Brainteasers

An archive of the puzzles I've posted in my blog. Solutions are left as an exercise for the reader, therefore they are not posted here. But feel free to email or IM me if you want to discuss your solutions.

You have received a new system of weights and measures from a slightly sketchy but very cheap scientific supply company. The weighing system consists of a super accurate two pan balance and a forty pound rock, and allows you to accurately weigh items from one to forty pounds, and every integer value in between.*

*Some disassembly required.

Obviously, the rock will have to be cut into pieces using a high-powered diamond-tipped saw (not included), as right now it can only be used to accurately weigh other forty pound rocks.

What is the smallest number of pieces you can cut the rock into so that you can measure any item with an integer weight between one and forty pounds, providing you can cut the rock into the precise fractions you want?

Who solved this puzzle: Tyson, Leyan, Timothy

A set of calendar cubes sits on a desk in a corporate office. The set consists of two cubes, with a number painted on each of its sides. Each day the cubes can be rearranged to display the current day of the month. How are the numbers arranged on the cubes?

Note: Both cubes are used every day. For instance, if it is May 8, the cubes will read 08.

Who solved this puzzle: Leyan, Timothy, Tyson

A set of calendar cubes sits on a desk in a corporate office. The set consists of three cubes, with a letter painted on each of its sides. Each month the cubes can be rearranged to display the three letter abbreviation of the month (JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC). How are the letters arranged on the cubes?

Note: Although I've written the abbreviations in all capitals, you may have to get creative with the fonts to make everything fit. Otherwise this puzzle could get insanely hard.

Who solved this puzzle: Leyan, Ambie

I have twelve colored pentominoes as shown in the picture. I take seven of the twelve and put them in a box, then cut holes in the lid of the box as shown so that three squares of color are visible. Which seven pentominoes are in the box, and how are they arranged? (Yes, you are allowed to flip them)

Who solved this puzzle: Tyson, Dan

You and a friend are lost in the desert. Luckily, you have a large bottle filled with water, which should be enough to last the two of you until you reach civilization. How would you divide the water equally between you and your friend?

Who solved this puzzle: Tyson

You have a cylindrical glass which is filled to the brim with water, and an empty bowl. Without any measuring equipment, how would you pour exactly half the contents of the glass into the bowl?

Hint (highlight to read): Don't drink the water!

Who solved this puzzle: Tyson, Leyan

From the inventors of Sudoku comes Nurikabe. The object of the game is to determine which squares are white and which are black. The black squares form one continuous region, but no 2x2 regions of black are allowed. There are ten continuous regions of white squares, each containing a number which defines how many white squares are in that region.

Who solved this puzzle: Dan

You have 3000 bushels of grass you need to transport across a 1000 km desert. You also have a camel which can carry a maximum of 1000 bushels of grass. However, this camel is very stubborn and will only move if it has something to eat, consuming grass at a rate of 1 bushel per kilometer.

What is the maximum amount of grass you can deliver to your destination?

Who solved this puzzle: Dave Z.

While I was in London I got into the habit of having tea with breakfast. Every morning I would make myself a cup of tea at the counter in the cafeteria and put sugar in it. Because I have what seems to be an unusually sensitive tongue, I'd usually have to wait until I'm at least halfway done with my breakfast before the tea was cooled to a drinkable temperature.

However some mornings the tea counter in the cafeteria would be busy, so I only grab a packet of sugar, not putting it in until after I've found a seat at a table. This way the tea has begun to cool before I put the sugar in.

Theoretically, which way should let me start drinking my tea faster?

Who solved this puzzle: Mike I.

A large population of gnomes lives in a certain forest. The gnomes all have either blue or green hair, which may randomly change color overnight. The gnomes consider it extremely rude to talk about hair colors (they can see and distinguish the others' hair colors; they just never talk about it), so much that they don't even know the color of their own hair. Every year the gnomes gather in the central forest clearing to be counted. Traditionally, they present themselves in two groups divided by the color of their hair. How do they do this efficiently without talking or otherwise communicating hair colors to each other during the sorting?

Who solved this puzzle: no one yet

One foggy night four teenagers are trapped on an island in the middle of a swamp. Which wouldn't have been so bad, except that it was a Friday the 13th. In October. During a full moon. In a horror film.

The only way to dry land is by an old bridge that can only support the weight of two people. Given the visibility conditions and the state of the bridge, crossing without a flashlight is impossible, and the group only has one flashlight between them.

Alison can sprint across the bridge in a minute, Bob can run it in two minutes, Christine can jog across in five, and Dave takes ten minutes to shuffle across. When two people cross the bridge, sharing the flashlight, they travel at the speed of the slower person.

The flashlight has seventeen minutes of battery life left. Can they all get across safely? What is lurking in the darkness waiting to devour them? Who gets eaten first?

