All Questions

Filter by
Sorted by
Tagged with
2
votes
4answers
2k views

character decoding problem at an interview [closed]

If "PSAKLJIUASP" is "PJIUAZAKLKP", then what is the word for "LIOQWERRPOIL"? I noticed that the first 3 characters are reverse of the last 3 characters in both words in question. A is mapped to I ...
15
votes
3answers
2k views

Optimal play for 2 by 2 dots and boxes

Consider the classic pencil and paper game Dots and Boxes . You can assume the 2 by 2 version (that is with 9 dots). Starting with an empty grid of dots, players take turns, adding a single ...
11
votes
7answers
2k views

The smallest crossword

I heard Martin Gardner in one of his books presented a crossword, which looks like 3x3 square. Could you help me to find it? Also, have been there a smaller crossword puzzle created?
15
votes
1answer
1k views

A haunted vending machine that you can't see inside

This question asks about a strange vending machine in which coins can fall out as well as being deposited in, and all the coins it asks for must be deposited before the machine will accept them. That ...
5
votes
2answers
1k views

How many digits can be removed from a division puzzle?

Similarly to How many digits can be removed from a multiplication puzzle and still give only one answer? I am curious about division puzzles. I know this puzzle: . It has only 2 out of 42 digits $\...
10
votes
3answers
2k views

Oskar van Deventer's “haunted vending machine puzzle”

Oskar van Deventer has created the “haunted vending machine puzzle”. You have to insert coins into the slots 1, 2, 3 or 4. A coin that hits a green switch on its head rests there; a coin ...
8
votes
1answer
869 views

Number of tries to guess M-1 letters from M-letters-code

There are $N$ letters in an alphabet. There is a combination lock, the code to it consists from $M$ different letters. You can input $M$ letters combination and try to open the lock. (But you can't ...
8
votes
4answers
1k views

How to lock a shared artefact

This answer reminded me of a nice puzzle. I present it as a challenge for you. N thieves had stolen a magical artefact. They bought a lock with N keys and attached the artefact to a loop on a wall ...
5
votes
1answer
469 views

Optimal strategy against a random opponent

Imagine a very big number (2N) of people, who do not know each other, and play the following game: Players are divided into two equal groups: A and B. In each group players are numbered from 1 ...
17
votes
8answers
6k views

When to be sure that we have counted all the squares in such problems

My first question: how would one solve such problems (in general)? What should be the general technique? My second question: When to be sure that we have counted all the squares in such problems?
5
votes
2answers
534 views

How to generalise hang picture puzzle?

There is well known problem: The picture is attached to a string and you want to hang it on N nails so that if one takes out any of the nails, the picture falls. How do you do it? For those who ...
6
votes
1answer
8k views

Maximal number of steps needed to solve 2x2x2 Rubik's Cube

What is the maximal number of steps that a computer (using the fastest algorithm) would need to solve an arbitrary 2x2x2 Rubik's Cube configuration? Are there any other known algorithms that will ...
11
votes
1answer
3k views

How to solve this crazy Chinese puzzle for children?

I have been shown this "Chinese puzzle from textbook for 2nd grade" like a joke. But it is intriguing, so I would like to know the answer, but I am quite bad in associative puzzles and can't find the ...
16
votes
4answers
31k views

How to solve this IQ test puzzle with arrows and pied squares?

What is correct answer for this IQ task and why?
11
votes
8answers
11k views

Survive from death by asking the right question from trolls

You are in the intersection of two roads, there is a troll in the beginning of each road. One of them is liar (always lies), and one of them always tells the truth. One of the roads, ends to your ...
3
votes
2answers
667 views

How to generalise Partition of the pie for N envy people?

There is well known task: How to divide a pie between two people, so each will think that he got equal or more that the other one? It has the following solution: I know that it is possible to ...
4
votes
2answers
1k views

Is there a brute-force solution of this puzzle?

