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### Logical Puzzles

Top 20 Logical Puzzles

Logical Puzzles 1 : Famous Probability puzzle SHOOT
Difficulty ★★★★☆     Popularity ★★★★☆

Mr. Black, Mr. Gray, and Mr. White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr. Black, who hits his shot 1/3 of the time, gets to shoot first. Mr. Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr. White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr. Black, where should you shoot first for the highest chance of survival?

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Logical Puzzles 2 : Challenging Puzzle

Difficulty ★★★★★     Popularity ★★★★☆

Outside a room there are three light switches. One of switch is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.

You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)

Your task is to then determine which switch controls the bulb ??

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Logical Puzzles 3 : Challenging Mind puzzles
Difficulty ★★★★★     Popularity ★★★★☆

You are the ruler of a medieval empire and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You've got 1000 bottles of wine you were planning to open for the celebration, but you find out that one of them is poisoned.

The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison.

You have over a thousand slaves at your disposal and just under 24 hours to determine which single bottle is poisoned.

You have a handful of prisoners about to be executed, and it would mar your celebration to have anyone else killed.

What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?

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Logical Puzzles 4 : Hardest Balance Logic Puzzle
Difficulty ★★★★★     Popularity ★★★★★

You are given a set of scales and 12 marbles. The scales are of the old balance variety. That is, a small dish hangs from each end of a rod that is balanced in the middle. The device enables you to conclude either that the contents of the dishes weigh the same or that the dish that falls lower has heavier contents than the other.
The 12 marbles appear to be identical. In fact, 11 of them are identical, and one is of a different weight. Your task is to identify the unusual marble and discard it. You are allowed to use the scales three times if you wish, but no more.

Note that the unusual marble may be heavier or lighter than the others. You are asked to both identify it and determine whether it is heavy or light.

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Logical Puzzles 5 : Cricket Puzzle
Difficulty ★★★☆☆     Popularity ★★★★★

Two batsman each on 94 runs. Seven runs needed to win in last 3 balls. Both make 100*. How?

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Logical Puzzles 6 : Unlock The Distance Puzzle
Difficulty ★★★★★     Popularity ★★★★★

Distances from you to certain cities are written below.
BERLIN 200 miles
PARIS 300 miles
ROME 400 milesAMSTERDAM 300 miles
CARDIFF ??? miles
How far should it be to Cardiff ?

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Logical Puzzles 7 : Cross Bridge Puzzle
Difficulty ★★★★☆     Popularity ★★★★☆

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

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Logical Puzzles 8 : Gold Bar Fewest Cut Puzzle
Difficulty ★★★☆☆     Popularity ★★★★☆

A worker is to perform work for you for seven straight days. In return for his work, you will pay him 1/7th of a bar of gold per day. The worker requires a daily payment of 1/7th of the bar of gold. What and where are the fewest number of cuts to the bar of gold that will allow you to pay him 1/7th each day?

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Logical Puzzles 9 : NewsPaper Puzzle
Difficulty ★★★☆☆     Popularity ★★★★☆

A newspaper is supposed to have 60 pages
but pages 24 and 41 are missing.
Which other pages won't be there?

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Logical Puzzles 10 : Unsolvable Riddle
Difficulty ★★★☆☆     Popularity ★★★★☆

In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.
How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly

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Logical Puzzles 11 : Alexander Puzzle
Difficulty ★★★★☆     Popularity ★★★★★

Alexander is stranded on an island covered in forest.

One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.

There are cliffs around the island, so he cannot jump off.

How can the Alexander survive the fire? (There are no buckets or any other means to put out the fire)

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Logical Puzzles 12 : Cipher Age Puzzle
Difficulty ★★★★★     Popularity ★★★★☆

If Susan is 10, Arabella is 20, and Jim and Neal are both 5, but Richard is 10, how much is Jennifer by the same system?

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Logical Puzzles 13 : February Maths Puzzle
Difficulty ★★★★☆     Popularity ★★★★★

Using eight eights and addition only, can you make 1000?

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Logical Puzzles 14 : Famous Elevator Puzzle
Difficulty ★★★★☆     Popularity ★★★★☆

A man who lives on the tenth floor takes the elevator down to the first floor every morning and goes to work. In the evening, when he comes back; on a rainy day, or if there are other people in the elevator, he goes to his floor directly. Otherwise, he goes to the seventh floor and walks up three flights of stairs to his apartment.
Can you explain why?

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Logical Puzzles 15 : Water Jugs Problem
Difficulty ★★☆☆☆     Popularity ★★★★☆

Six jugs are in a row.
The first three are filled with coke, and the last three are empty.
By moving only one glass, can you arrange them so that the full and the empty glasses alternate?

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Logical Puzzles 16 : Aeroplane Hijack puzzle
Difficulty ★★★★☆     Popularity ★★★★★

A man hijacks an aeroplane transporting both passengers(8 of them) and valuable cargo. After taking the cargo, the man demands nine parachutes, puts one of them on, and jumps, leaving the other eight behind. Why did he want eight?

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Logical Puzzles 17 : Secret Code puzzle
Difficulty ★★★☆☆     Popularity ★★★★☆

A man wanted to get into his work building, but he had forgotten his code. However, he did remember five clues. These are what those clues were:

The fifth number plus the third number equals fourteen.

The fourth number is one more than the second number.

The first number is one less than twice the second number.

The second number plus the third number equals ten.

The sum of all five numbers is 30.

What were the five numbers and in what order?

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Logical Puzzles 18 : Challenging Logic Puzzle
Difficulty ★★★☆☆     Popularity ★★★★☆

In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?

