is short and can only reach up to the button for the 20th floor. If there's no one else in the elevator with him that he can ask to press 31 for him, he can only go up to 20, but he can always reach one.

Men 1 and 2 travel over and man 2 brings back the flashlight: 4 min.
Men 3 and 4 travel over and man 1 brings back the flashlight: 11 min.
Men 1 and 2 travel over: 2 min.
Total: 17 min.

Question Mark.

The man shot his rooster, which had awakened him with its crowing every morning for the past ten years. Since he had recently retired, there was no longer any reason to be wakened at such an early hour.
posted by FAMOUS MONSTER at 10:55 AM on April 30, 2014

I think I should have asked for answers as well as questions.

Awwww, but that spoils the fun of solving the brain teasers others have posted here during my lunch break.

Okay. For my first teaser, the answer is that the person is a midget ("little person" I guess would be the PC term these days, but I heard it in 1987). Since the buttons for the higher numbered floors are higher up, the 20 is the highest button s/he can reach. I suppose it also works if s/he is confined to a wheelchair.

If someone's in the elevator with him/her, s/he can ask that person to press the 31 button. But if alone, it's only up to the 20th floor.

For my second teaser, the answers are: HLL or LHH.
posted by tckma at 10:56 AM on April 30, 2014

Punctuate the following so that it makes sense:

(see also: "Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo" or "Dogs dogs dog dog dogs.")
posted by tckma at 11:07 AM on April 30, 2014 [2 favorites]

Our CEO asks you, in casual conversation, if there is a way to guarantee, without feeling the seat, and without knowing the current setting, that the heater is off. What do you tell them?

Yes. Turn the car off and I guarantee the heater is off.
posted by Jacob G at 11:21 AM on April 30, 2014 [6 favorites]

I've always heard the elevator question posed as being a child who lives in a high rise. Not "he took the elevator to his office" but "George takes the elevator to his apartment." Framing it that way gets around the little person/wheelchair/whatever thing entirely so you can avoid that.
posted by phunniemee at 11:21 AM on April 30, 2014 [2 favorites]

You might consider not using the Monty Hall problem. It can start a serious argument if you're not careful.

Psychologist and author Richard Wiseman posts a weekly Friday puzzle on his blog. One of those might do. Here's an example:

Yesterday my friend and I started to walk down a road. We began our walk at the same time, from the same point, and headed in the same direction. I walk at 5 km/h and my friend walks at 6 km/h. Throughout the walk a dog ran between the two of us again and again, with a constant speed of 10 km/h. How far did the dog travel in 1 hour?
posted by Flexagon at 11:24 AM on April 30, 2014 [2 favorites]

What is the largest amount of money that you can have in coins and still not be able to give change for a dollar? Hint--it's not 99 cents.
posted by MrMoonPie at 11:25 AM on April 30, 2014

The man is short and can only reach up to the button for the 20th floor. If there's no one else in the elevator with him that he can ask to press 31 for him, he can only go up to 20, but he can always reach one.

The variation on this one that I always heard was that he/she takes the elevator up to 31 on rainy days, but not on dry days. Because he/she has an umbrella on those days, and can use it to press the higher button.
posted by jbickers at 11:27 AM on April 30, 2014 [4 favorites]

How can two fathers and two sons divide three automobiles among themselves with each receiving one?

If the men are grandfather, father and son.
posted by Michele in California at 11:51 AM on April 30, 2014 [2 favorites]

no thelonius, a knight's tour is 63 moves, and each odd-numbered move puts it on a square opposite in color from the original square. the square at the other end of the long diagonal is the same color square.

when you die, there's a fork in the road, one way to heaven, the other to hell. there are two talking skulls at the fork, one which always tells the truth, and the other which always lies, and you can't tell them apart. what one question can you ask one of the skulls to ensure that you end up in heaven?
posted by bruce at 12:08 PM on April 30, 2014

MrMoonPie:

1. Does a dollar coin count as change for a dollar?

2. Breaking the assumption that we are in the US for a moment here: Canada has \$2 coins (and no bills smaller than \$5). If the OP is in Canada, one could conceivably have an infinite supply of \$2 coins (and no coins of other denominations) and still not be able to give change for a dollar.
posted by tckma at 12:46 PM on April 30, 2014

mrmoonpie, three quarters, nine dimes and four pennies.
posted by bruce at 12:56 PM on April 30, 2014

Can't be nine dimesbbecause 5 dimes plus two quarters is change.
posted by Carillon at 12:57 PM on April 30, 2014 [1 favorite]

Three quarters: \$0.75 (or a half-dollar and one quarter)
Four dimes: \$0.40
One nickel: \$0.05 (that doesn't work: three quarters, a nickel, and two dimes is change)
Four pennies: \$0.04

Total: \$1.24 \$1.19
posted by tckma at 12:59 PM on April 30, 2014 [1 favorite]

You've just been hired to work as an engineer at our company. Our CEO drives one of these expensive luxury cars with heated seats. The switch for the heated seats has two positions, H for High and L for low. If the heater is off, pushing H or L will switch it on to the high or low setting, respectively. If the heater is on, pushing the same setting it's on will switch it off, but pushing the other setting will switch it to that setting.

Our CEO asks you, in casual conversation, if there is a way to guarantee, without feeling the seat, and without knowing the current setting, that the heater is off. What do you tell them?

