# Logic Puzzles

A collection of logic puzzles for fun and pleasure! Tease your brain with these logic puzzles,
then click to show or hide the answer.
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Also visit our Math Trivia page for more arithmetic riddles, geometry riddles, statistics riddles, calculus riddles etc.

## The Man with the Hat

There are four men standing in front of a firing squad. Two of them (no. 1 & 3) wear a black hat and two of them (no. 2 & 4) wear a white hat. They are all facing in the same direction and there is a brick wall between 3 and 4. So no. 1 can see no. 2 and 3, no. 2 can only see no. 3, no. 3 can only see the wall and no. 4 doesn’t see anything.

The commander of the firing squad is willing to let the men go if one of them can say what color hat he is wearing. They all know that there are two white and two black hats in total. The men are not allowed to talk, save "I'm wearing a white/black hat". If one of the men knows which hat he is wearing he must say it and set them all free.

Which man knows 100% sure what color hat he's wearing?

No. 2. No. 1 sees a white and black hat. From this he cannot tell what hat he is wearing, so he keeps quiet (if he saw two white hats, for example, his would be black). No. 2 doesn’t hear No. 1 say anything, so he knows that No. 1 sees a white and black hat. Since he himself can see No. 3 wearing a black hat, he knows that his is white.
## Burning Rope

You have two ropes. Each one takes exactly an hour to burn, but they are not the same length or width, and their width is not uniform (so burning half the length of a rope does not mean half an hour has elapsed).

By burning the ropes, how do you measure exactly 45 minutes? (Hint: you can burn the ropes however you like.)

Light both ends of one rope and one end of the second rope. When the first rope burns out, half an hour will have elapsed (since it was burning twice as fast), and so the second rope has half an hour left to burn. Now light the other end of the second rope, halving this time to 15 minutes, thereby measuring the exact 45 minutes.
## The fox, the rabbit and the carrots

A boatman has been hired to take a fox, a rabbit, and a bag of carrots across the river. However, the boat only has room for one passenger. The fox will eat the rabbit if left alone on one side, and the rabbit will do the same with the carrots.

How do you get all three across without any of them being eaten?

Take the rabbit across first. Then take the fox across, and take the rabbit back. Take the carrots across to where the fox is. Then come back for the rabbit.
## A Good Bargain

A person building a house forgets an important part of his project. He then calls a hardware store to order the missing item. He finds that 1 will cost him $2, and 2 will cost him $2, but 12 will cost him $4 and 144 will cost him $6.

What was the item he needed?

An address number. Assuming that each digit costs $2, 1 and 2 would cost the same, but 12, having two digits, would cost $4, and likewise 144 would cost $6. (If it were anything else, the store would go out of business.)
## The Fruit Stand

At my favorite fruit stand in Puzzleland, an orange costs 18 cents, a pineapple costs 27 cents, and a grape costs 15 cents. Using the same logic, how much does a mango cost?
15 cents. The “logic” is 3 cents per letter (that’s the way stores in Puzzleland operate).

## Strange Tastes

Margot likes knights but not battlers; she likes writing but not typing; she likes to listen but not to sing. Does she like an unknown or a famous author?
Margot likes unknown writers. She only likes words with a silent letter.
## Doctor Livingstump

Doctor Livingstump was very proud indeed of his big-game hunting exploits. He had published several monographs about his life among the pygmies, his exploits during the Boer War, and his single-handed capture of an entire tribe of blow-dart hunting natives. He had even brought home a poisoned blow-dart as evidence, and he told friends he was going to use it to start a museum collection. This particular day, dressed in his usual explorer clothes, he was sitting comfortably in an armchair, being interviewed by the Explorer’s Club membership committee.
“As I said,” he continued, “my reputation had spread before me, and these poor chappies sent word via the drums that they needed me desperately. Two of their babies, one of their women, and two warriors had been snatched right out of the village by this man-eating tiger. They were desperately short of warriors, the drums said.” He nodded for emphasis. “So I assembled my bearers, my full set of guns, and set off for the village. It was at the headwaters of the Nile, in territory so remote no white man had been before. I learned all I could from my bearers about the habits of nocturnal hunters like that tiger-” Here, the four committee members unceremoniously cut him off by seizing one of the doctor’s limbs each and hurling him down the steps into the street. Why?
There are no tigers in the headwaters of the Nile, or anywhere in Africa for that matter. The good doctor was lying.

## The Blue House

You are strolling along in the countryside one day, and you reach a hill. On top of the hill is a large single-storey house. It looked like any ordinary house, except that it was completely blue. You decide to take a closer look, and find that it is, indeed, completely blue – the drainpipes, the doorframe, the windowsill – everything is blue. You think this is rather strange, and you decide to see what the house is like inside. You open the door (which happened to be unlocked) and look around. Everything inside is blue as well, right down to the furniture and the tea set on the (blue) dining table. What color are the stairs?
There are no stairs. It is a single-storey house.
## Safe Travels

I agreed to meet my brother for lunch in New Haven. He was traveling from Boston, while I was traveling from New York. When we met at New Haven, which of us was further from Boston?
We are both already in New Haven, hence the same distance from Boston.
## The Test Pilot

I met my friend the test pilot, who had just received a lot of publicity for a record round-the-world flight by hot-air balloon. With my friend was a little girl of about two. “What’s her name?” I asked my friend, whom I hadn’t seen in 5 or 6 years and had married in that time. “Same as her mother,” was the reply. “Hello, Susan,” I said to the little girl. How did I know if I had never seen the wedding announcement?
My friend the test pilot is named Susan. Shame on you for thinking only guys could be pilots.

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