Engaging Logic Puzzles and Riddles
Solve challenging logic puzzles and riddles involving switches, bridges, marbles, money transactions, and evaluating statements for truth or falsity. Test your problem-solving skills with thought-provoking scenarios and brainteasers.
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Logic Puzzles CS 1511
Three Switches, One Lightbulb There are 3 switches outside of a room, all in the 'off' setting. One of them controls a lightbulb inside the room, the other two do nothing. You cannot see into the room, and once you open the door to the room, you cannot flip any of the switches any more. Before going into the room, how would you flip the switches in order to be able to tell which switch controls the light bulb?
Four men crossing a bridge Four people come to an old bridge in the middle of the night. The bridge is rickety and can only support 2 people at a time. The people have one flashlight, which needs to be held by any group crossing the bridge because of how dark it is. Each person can cross the bridge at a different rate: one person takes 1 minute, one person takes 2 minutes, one takes 5 minutes, and the one person takes 10 minutes. If two people are crossing the bridge together, it will take both of them the time that it takes the slower person to cross. Unfortunately, there are only 17 minutes worth of batteries left in the flashlight. How can the four travelers cross the bridge before time runs out?
12 Marbles You have twelve marbles, identical in every way except that one of them weighs slightly less or more than the balls. You have a balance scale, and are allowed to do 3 weighings to determine which marble has the different weight, and whether the marble weighs more or less than the other marbles. What process would you use to weigh the marbles in order to figure out which marble weighs a different amount, and whether it weighs more or less than the other marble?
Every Dollar Counts A woman walked up to a man behind a counter and handed him a book. He looked at it and said, That will be four dollars. She paid the man and then walked out without the book. He saw her leave without it but did not call her back. Why?
Evaluate each of the following statements as to its truth or falsity: Exactly one statement on this list is false. Exactly two statements on this list are false. Exactly three statements on this list are false. Exactly four statements on this list are false. Exactly five statements on this list are false. Exactly six statements on this list are false. Exactly seven statements on this list are false. Exactly eight statements on this list are false. Exactly nine statements on this list are false. Exactly ten statements on this list are false.
ABCD DCBA + * * * * 12300 A, B, C, and D are consecutive digits in increasing order. The * each represent the A, B, C and D in an unknown order. Find ABCD and the order for the third line.
Push that Car A man pushed his car. He stopped when he reached a hotel at which point he knew he was bankrupt. Why?
Missing Dollar Three people check into a hotel room. The bill is $30 so they each pay $10. After they go to the room, the hotel's cashier realizes that the bill should have only been $25. So he gives $5 to the bellhop and tells him to return the money to the guests. The bellhop notices that $5 can't be split evenly between the three guests, so he keeps $2 for himself and then gives the other $3 to the guests. Now the guests, with their dollars back, have each paid $9 for a total of $27. And the bellhop has pocketed $2. So there is $27 + $2 = $29 accounted for. But the guests originally paid $30. What happened to the other dollar?
Wires, Batteries and Lightbulbs You are standing in a house in the middle of the countryside. There is a small hole in one of the interior walls of the house, through which 100 identical wires are protruding. From this hole, the wires run underground all the way to a small shed exactly 1 mile away from the house, and are protruding from one of the shed's walls so that they are accessible from inside the shed. The ends of the wires coming out of the house wall each have a small tag on them, labeled with each number from 1 to 100 (so one of the wires is labeled "1", one is labeled "2", and so on, all the way through "100"). Your task is to label the ends of the wires protruding from the shed wall with the same number as the other end of the wire from the house (so, for example, the wire with its end labeled "47" in the house should have its other end in the shed labeled "47" as well). To help you label the ends of the wires in the shed, there are an unlimited supply of batteries in the house, and a single lightbulb in the shed. The way it works is that in the house, you can take any two wires and attach them to a single battery. If you then go to the shed and touch those two wires to the lightbulb, it will light up. The lightbulb will only light up if you touch it to two wires that are attached to the same battery. You can use as many of the batteries as you want, but you cannot attach any given wire to more than one battery at a time. Also, you cannot attach more than two wires to a given battery at one time. (Basically, each battery you use will have exactly two wires attached to it). Note that you don't have to attach all of the wires to batteries if you don't want to. Your goal, starting in the house, is to travel as little distance as possible in order to label all of the wires in the shed. You tell a few friends about the task at hand. "That will require you to travel 15 miles!" of of them exclaims. "Pish posh," yells another. "You'll only have to travel 5 miles!" "That's nonsense," a third replies. "You can do it in 3 miles!" Which of your friends is correct? And what strategy would you use to travel that number of miles to label all of the wires in the shed?