Jacob's answer above notwithstanding, I think the desired answer is: Hit the switch one way once, then hit the switch the other way twice. That is, either "H L L" or "L H H". Using the first solution as the example, the H push ensures the seat is either on High or Off. The first L push puts the seat definitively in Low. The final L push turns the seat Off. The second solution works similarly but with Low and High reversed.
posted by stoffer at 1:31 PM on April 30, 2014 [1 favorite]

[Bunch of stuff removed. Folks, this is Ask Metafilter, not a chatroom. Link to a page of riddles if you think it'll be helpful, don't dole them out here without answers or play at question-and-answer; just help the asker out directly.]
posted by cortex at 2:22 PM on April 30, 2014 [3 favorites]

Here's one in the capricious prison wardens category. A warden offers two prisoners a chance to earn their freedom. They will be taken separately into a room with a fair coin. Each prisoner will flip the coin and then guess the result of the other's flip. If either prisoner guesses correctly, both will be freed. They are allowed to communicate freely before the coin flips, but not at all after. What strategy can they adopt to maximize their chance of freedom?

Prisoner A guesses that Prisoner B got the same result he did. Prisoner B guesses Prisoner A got the opposite. No matter how the flips come out, one of them is guaranteed to be correct.
posted by eruonna at 2:24 PM on April 30, 2014 [1 favorite]

Martin Gardner's books are great for the mathy sort of puzzles.

I also like this one, but working it out can take quite a while:

You have 12 coins, of which one is counterfeit and has the incorrect weight. The rest are identical, and you don't know if the false coin is too light or too heavy. You have a balance, but it's liable to fall apart if you tax it too much. How can you find the counterfeit coin in only three weighings?
posted by Westringia F. at 2:28 PM on April 30, 2014

A man looks at a portrait and says, "Brothers and sisters, I have none. But that man's father is my father's son." What is the relationship of the man in the portrait to the speaker?
posted by msali at 8:12 PM on April 30, 2014

I've had success doing team-building type games with the genre of puzzle that some of these fit into - puzzles where you present a seemingly weird situation, and people have to figure out what happened by asking you yes/no questions (which is how I've always seen the elevator one presented). My two favorites:

(1) A man and a woman are driving together when the man suddenly pulls the car over to a nearby house, locks the car door with the woman inside, and runs into the house. When he comes back outside, the woman is dead, there's a stranger in the car, and the car door is still locked. When the police arrive, the stranger isn't arrested or even questioned. What happened?

(2) A man walks into a bar and asks the bartender for a glass of water. Instead, the bartender reaches under the bar, pulls out a loaded gun, and points it directly at the man. The man says "Thank you," and leaves. What happened?

(1) The woman was pregnant and the man pulled over to get help when she went into labor. She died in childbirth - the stranger was the baby.
(2) The man had the hiccups, so the bartender gave him a scare to help cure them.
posted by violetish at 9:13 PM on April 30, 2014

A man stands on one side of a river, his dog on the other. The man calls his dog, who immediately crosses the river without getting wet and without using a bridge or a boat. How did the dog do it?

SOLUTION: The river was frozen.
posted by ObscureReferenceMan at 6:34 AM on May 1, 2014

A sundial has the fewest moving parts of any timepiece. Which has the most?

SOLUTION: An hourglass, with thousands of grains of sand.
posted by ObscureReferenceMan at 6:35 AM on May 1, 2014

What makes this number unique – 8,549,176,320?

SOLUTION: It contains each number, zero through nine, in alphabetical order.
posted by ObscureReferenceMan at 6:36 AM on May 1, 2014

Oh, here's a good one.

There is a square tray in front of you that spins. At each corner there is a disk that is white on one side and black on the other. You can flip either one or two disks each turn. Your goal is to get all the disks to show the same color.

Complication #1 - you are blindfolded and do not know the starting condition of the disks

Complication #2 - after each turn, the tray is rotated by some random amount in an unknown direction

Clarification - if you flip two disks, they are flipped simultaneously.

You don't have to know when they are all showing the same color, it just has to be the case that, after some turn, all the disks are showing the same color (imagine a judge who can see the disks and will stop the game if they are all showing the same color).

There is no trick or gimmick here. It's a genuine puzzle.
posted by It's Never Lurgi at 9:44 AM on May 1, 2014

I'll give the solution here.

Obviously if the disks start off showing all white or all black then you are done before you start.

Imagine that there are two white and two black. If that's the case then the following will work: Flip any two diagonally opposite disks. Flip any two adjacent disks. Flip any two diagonally opposite disks.

If you start off with two disks showing black and two disks showing white then at some point in this process (maybe the end, maybe part way through) all the disks will show the same color.

If this doesn't work then you have to assume that you have three of one color and one of the other. Flip any one disk. That either gets to you four of one color (you win) or two and two, and you know how to win that.
posted by It's Never Lurgi at 9:48 AM on May 1, 2014

Three people check into a hotel. They pay \$30 to the manager and go to their room. The manager finds out that the room rate is \$25 and gives \$5 to the bellboy to return.
On the way to the room the bellboy reasons that \$5 would be difficult to share among three people so he pockets \$2 and gives \$1 to each person. Now each person paid \$10 and got back \$1. So they paid \$9 each, totalling \$27. The bellboy has \$2, totalling \$29.
Where is the remaining dollar?

He takes the five dollars & gives three back to the people \$25 + \$3 = \$28 + the \$2 pocketed = the original \$30

In other words, it's sort of misdirection.. it's not supposed to add up to \$30 anymore, but add up to \$25 plus \$2 to bellboy and \$1 to each of the three people.

(source)
posted by starman at 2:36 PM on May 1, 2014 [1 favorite]

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