Who solved this puzzle: Jessica

You have a 5x5 square of grid paper with two opposite corners truncated as shown below. Using a pair of scissors, make one continuous cut so that the two resulting pieces can be rearranged to form a 6x4 rectangle.

Who solved this puzzle: Jessica

Grandfather is a very hard-boiled customer. In fact, his eggs must be boiled for exactly 15 minutes, no more, no less. One day, he asks you to prepare breakfast for him, and the only timepieces in the house are two hourglasses. The larger hourglass takes 11 minutes for all the sand to descend; the smaller, 7 minutes. How do you prepare Grandfather's breakfast in the shortest possible time?

Who solved this puzzle: Dan

Variation: How quickly can you prepare a 9 minute egg using hourglasses measuring 7 and 4 minutes?

Who solved this puzzle: Tyson

Five pirates have come upon a stash of 1000 gold coins which must be split among the five pirates. In order of rank, each pirate can make a proposal about how to split up the treasure. The proposal is accepted if and only if a majority agrees on it, or the proposing pirate is thrown overboard and the next pirate makes a proposal on how to divide the booty among the remaining pirates. The pirates are perfectly logical and perfectly greedy (i.e. they will want to keep as much gold for themselves as possible). How should the captain propose the treasure be split?

Who solved this puzzle: "Suraimu"

Adam, Bob and Carl have been competing for the affections of the same girl. Or perhaps they were three brothers fighting over their wealthy father's inheritance. Whatever it is, they decide that the best way to settle this once and for all is with a three way duel (a triel?). Adam is an expert swordsman, which is really too bad, as this is to be a pistol duel. As a pistol shot, his accuracy rate is only 33%. Bob has an accuracy rate of 50%, and Carl has perfect marksmanship skills - he never misses his target (he used work as a guard for a high-tech force field jail...). The three men stand equidistant from each other and take turns firing one shot. Because Adam has the lowest accuracy rate, he gets to go first, followed by Bob and then Carl. The turns go in this order until only one man is left standing. What should Adam do to maximize his chances of winning?

Who solved this puzzle: Dan

You've angered the spirit of Halloween by failing to revere the Great Pumpkin, and now a curse has befallen you. On the walkway to your house is a Ward of Seven Jack O' Lanterns arranged in a circle. If midnight comes and any of the seven are still lit, a dark reaper and seven dark horses with seven dark riders shall visit thy abode. They shall surround thy domicile and circle it seven times seven times. And the seven riders having circled thy dwelling seven times seven times, they shall proceed with the throwing of the eggs and the cream of shaving. And come morn there will be a great mess to be reckoned with. Verily.

So you'd better get those lanterns out.

You quickly discover something odd about these lanterns. When you blow out the first one, the lanterns on either side extinguish as well! But there's more- if you blow out a lantern adjacent to one that is extinguished, the extinguished one(s) will relight. It seems that blowing on any lantern will change the state of three- the one you blew on, and its two neighbors. Finally, you can blow on an extinguished lantern and it will relight, and its two neighbors will extinguish/ignite.

After a frustrating exercise of playing "Whack-A-Mole" with the lanterns, you find yourself back where you started, with all seven lit. Being the excellent puzzler you are, you sit down and examine the puzzle logically. But be quick, hoofsteps approach...

Who solved this puzzle: Dave Z. got one of many solutions. Fred got the general solution (who's Fred?)

You are trapped in narrow phone booth shaped room. Each of the four walls has a hole in the middle big enough for you to reach in. Reaching through the hole, you can feel a switch, mounted on a circular outer wall, that is in either an up or down position. You can only be freed when all four switches are in the same position. You can't see the switches, you can only feel their position by reaching through the holes. Since you have two hands, on one turn you can reach into two adjacent holes or two opposite holes to feel/flip switches. As soon as you remove a hand from any hole, the outer wall spins rapidly for a random number of quarter turns, changing the positions of the switches. What strategy should you use to free yourself in a finite, and preferably small, number of attempts?

Who solved this puzzle: Dan

Add punctuation so that the following sequence of words makes grammatical sense:

is is not not not is not is is is is not is not is it not

Who solved this puzzle: Stephanie, Tyson

A king has 1000 bottles of wine which he was planning to open for an important banquet in a month. His guards capture an assassin in his wine cellar trying to poison the wine. Interrogation reveals that he has only managed to poison one bottle, and the poison is so potent that it is fatal even when diluted 1000 times. However, the poison is slow acting and exhibits no symptoms until death occurs three weeks (plus or minus a few days) after ingesting even a miniscule amount.

As the ruler of a large kingdom, the king has many prisoners in his dungeons on which to test the wine. He wants to know which bottle is poisoned in time so that he can use the remaining 999 bottles at the banquet. What is the smallest number of prisoners needed to drink from the bottles to accomplish this?

