# Questions tagged [logical-deduction]

A puzzle that requires formal logical deduction to arrive at the solution. This suggests more than merely reasoning through clues to find an answer (you might want [situation] for that).

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### Can you find me

if you divide my first digit by my last digit then you can find me for ever If you multiply me by any number equal to or less than my length (but greater than zero) and I will only cycle. If you ...
4k views

### Which sister to marry? [duplicate]

Tomorrow you will meet three sisters, and be married to one of them. The eldest always tells the truth, the youngest always lies. The middle sister lies or tells the truth at random. Knowing this, you ...
5k views

### Unhelpful House Number Reminders

(Got this from my facebook news feed.) A friend of mine, upset after the earlier housing number conundrum, decided to make me guess his. He said: If my house number is a multiple of 3, it's from ...
39k views

### Mysterious Murder Mystery [closed]

Last year, December 21, 2013, you were awarded the "#1 Detective in the World" for solving more than 50 murders. Your boss gave you a promotion, contingent upon your moving to Chicago. You agreed and ...
46k views

### How many balls can fit in the box? [closed]

I think the answer isn't as simple as the question. So, I need your help. :) Assumed I have a box, sized 100cm X 100cm X 100cm (width X length X height). How many balls can fit in that box (the ball ...
296 views

### How many stamps?

Cade has six red stamps and three blue ones. In his collection, seven stamps are from Argentina and six stamps are from Sweden. One stamp is purple and it is not from Argentina or Sweden. Two of his ...
586 views

### A Strange Sequence [duplicate]

This puzzle is taken from a French bestseller I read years ago. The solution is much simpler than it looks... Find the following line in this sequence : ...
1k views

### Can you find my friends' birthday

A friend of mine has an interesting birthday. If you shorten the date month and year and use UK date format, it reads the year in full, his birthday falls on a Friday. When he is as old as the year ...
2k views

### Banana? Or Orange?

25 kids were in a class, they were all trading lunches. Each kid traded their lunch 5 times. At first 12 kids had bananas. At first 13 kids had oranges 16 kids like bananas 14 kids like oranges In ...
478 views

### From Knights to Kings on a rectangle

In From knights to kings, we were asked On a NxN chess board $N^2$ knights are placed (one per cell). Each pair of knights, who control each other (i.e. one move away from each other) are friends. ...
1k views

### Is it Always Possible? Colour Flipping

There's a 4x4 square, where switches are either red or green. When you flip a switch, all the buttons on that row and column will change color. Is every starting position possible to complete? If not ...
1k views

### 16 Buttons, Turn them all Red or Green?

There's 16 buttons arranged in a 4 by 4 square. They are coloured either red, or green. They appear like this (red being 1, green being 0) 1010 0101 1100 0011 Each press will switch all the ...
2k views

### A puzzle of trust and lies, allies and spies

Here is a puzzle involving distrust and asymmetric knowledge. (It was inspired by, but not exactly following, the board game The Resistance: Avalon.) There are ten resistance fighters trying to ...
840 views

### Way to memorize shape - number combinations in short time [closed]

A visual memory test application gives some time to memorize images - numbers combinations, after that it shows a random shape and asks what the number is. What is to trick for such an application if ...
4k views

### What is the result of the equation?

Considering from $a$ until $z$: $x = (x -a) \cdot (x -b) \cdot (x -c) \dots (x - z)$ What I want is the value of $x$ It´s something easy, but I could not find this here and I think it´s a nice ...
1k views

### How to divide the vibranium bar into 3 pieces? [duplicate]

You have a bar of vibranium and the Cap needs to use it (not used up or consumed) every day but he only needs 1/7th on the first day, 2/7th on the second day and so on for 7 days. You have a ...
3k views

### Everybody loves my baby

James is in a room with three other people: Alice, Bob, and Spencer. Alice and Bob are married to each other, but James knows that Bob is secretly having an affair with Spencer. James is going to ...
3k views

### Water glass and wine glass [duplicate]

You have two equal glasses. One is filled with water. One is filled with wine. Now you take a spoonful from the water glass, put it into the wine glass, and stir until it is well mixed. Then you take ...
6k views

### Poisoned Bottle of Wine! [duplicate]

This puzzle is taken directly from a site and reworded. The site can be found at the bottom of this question. You are king of an empire and you are going to have a party soon. The party is the most ...
17k views

### Is the Glass Half Full with water?

You, a right cylinder glass of water, 3 buttons, instructions, and a large flat land that seems to go on forever, are the only things that exist in a universe. In this weird universe, the exact same ...
7k views

### How do I arrange pencils so they all touch each other?

How do you arrange 6 pencils so that each one touches the other five? And what about 7 or 8?
2k views

### A Drawer of Socks

Bob wakes up one morning, and he needs to grab a pair of socks for work. In his sock drawer, he has 5 pairs of blue socks, 3 pairs of red socks, and 4 pairs of white socks (Bob is American and very ...
2k views

### How do we get those dang Illuminati?

The Illuminati just stole our office They shot JFK and have committed numerous crimes against humanity (not really) but we usually let that slide. But for stealing our offices, we have decided to ...
2k views