There is a puzzle Suppose a standard $8x8$ chessboard has two (arbitrary) squares removed. The only thing known is that these two squares have different colours. Is it always possible to place 31 ...
6
votes
2answers
969 views

Lighthouse keeper stuck the bath [closed]

A lighthouse keeper decides to take a bath an hour before the next lighthouse keeper comes to relieve him of his shift. This lighthouse keeper is having a bad day. First he accidentally locks ...
9
votes
1answer
699 views

Discover the relation of two babies of a awkward marriage

There are two friends, they are not related. Each has a daughter. Their wives are dead. Each man marries his friend's daughter, and after a while, both couples will have a child (a daughter). What ...
115
votes
9answers
19k views

Paying the Troll toll

You are on your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made. Between your house and her house, you have to cross 7 ...
30
votes
5answers
6k views

Two spies throwing stones into a river

There is a puzzle about two spies: Two spies must pass each other two secret numbers (one number per spy), unnoticed by their enemies. They have agreed on a method for doing this using only 26 ...
17
votes
2answers
13k views

Write twenty-four from four numbers

Write 24 using the four numbers 1, 3, 4, 6 and basic arithmetic. Explanations: The given are numbers, not digits, so you can't group them using decimal notation. For example, you can't create the ...
4
votes
6answers
4k views

Writing numbers puzzle

How do you write 23 using only the number 2? 34 using only the number 3? 56 using only the number 5? 100 using only the number 9? You can use only the numbers said, but any math you want in order ...
8
votes
1answer
355 views

Kruskal's hard to refold envelope

In Wikipedia's bibliography of Martin Kruskal it is said: Martin, who had a great love of games, puzzles, and word play of all kinds, also invented several quite unusual origami models including ...
7
votes
1answer
693 views

How do I necessitate the use of the X-Wing pattern during Sudoku creation?

I want to create a Sudoku puzzle, and I want it to be of moderate difficulty. There's a specific pattern I want to include, called the X-Wing pattern: This occurs when two numbers form locked ...
3
votes
2answers
622 views

Does this strategy work?

I'm thinking about the following strategy for Fastest way to collect an arbitrary army: When a soldier decides to go to some house he "reserves" it. Once a soldier is free (has delivered the news to ...
8
votes
2answers
2k views

How many Queens and Knights does it take to cover a chessboard?

Given an 8x8 chessboard, your goal is to "cover" each space on the board. A space is "covered" if there is a piece on it, or if a piece on the board can be moved to that space in one move. If you ...
10
votes
1answer
665 views

Find the color of the chess pieces

The colors of the pieces in the diagram is unknown. The diagram can be obtained from a real game. One needs to find the color of each piece: Black or White. I do not know the full solution. ...
6
votes
1answer
619 views

What is the expected length of the longest piece?

If a rod of unit length is broken into $n$ pieces, what is the expected length of the longest piece? The positions at which the rod is broken are chosen randomly uniformly. This is a generalization ...
18
votes
3answers
3k views

Knights and jokers

There are $N$ men. $K$ of them are knights, $M$ of them are jokers. $N$ is known, $K$ and $M$ are unknown. You know that: $K + M = N$, $K \gt M$, $M \ge 1$, $N$ is odd. Knights always tell ...
7
votes
2answers
599 views

Identify unique Verbal Arithmetic Puzzles

I am attempting to create original Verbal Arithmetic puzzles such as the famous one from this question Alphametic (Verbal Arithmetic) general strategy : SEND+MORE=MONEY For these problems each ...
19
votes
2answers
2k views

How to create a pure mathematical-logical based puzzle equivalent to resistance based physical puzzle?

I am thinking how to reformulate a physical puzzle in a way that it becomes purely logic based (doesn't uses physical lows and can be solved by a person, who knows nothing about physics). The puzzle: ...
9
votes
1answer
794 views

Is there a retrograde analysis puzzle like “Point on the incorrectly drawn chess piece”?