Who solved this puzzle: Matt, Leyan

You have 12 coins, all of which are the same weight except for one. You don't know whether this odd coin is heavier or lighter than the others. Using a two-pan scale, determine using three weighings which is the odd coin and whether it is heavier or lighter.

Who solved this puzzle: Dan

A group of prisoners are trapped in a forcefield. These prisoners are perfectly brave, meaning that they would attempt an escape on any positive probability of success. The prisoners are monitored by a guard who has only one bullet in his gun, but who also has perfect marksmanship skills (he never misses). A maintenance technician needs to tune up the forcefield generator, and so for one second, the forcefield will be released. How can the guard still keep all the prisoners detained?

Who solved this puzzle: Tyson

Given the following information, what is 10+10?

1+1=0; 2+2=0; 3+3=0; 4+4=2; 5+5=0; 6+6=2; 7+7=0; 8+8=4; 9+9=2; 10+10=?

Note: Admittedly, this puzzle is quite unfair. Supposedly it was on an entrance exam to a Japanese kindergarten (hint).

Who solved this puzzle: Ken

Monty Hall has a new game show. There four boxes on the stage, each with different amount of money inside. Before the game starts, you don't know how much money is in each, or even what the range of values is. You do know that no two boxes have the same amount.

The host will let you open the boxes, one at a time, in whatever order you wish and examine the money inside. You may then choose (above the inane hooting of the audience) to take the visible money or open another box.

Once passed, you may not return to a previous box; e.g., if upon seeing the contents of the first box you decide to open the second box, you may not then opt for the first box. If you pass the first three boxes, the fourth box will automatically be your choice.

Now here's the catch: You only get to keep the money in the box you chose if it turns out to be the box with the most money.

Is there a strategy you can use to play this game, or is blind guessing as good a system as any?

Who solved this puzzle: Jed

You have two strings that, when lit at one end, burn down in exactly one hour. These strings are non-homogeneous and do not burn at a constant rate.

Measure 45 minutes using these two strings and a lighter.

Who solved this puzzle: David Y.

You have two metal rods identical in appearance and weight. One is a permanent magnet, the other is just iron - it is attracted by magnets but not a magnet itself. You also have the following items:

• a glass of water
• a 5-1/4" floppy disk
• a ball of string

With only these items to work with, what is the easiest way to determine which of the rods is the magnet?

Who solved this puzzle: Tyson

There is a prison guard in charge of a certain number of prisoners. Let's say 27, though the actual number may vary. The guard decides to have the prisoners play a game to win their freedom.

All the prisoners are locked in separate cells so that they cannot communicate with each other. Every once in a while, the guard will take a prisoner into a room with two switches labeled A and B. The prisoner is required to flip one of the switches every time he is brought to the room.

The guard chooses the prisoners randomly; he may skip over one, he may choose the same one three times in a row. Eventually, however, all of the prisoners will have visited the switch room at least once.

At any point, a prisoner brought into the switch room may declare "Everyone has been in this room." If he is correct, all the prisoners are free. If he is wrong, they are all executed.

Obviously, no one is allowed to make marks on the wall or leave messages of any kind in the switch room. All they can do is flip one of the switches.

As usual they are given time to deliberate a strategy before the game starts. What strategy will guarantee the prisoners' survival?

Who solved this puzzle: Dan, Leyan, Tyson

It is the year 2525, and man is still alive. Advancements in science have enabled humans to engage in dumber and dumber activities and survive. One example is the popular cannonball dive. Participants don a suit of steel electro-shielding armor, jump off a diving board, curl into a ball, and plunge to the bottom of a pool.

Anyway, as part of the end of year celebrations seven participants will be cannonballing in various situations.

A prize of $1,000,000 will be awarded to anyone who can successfully guess the order in which the cannonballers will reach the bottom of the pool. You'd like that $1,000,000.

First, the ground rules: Unless otherwise noted, all participants may be assumed to be 100kg perfect spheres with a diameter of half a meter (mankind is kind of out of shape). All dives start from one kilometer above the surface of the pool. All pools are 10 meters deep. If a diver is wearing a parachute, the chute detaches automatically on contact with the water.

1. Cannonballer #1 is doing a "Classic Earth" jump. No special conditions, and the air and water temperature is 50° F.
2. Cannonballer #2 will be doing the same, but he's wearing a parachute that deploys immediately.
3. Cannonballer #3 is doing a "Classic Moon" jump, starting 1km above the moon into a pool of 50° F water (moon pools have a thin force-field over them that doesn't affect the cannonballer, keeping water pressure equal to Earth sea level).
4. Cannonballer #4 is doing a "Classic Earth" in a more southern climate, with an air and water temperature of 75° F.
5. Cannonballer #5 is doing a moon jump with a parachute into a pool of 75° F water.
6. Cannonballer #6 is doing an Earth jump with a parachute with a 25° F air and water temperature.
7. Cannonballer #7 is doing a "Classic Earth" jump, but he has put on a little padding over the holidays, and has a diameter of one meter, and a mass of 500kg. Air and water temperature is 50° F.