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Logical Puzzles 19 : Popular Age Problem
Difficulty ★★★★☆     Popularity ★★★★★

Two old friends, Jack and Bill, meet after a long time.

Three kids
Jack: Hey, how are you man?
Bill: Not bad, got married and I have three kids now.
Jack: That’s awesome. How old are they?
Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Jack: Cool… But I still don’t know.
Bill: My eldest kid just started taking piano lessons.
Jack: Oh now I get it.

How old are Bill’s kids?

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Logical Puzzles 20 : Water Pails Puzzle
Difficulty ★★★☆☆     Popularity ★★★★☆

If you had an infinite supply of water and a 5 quart and 3 quart pails, how would you measure exactly 4 quarts? and What is the least number of steps you need?

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Last Updated:2012-04-21

1. Good Collection

2. thats true...put on some more questions

3. I think I'll try some of these on my family! Great collection!

4. I. The story (premises)

There once was a town devastated by the conflict between justice, love and logic. In this town lived three single lovely young ladies, Aida, Beatrice and Camille, and each owned one and only one of three jewels: a diamond, an emerald, or a ruby. It was not known exactly who owned what. One night three famously dangerous thieves, Melvin, Norman and Oscar, each stole one and only one of the three jewels from its owner. No one else was involved. As fate would have it, each of the young ladies was in love with one of the three thieves and this was well known in the town, but since at least one of the thieves was married the three young ladies never revealed their specific love interest. When the young ladies reported the robberies they also confessed to police that they had each caught a glimpse of their thief and realized they were each being robbed by the one they loved. Heartbroken and torn between love and justice, the three ladies locked themselves in their rooms and refused to further cooperate with police. Although the three ladies never revealed the identity of their love interest, it transpired that Beatrice did not love Melvin. Good police work uncovered a series of pieces of information but investigators were still baffled by this predicament: the witnesses would not cooperate, there was no forensics available, and it appeared that only little circumstantial evidence existed. Fortunately, a student of logic was vacationing in town and offered to help in the investigation. Police shared the rest of the information they had with the student, as follows:
- The one who stole the diamond was a bachelor and was also the most dangerous of the three thieves. (*)
- Aida was less pretty than the young lady who owned the emerald.
- Melvin's brother-in-law Norman, who stole from the prettiest of the three young ladies, was less dangerous than the one who stole the emerald.
- The thief who stole from Aida was an only child.
Our logical hero reasoned correctly that the above information was sufficient to solve the crime conclusively, and did so to police's astonishment and logic's glory. The thieves were arrested and jailed, served time but were released early for good behavior. Later on news traveled that one of the young ladies who was robbed by a bachelor forgave him in the end, they married and lived happily ever after. The matrimonial fate of the other people involved in this drama is still unknown.

5. II. The assignment

1. (10 points) List and number every relevant premise. Have lots of very short, numbered premises, otherwise it is very difficult to keep track of the info and relate the steps in the proof to specific premises)

2. (25 points) Provide a detailed informal proof; that is, a proof in English language not symbols:
a. continue to number each individual deductive step in the proof (each logical derivation)
b. explain each deductive step (derivation) thoroughly, by reference to specific premises or previous deductive steps
- a proof ends with the first invalid step ( the logical deductive chain which preserves the truth from premises through deductive steps is broken) OR when the final conclusion of the "project" is reached deductively (that is, all steps are valid inferential/deductive steps - ONLY documented/proven rules/theorems of natural deduction guarantee validity of steps/inferences)

3, (10 points) While you will not be able to do so for all deductive steps, identify, whenever you can, logical rules/theorems from natural deduction (patterns of correct reasoning) - MP, MT, HS, DS, DeM, etc - AND the premises or previous deductive steps on which they apply ; identify at least five different rules/theorems

3. (5 point) State clearly the final conclusion that follows validly from your proof (each of the following must have been proven already at some step in your proof): Who stole what from whom? Who is prettiest, less pretty least pretty? Who is most dangerous, less dangerous least dangerous? Who married whom? Can we identify any bachelor? etc.

NOTES:
* the above argument requires predicate logic for translation, hence more complex translations and additional rules of natural deduction (as they apply to predicate logic); however, many patterns of reasoning learned in class (theorem of logic applicable to sentential/propositional logic) can be identified AND related to premises or previous steps in the proof, so long as you number them. In other words, do as you would when constructing a deductive proof in symbolic logic, EXCEPT that you do NOT symbolize; this is what an informal proof is - a proof given in a natural language (English, in our case) rather than formal languages (such symbolic logic or math); number everything, justify whatever you can

* AGAIN: do NOT pack too much info in any of the premises and in any of the deductive steps; it will be very hard to reference steps, hard to solve the problem and hard to identify patterns of reasoning (since they will be compounded beyond recognition); better lots of simple premises and steps than few complex premises and convoluted explanations. For ex., the info/data in the line/statement market by (*) can be written into 2 different premises: (n) The diamond thief is a bachelor. (n+1) The diamond thief is the most dangerous. You may use present tense when writing premises and steps since logic per se is indifferent to classical conception of time ('time' is a non-logical concept).

1. Why is the last statement there? Aida's thief being an only child tells you nothing since no other familial relationships are given (having a brother-in-law does not prevent you being an only child)

6. Aida ... Diamond ... Oscar
Beatrice ... Ruby ... Norman
Camille ... Emerald ... Melvin

7. Two mathematicians meet on the street in New York City. They haven't seen each other in ten years. One says to the other "what's new since I saw you last?" "Well" he says, "since you saw me last, I got married and now have three sons". "How old are the boys?" asks the first guy.

Here is the second guy's response:

1. "The product of their ages is thirty-six."

2. "The sum of their ages is equal to the number of windows on the second floor of the building across the street."