We have provided the solutions as links at the end of each puzzle below, in case you want to have a go before checking your answers. Enjoy, and good luck!
What are some difficult logical puzzles that will sharpen your mind?
So, without further ado, here are some examples of difficult puzzles that will certainly hone your mental acuity. Trust us when we say this list is far from exhaustive and is in no particular order.
1. The riddle of the farmer
This first puzzle is a bit of a classic. Just suppose you had a farmer who needs to transport a fox, a chicken and some corn across a river.
He only has a small boat that can only carry him and one of them with him per crossing. The farmer needs to get all three items across the river in one piece.
But there is a problem. He can't leave the fox and chicken alone as the fox will eat the chicken. Likewise, he can't leave the chicken with the corn as the chicken will munch down on the corn.
So, can you figure out how the farmer could solve this problem?
Here is the solution if you want to test your workings.
2. The rope bridge at night problem
This next puzzle is another head-scratcher. Suppose there are four people trying to cross a rather dodgy rope bridge in the middle of the night.
Only two of them can cross it any one time and they only have a single flashlight between them. For this reason, one person of each pair must return to help the others get across.
But time is limited; they are being chased and need to get across within 17 minutes total. Sounds simple enough, except each person can only cross the bridge at a certain rate.
One person takes 1 minute to cross the bridge. The second takes 2 minutes, the third 5 and the last person 10 minutes.
Each pair can only cross as fast as the slowest member of the pair. How can they all cross the bridge in time?
Here is the solution if you want to see if you were right.
3. The burning rope timer problem
Let's suppose you needed to measure a time of exactly 45 minutes but only had a couple of old ropes coated in oil and a lighter. You know that each rope takes exactly 1 hour to burn all the way through.
But, the ropes do not burn at a uniform rate with spots that will burn a little faster than others. Whatever the case, and location of these slow and fast burn spots, the entire rope still burns up in exactly an hour.
You can burn the ropes at either end or at multiple points at the same time. How would you measure exactly three-quarters of an hour?
4. The heads or tails coin problem
Just suppose you are sat at a table strewn with hundreds or thousands of coins. You are blindfolded, so you cannot see the coins, and you don't know how many there are.
You are told that 20 of the coins are tails-side up while the rest are heads up. You can move the coins and flip them over as much as you want but you will never be able to see what you doing.
While you can feel the coins, you are unable to determine which side is which.
How then, would you separate the coins into two piles that have the same number of tails-side-up coins? Remember the number of coins per pile does not need to be the same.
Here is the solution, if you are curious.
5. The classic water jug problem
Here is another classic puzzle that will sharpen your mind. Let's suppose you need to measure out exactly 4 liters of water.
But, of course, you have a problem. You have two containers each 3 and 5 liters in volume respectively.
Each container has no other marking except for the fact that it only provides its known volume. Using a running tap to fill them how would you measure out exactly 4 liters?
Here is the solution, if you want to check your answer.
6. The riddle of the Gods
Touted as one of the hardest puzzles to solve ever, this one is certainly a fun challenge. Let's suppose we have three gods called, in no particular order, "True", "False" and "Random".
We don't know which is which, so, for now, we will label them A, B, and C respectively.
"True" always tells the truth. "False" always lies, and "Random" lies or tells the truth at random.
You are tasked with identifying which one is which by asking three yes-no questions. Also, you can only ask one god one question at any one time.
But it's a little more complex than that. Each god understands English but will only answer in their own language as "da" or "ja" -- but you can't understand if the answers are in the affirmative or not.
How would you solve this? Here is the solution.
7. Escape from the field
Let's suppose you have been placed in a circular field of unknown radius R. The field has a low fence around it.
Attached to the wire fence is a large, angry, sharp-fanged and hungry dog who loves nothing more than eating human flesh. You can run at a speed v, while the dog can run exactly 4-times as fast as you.
The dog, as it is attached to the fence can only travel around the perimeter. How would you escape from the field in one piece?
8. The apples and oranges puzzle
Here is another annoying problem that needs solving. Let's suppose you work in a fruit factory that boxes apples and oranges.
One day, the labeling machine goes haywire and incorrectly labels the crates of fruit. Your coworker decides to have a bit of fun and pulls out three crates of fruit and tells you that one has just oranges in it, the second just apples, and the third a mixture of the two.
One of the crates is labeled "O" for oranges, another "A" for apples and the third "A+O" for apples and oranges. But the labels lie.
You can pick one crate and your coworker will pull a single fruit from it to show you. You are only able to do this once.
How can you figure out which crate actually has only oranges, only apples and a mixture of the two? Here is the solution.
9. The mystery hat puzzle
And finally, let suppose you have a dark closet with five hats in it. There are three blue, and two red ones.
Three men go into the closet and each selects a hat at random in the dark and places it on their head. Once outside the closet, each man is unable to tell what color their own hat is.
The first man looks at the others and says "I cannot tell what color my hat is!". The second hears this, looks at the other two and declares "I cannot tell what color my hat is either!".
The third man, who is blind, confidently declares "I know exactly what color mine is!".
What color is his hat? Here is the solution.