When you have some free time, it’s hard to resist watching some television or spending time on social media. Basically, anything to avoid using your brain! There’s no shame in relaxing with something undemanding every once in a while.
That being said, it’s nice to challenge yourself every once in a while, too. Just as you should exercise your body to stay strong and healthy, you need to treat your brain like a muscle that requires as much training as anything else!
That’s where these challenging logic puzzles come into play. Take as much time as you need on each of them to give your brain a workout!
1. Four criminals, all facing the same direction, are on a few steps in a line. The fourth man is separated from the other three by a wall. Because of this, the first man can see the second and third man in front of him, the second man can only see the third man, and the third and fourth men can see no one.
Each criminal is wearing a hat, but they don’t know which color their own hats are. They are told, however, that there are two black hats and two white hats among them. They are instructed to shout out their hat colors once they’ve figured out which color it is.
They also have been given rules: They may not move or turn around at all, they may not speak a word to each other, and they must not take their hats off at any point. Assuming they all follow the rules, which one of them is the first to speak up, and why?
Answer: After taking some time to think about it, Man 2 is the first one who yells out the color of his hat before anyone else. Did you guess correctly? There’s a rhyme and a reason to why this is the answer, of course. So, why is it that he’s the one who speaks first? That’s because the third and fourth men can’t see anyone else, while the first man knows his hat is either black or white because he sees both in front of him.
Man 2 only saw a black hat in front of him. Since he knew that the man behind him—Man 1—could see two hats, that man should’ve shouted out his own hat’s color if Man 2 was also wearing black. (Two black hats would mean that Man 1 was wearing a white one.) But since Man 1 didn’t say anything, the second man was able to deduce that he was wearing a white hat. Hats off to you if you answered this correctly!
2. Prince Charming was searching everywhere for his true love. Just as summer was coming to an end, he encountered an old witch’s shack. Exhausted, the prince asked if she could take him in for just one night. The witch agreed, and was quite hospitable as she gave him a bed, water, and food.
Before the prince left the next day, the witch gave him a gift. “One day,” she began, “you will find your passage blocked by a wide river without a bridge to pass over it. You will have no choice but to swim to the other side. Luckily, you’ll never be let down by this magical tunic!”
Prince Charming thanked her and resumed his quest. A hundred days and nights passed before he found the river that the old witch had spoken of. As it turned out, he was able to cross the bridge without the magic tunic! Can you explain why?
Answer: it was the end of summer—September—when Prince Charming visited the witch, and 100 days went by before he got to the river. It was already the winter by that point, so he was able to walk across the frozen river to the opposite bank with ease!
Kumar Vivek / Wikimedia Commons
3. One dark night, there was a hit-and-run in which a car struck a pedestrian in a narrow side road. A police officer at the scene of the crime said that the car was moving very quickly. Six bystanders saw the accident as it happened, but their reports were contradictory.
The first witness said that he saw a man driving a blue car. The second witness said that the headlights were off as the car moved at a high speed. The third witness said that the car wasn’t actually going very fast, and she noticed license plates. The fourth witness said it was a Toyota with its headlights switched off. The fifth witness said that a woman drove the car, and that it didn’t have license plates. The sixth witness said that it was a gray Ford.
Luckily, the driver was caught along with the vehicle, but it was revealed that only one of the six eyewitnesses gave a completely correct report. Everyone else provided one piece of information that was true, and another that was false. With that in mind, consider the following questions:
What was the brand of the car? What color was it? Was it going quickly or slowly? Were there license plates? Were the headlights on or off? And was the driver a woman or a man?
Answer: the vehicle was a blue Ford with license plates that was driven very fast by a woman with the headlights turned off. Start with the information that the policeman provided—that the car was moving very fast. Since each witness (except for one) provided a false statement and a true one, we can use the process of elimination to determine the correct facts.
For example, the witness who correctly claimed the car was moving at high speeds—the policeman could back her up on that fact—would also have been correct about her other statement: the car’s headlights were off. That means the other witness who claimed the headlights were off was correct on that fact, but wrong on their second statement (that it was a Toyota). From there, you can keep eliminating details until you find the accurate details!
4. A driver was changing a tire when all four of his lug nuts fell into a sewer grate. It was practically impossible to get them back, and the man feared he’d have to spend a great deal of time waiting at the side of the road. He had no reason to worry, though: a child riding a bike at that moment provided a solution, and the man was able to put in a new tire and safely drive the car to the nearest gas station. Can you guess what the kid told him?
Kurt Nordstrom / Wikimedia Commons
Answer: the boy on the bicycle told the motorist to borrow one lug nut from each of the other tires on the car, and use them to tighten the new tire on the vehicle as best as he could. That way, each tire had three lug nuts.
5. A farmer has three big hutches in a row in his backyard where he keeps his rabbits. One hutch is painted red, another is yellow, and the third one is green. There were twice as many rabbits in the green hutch as there were in the yellow hutch, but that changed recently.
One day, the farmer decided to take five rabbits from the left-hand hutch and donate them to a local school. In addition, he took half of the rabbits that remained in the left hutch and placed them in the red hutch. Which color is the left hutch?
Answer: The left-side hutch is yellow! Think about it this way: we knew from the start that there were twice as many rabbits in the green hutch as there were in the yellow one, right? That means there was an even number of rabbits in the green hutch.
When the farmer moved five rabbits out of the hutch on the left, the number of rabbits that were still there became even (which we know because it had to be divisible by two). As such, the left hutch had an odd number of rabbits before some of them were removed. Thus, the left hutch couldn’t have been green, nor could it have been red given the information that’s been provided!
Wow, all of those logic puzzles were sure to give anyone’s brain a nice workout! Wouldn’t you love to find out how you stack up to everyone else?
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