### The Illuminati and the Knights Templar

Some people in the American Senate are working for secret organizations. Some work for the Illuminati, some work for the Knights Templar, and some work for both. The are also innocent citizens who are ...
904 views

### The generous team puzzle

An intelligent team, ‘Smarty Pants’, applying to a competition completes an evaluation form early. Since they are feeling generous they randomly spread their assignment to all 10 teams applying from ...
1k views

### The way to Acarien, with Knights and Knaves

Once again, you're on your way to Acarien. You find yourself in a land of Knights and Knaves, who understand your language but don't speak it. You understand nor speak their language, but you do know ...
3k views

### Are you Really Smart

The government has introduced a standardised test to identify dumb people and make them ineligible to apply for any government jobs, a pass in the exam is mandatory for applications in future. It ...
2k views

### The way to Acarien puzzle

You are on a quest to the find the lost kingdom of Acarien. On your way, you end up at a fork in the road. Both paths look exactly the same. At the junction sits a wise man. The wise man will only ...
334 views

### Apples and Oranges

You were on a grocery shopping day, you go to the store, and your friend tells you he'd like you to pick him up some fruit, naturally you try and be a kind friend and agrees to pick it up for him, you ...
3k views

### House Number Mastermind

I was having a house-leaving party at my old house, and challenged four of my friends to guess the number of the new address, which had three digits. The responses I got were 280, 376, 304, and 370....
4k views

### Is my sibling a sister [duplicate]

A male friend of yours wants to test if you are ok at Math and logical thinking, he says I am one of two children of my parents, and asks you to find out the probability that his sibling is a sister, ...
1k views

### The Old Millionaire

A very old man has a million dollars, which he's going to pass down to you! He has 3 associates who have been ordered to help you. The 3 associates know the location where it is, and they tell you it ...
3k views

### Up to your head in trouble

You've gotten in trouble with a Mob Boss, and as punishment have been brought to a sandy beach. You're ordered by him at gunpoint to bury yourself in the sand up to your neck. He specifies a spot ...
485 views

### The 3 Boxes Show! [duplicate]

A variation of the Monty Hall, where the values inside the choices are changed You were just out gambling and lost 5000 dollars! Of course being the gambler that you are, you pay 2500 to play this ...
704 views

### 4 Doors and a Half Value prize

You're on a game show, playing for 1 million dollars! You've made it to the final round, there are 4 doors, you pick a random door (obviously, there's a 1/4 chance for all of them, let's say you ...
1k views

### Knight/Knave/Joker - impasse challenge

You are at an impasse with 30 doors - 29 of them lead to endless wandering the depths of hell - and one of them leads to paradise. In front of them stand the typical trio of good friends, a Knight, a ...
3k views

### First day of school

Here's a pretty easy one. A new student (a male) was wandering down the hall of his new school looking for the boys' locker room. He asks a nearby student (who happens to be the school bully) to ...
2k views

### Can you help the traveller

A traveller decided to explore a square desert. He started from a point on the edge to point B, travelling perpendicular to the edge of the desert he started on. On reaching B, he then decided to take ...
587 views

### How do I count Hamiltonian paths of grid?

Let's say there is a 5x5 grid with a starting position in the upper left corner, and an ending position is lower left corner. How do I count how many Hamiltonian paths there are through the grid? I ...
593 views

### When will the matrix turn to black?

For the following pattern of filling the $5*5$ matrix, how many steps does it take to turn all cells of the matrix to black? Pattern has revealed by eBusiness: I guess after some steps next pointed ...
394 views

### Housing crisis in heaven

Heaven has a countably infinite number of cloud for people to stay, each of which has a good soul living on it. A countably infinite number of infinite universes are extinguished by God (their beta ...
638 views

### The three inheritors

A wealthy person has passed away, naming three siblings as beneficiaries of the vast estate. Unfortunately, the will states that: My estate shall be divided evenly, such that no sibling shall feel ...
1k views

### Percentages and the watermelon size reduction

Ok, so my friends and I had a disagreement over this seemingly simple problem and we would very much like to know the answer for it. Question Initially a 100 kgs watermelon is 96pc water and ...
4k views

### How many Chess Pieces are needed to control every square on the board?

You may only use pieces in the original set, and all your pieces must be the same color. The king is not allowed. Pawns do not get promoted. Pieces do not control the square they occupy. Accepted ...
2k views

### Fewest possible weighings to determine which ball is heavier/lighter

You are given 4 balls, all equal in weight except for one that is either heavier or lighter. You are also given a two-pan balance to use. In each use of the balance you may put any number of the 4 ...
784 views

### The knaves come out at night

Standard knights and knaves problem. There are 10 people in a room, you know that each person will either always tell the truth or always lie, but you don't know who is a truth teller or liar. You ...
1k views

### How Many Queens to Threat Themselves?

How many queens can be placed in a standard $8*8$ chessboard to threat each of them exactly once by other queens?
814 views

### A different extension of the sum and product puzzle

How far down the rabbit hole of not knowing can we go? While working on the generalization of I don't know the two numbers... but now I do, I thought of these two extensions. Both have the same ...