Getting Past the Bridge Guard A guard is stationed at the entrance to a bridge. He is tasked to shoot anyone who tries to cross to the other side of the bridge, and to turn away anyone who comes in from the opposite side of the bridge. You are on his side of the bridge and want to escape to the other side. Because the bridge is old and rickety, anyone who tries to cross it does so at a constant speed, and it always takes exactly 10 minutes to cross. The guard comes out of his post every 6 minutes and looks down the bridge for any people trying to leave, and at all other times he sits in his post and snoozes. You know you can sneak past him when he's sleeping, but the problem is that you won't be able to make it all the way to the other side of the bridge before he sees you (since he comes out every 6 minutes, but it takes 10 minutes to cross). One day a brilliant idea comes to you, and soon you've successfully crossed to the other side of the bridge without being shot. How did you do it?
Ten Pirates and their Gold Ten pirates find a buried treasure of 100 pieces of gold. The pirates have a strict ranking in their group: Pirate 1 is the lead pirate, Pirate 2 is second-in-command, Pirate 3 is the third most powerful pirate, and so on. Based on this ranking, the pirates decide on a system to determine how to split up the 100 pieces of gold. The lead pirate (Pirate 1) will propose a way to divy it up. Then all the pirates (including the lead pirate) will vote on that proposal. If 50% or more of the pirates agree on the system, then that is how the gold will be divied up. However, if less than 50% of the pirates vote for the proposal, then the lead pirate will be be killed. The next-most powerful pirate will then become the lead pirate, and they'll restart the process (Pirate 2 will suggest a way to divy up the gold and it will be voted on by the rest of the pirates). This will keep going on until finally a proposal is agreed upon. All of the pirates are very smart and very greedy. Each pirate will vote against a proposal if they know that they would end up with more gold if that proposal were to fail. A pirate also will never vote for a proposal that gives him 0 pieces of gold. You are Pirate 1. You must come up with a proposal that will give you as much gold as possible, without getting yourself killed. Keep in mind that the rest of the pirates all know that if your proposal fails, then Pirate 2 will succeed at coming up with a plan that benefits him the most while not getting him killed. What's your proposal?
A Liar AND a Truth Teller You are walking down a path when you come to two doors. Opening one of the doors will lead you to a life of prosperity and happiness, while opening the other door will lead to a life of misery and sorrow. You don't know which door leads to which life. In front of the doors are two twin brothers who know which door leads where. One of the brothers always lies, and the other always tells the truth. You don't know which brother is the liar and which is the truth-teller. You are allowed to ask one single question to one of the brothers (not both) to figure out which door to open. What question should you ask?
A Liar OR a Truth Teller You're walking down a path and come to two doors. One of the doors leads to a life of prosperity and happiness, and the other door leads to a life of misery and sorrow. You don't know which door is which. In front of the door is ONE man. You know that this man either always lies, or always tells the truth, but you don't know which. The man knows which door is which. You are allowed to ask the man ONE yes-or-no question to figure out which door to go through. To make things more difficult, the man is very self- centered, so you are only allowed to ask him a question about what he thinks or knows; your question cannot involve what any other person or object (real or hypothetical) might say. What question should you ask to ensure you go through the good door?
Number of Handshakes At a dinner party, many of the guests exchange greetings by shaking hands with each other while they wait for the host to finish cooking. After all this handshaking, the host, who didn't take part in or see any of the handshaking, gets everybody's attention and says: "I know for a fact that at least two people at this party shook the same number of other people's hands." How could the host know this? Note that nobody shakes his or her own hand.