Can you correctly guess the order in which divers will arrive at the bottom of their respective pools? If you can, that $1,000,000 is yours, because the rest of humanity is out of shape and bad at science.

Who solved this puzzle: Dave Z.

While travelling through the uncharted highlands, you are waylaid and captured by a group of the nomadic barbarians that live in the area. More likely than not, they intend to sacrifice you to their dark god. Or maybe feast upon your flesh. Or perhaps just kill you for fun. Whatever the case may be, their plans for you are not something you'd enjoy. Still, this is the sort of thing one has to expect when one is an Adventuring Puzzler.

But perhaps all is not lost... As is customary in these circumstances, you are offered freedom if you can beat their challenge. Deciding that you don't have much of a choice, you agree. You are blindfolded and led into a tent. At the beckoning of your captors, you kneel and touch the ground in front of you. On the packed earth floor of the tent are hundreds of small, smooth, circular discs. It is explained to you that each of the reindeer bone tokens in front of you has one side that is dyed red, and another that is dyed green. There are currently 129 tokens that have their red side facing up. The task you must complete is to divide the tokens into two groups, such that each group have the same amount of tokens showing red. They add that, should you decide to lift your blindfold, the man behind you will ensure that all of the tokens rather quickly turn a bright crimson.

So. Now what?

Who solved this puzzle: Eddie

Two mathematicians, Igor and Pavel, meet on the street. "How is your family," says Igor. "As I recall, you have three sons, but I don't remember their ages."

"That's easy," says Pavel. "The product of their ages is 36." Igor still looks confused, so Pavel points across the street. "See that building? The sum of their ages is the same as the number of windows facing us."

Igor thinks for a minute and says, "I still don't know their ages."

"I'm sorry," says Pavel, "I forgot to tell you: my oldest son has red hair."

"Now I know their ages," says Igor.

Do you?

Who solved this puzzle: Ken

An evil wizard has captured ten gnomes. Before he kills them, he decides to play a game, because... he's the kind of evil wizard that likes to give his victims a chance?

He lines the gnomes up in single file, so that each gnome can see all the other gnomes in front of him. (i.e. the second gnome can see the first gnome, the third can see the second and first, etc. The first gnome can't see anyone, and the tenth gnome can see the other nine.) He then reaches into a bag of an indeterminate number of black and white hats, and puts a hat on each gnome's head.

He then points a gun (staff, wand, whatever) to the head of the tenth gnome in line, and asks "What is the color of your hat?" If the gnome answers correctly, he lives and is set free. If not, he is killed. The wizard then moves up the line in this fashion. Before beginning the game, however, the wizard leaves the room, giving the gnomes five minutes to talk among themselves.

You are one of the gnomes. What strategy do you propose to minimize casualties? What is the expected number of freed gnomes using your strategy? Remember, on each gnome's turn he can only say "white" or "black." If he says anything else, the wizard will shoot him and all the remaining gnomes.

Who solved this puzzle: Angie

You're trapped in the Prison Tower of Contrivances. Fortunately, you've managed to pry open bars on the window to your cell. Unfortunately, the window is half way up the two hundred foot tall tower.

Conveniently, two fifty-foot ropes are tied to two iron rings in the ceiling of your fifty-foot tall cell. The iron rings (and consequently the ropes) are about a foot apart.

Your confinement has weakened your bones somewhat, so you cannot safely fall more than a few feet without risking serious injury. But your upper-body strength and climbing skills are top-notch.

Armed only with a pocket knife, how much of the rope can you liberate to aid in your escape?

Who solved this puzzle: David

There is a (dysfunctional) family - Mom, Dad, two girls and two boys - as well as a hunter and his dog who need to cross a river. There is a boat, but it's only big enough to hold two people (dog counts as a person).

• If the hunter is not on the same side as his dog, the dog will go crazy and attack everyone in sight.
• If Mom is gone, Dad will molest any little girl within reach.
• If Dad is gone, Mom will beat any little boy within reach.
• Only adults (Mom, Dad or hunter) can pilot the boat.

Get all 8 people across the river without anyone being beaten or otherwise maimed.

Who solved this puzzle: Dave Z.

You have ten jars of pills. Some jars are of contaminated pills, you don't know which ones. All you have are a digital scale and the knowledge that normal pills weigh 1 gram and contaminated pills weigh 1.1 grams. Determine with just one weighing which jars contain 1 gram pills and which jars contain 1.1 gram pills.

Who solved this puzzle: Dave Z.