9 Dots, 4 Lines Look at the 9 dots in this image. Can you draw 4 straight lines, without picking up your pen, that go through all 9 dots?
The Circular Lake A swan sits at the center of a perfectly circular lake. At an edge of the lake stands a ravenous monster waiting to devour the swan. The monster can not enter the water, but it will run around the circumference of the lake to try to catch the swan as soon as it reaches the shore. The monster moves at 4 times the speed of the swan, and it will always move in the direction along the shore that brings it closer to the swan the quickest. Both the swan and the the monster can change directions in an instant. The swan knows that if it can reach the lake's shore without the monster right on top of it, it can instantly escape into the surrounding forest. How can the swan successfully escape?
Dividing the Cake Two twin brothers share the same birthday. Their father gets them a perfectly rectangular birthday cake, and the brothers decide to split the cake into two equal halves so that they each get to eat the same amount of cake. However, before they can divide it, their father cuts out a perfectly circular (or more precisely, cylindrical) piece from the cake and eats it. How can the brothers divide the rest of the cake with exactly one straight-line slice? The slice must be a vertical slice straight down through the cake, and is allowed to pass through the removed circle if needed. The brothers have a ruler and a compass to help them choose where to slice the cake.
Magic Square How can you place the numbers 1 through 9 in a 3x3 grid such that every row, column, and the two diagonals all add up to 15?
Open and Closed Lockers There are 1 million closed school lockers in a row, labeled 1 through 1,000,000. You first go through and flip every locker open. Then you go through and flip every other locker (locker 2, 4, 6, etc...). When you're done, all the even-numbered lockers are closed. You then go through and flip every third locker (3, 6, 9, etc...). "Flipping" mean you open it if it's closed, and close it if it's open. For example, as you go through this time, you close locker 3 (because it was still open after the previous run through), but you open locker 6, since you had closed it in the previous run through. Then you go through and flip every fourth locker (4, 8, 12, etc...), then every fifth locker (5, 10, 15, etc...), then every sixth locker (6, 12, 18, etc...) and so on. At the end, you're going through and flipping every 999,998th locker (which is just locker 999,998), then every 999,999th locker (which is just locker 999,999), and finally, every 1,000,000th locker (which is just locker 1,000,000). At the end of this, is locker 1,000,000 open or closed?
Going to St. Ives As I was going to St. Ives I met a man with seven wives The seven wives had seven sacks The seven sacks had seven cats The seven cats had seven kits Kits, cats, sacks and wives How many were going to St. Ives?
Truck Crossing a Bridge A truck stops at a weigh station at the entrance to a bridge and is shown to weigh exactly 2000 lbs. The operator of the weigh station notes that the bridge can hold exactly 2000 lbs, but would crumble if it were subjected to even a fraction of an ounce more. But he says that no other vehicles ever cross over the bridge and so it's fine if the truck crosses. The truck continues on. Once the truck is halfway across the 10-mile long bridge, a sparrow flies over to the truck and lands on the hood. The truck driver sees the bird lands and his heart drops as he realizes the bridge is about to collapse, but even after the bird lands, the bridge doesn't crumble. How was the bridge able to hold up despite the extra weight from the bird?
The Millers Daughter A poor miller living with his daughter comes onto hard times and is not able to pay his rent. His evil landlord threatens to evict them unless the daughter marries him. The daughter, not wanting to marry the landlord but fearing that her father won't be able to take being evicted, suggests the following proposition to the landlord. He will put two stones, one white and one black, into a bag in front of the rest of the townspeople. She will pick one stone out of the bag. If she picks the white stone, the landlord will forgive their debt and let them stay, but if she picks the black stone, she will marry the landlord, and her father will be evicted anyway. The landlord agrees to the proposal. Everybody meets in the center of the town. The landlord picks up two stones to put in the bag, but the daughter notices that he secretly picked two black stones. She is about to reveal his deception but realizes that this would embarrass him in front of the townspeople, and he would evict them. She quickly comes up with another plan. What can she do that will allow the landlord save face, while also ensuring that she and her father can stay and that she won't have to marry the landlord?