Does anybody know a nice chess puzzle, where the question states: Exactly one piece is drawn incorrectly on this diagram; another piece must be drawn on its position. Find the incorrectly drawn ...
17
votes
0answers
1k views

Is there a more efficient way to rotate the centre pieces on the Octo-Star?

I'm looking for a more efficient algorithm to rotate the center column of the Octo-Star puzzle 45 degrees. The situation below occurs when four properly-oriented edges are next to each other, ...
15
votes
3answers
58k views

Which way is the bus going?

If I'm not mistaken, this is a children's puzzle, but it got me thinking for a while. The bus is driving on the autobahn. Relative to you, which way is the bus going? Left or Right?
7
votes
3answers
28k views

How can I solve the Gear Cube Extreme?

The Gear Cube Extreme is another Mechanical Puzzle. I ordered it not so long ago and a friend of mine "accidentally" scrambled it. Now I want to solve it again but I have no idea how or even where to ...
4
votes
3answers
5k views

Is there any way to 'trap' my opponent on Connect Four?

I am trying to find out if there are any 'optimal' moves in the game, so as to trap my enemy to put his pawns in the place where I need them
10
votes
2answers
2k views

5x5x5 Rubik's Cube Smiley

I did some turning on my 5x5x5 Rubik's Cube and I now have the cube like on the image below. 4 times a smiley -_- and 2 times a solved plane. But I have no idea how ...
5
votes
4answers
2k views

Is there a rating system for crossword puzzles?

On searching the internet for difficult crossword puzzles I find that the New York Times is often mentioned. But is there a rating system? If so how does it work?
-1
votes
3answers
2k views

Why must a sudoku have a unique solution [closed]

Why must a sudoku have a unique solution. In my books I don't guarantee it. But I am sure there are not many which don't. I doubt if one in a thousand dont have. And even if they don't its only a ...
8
votes
1answer
2k views

What is the position in chess with the longest string of moves before mate?

In chess puzzles, the objective of the puzzle is usually to checkmate the opponent using some form of novel strategy or tactic. For example, the following puzzle (from here): has white to play and ...
12
votes
7answers
3k views

Fastest way to collect an arbitrary army

I am looking for solution of this puzzle: There is a kingdom with a square shape with sides of length 1. The castle is located at the center of the square. At the castle the king lives under the ...
29
votes
7answers
108k views

Clever ways to solve Mastermind?

Is there any specific way to solve Mastermind? Apart from the first step that is pure chance, is there any way to continue based on the colors that you think are correct?
-1
votes
2answers
235 views

How does one make a program to provide all the 'possible' numbers in an empty cell

To be able to solve a sudoku one usually has to first work out all the 'possible' numbers in an empty cell. How can one make a program to do this? In this case 'possible numbers' are ones which have ...
13
votes
2answers
3k views

How many distinct unsolvable Rubik's cubes exist?

I wanted to answer this question: Why can't I have only one edge piece flipped on a 3X3 Rubik's cube? by saying that it is homomorphic to the illegal state in this question: Why is a ...
4
votes
1answer
955 views

Odds of duplicate birthdays

I found the following problem in an number of places online: John once bet a fellow gambler that two of the first thirty persons they met and spoke to would prove to have the same birthday. Strong ...
7
votes
1answer
2k views

Why can't I have only one edge piece flipped on a 3X3 Rubik's cube? [duplicate]

I was using the beginner method to deliberately solve a 3X3 cube with one edge piece flipped. But, by the time I got to the top I discovered that I couldn't solve it with only one edge flipped. I had ...
10
votes
3answers
2k views

The Magic Stick

Here's a relatively easy puzzle that's actually entirely my own creation. An old guru in an Asian monastery is showing his beloved student his gallery of items that he has either collected or kept ...
5
votes
2answers
600 views

Cryptic clue “Injured person's mostly easy-going (8)”

I'm stumped on the last clue in another cryptic crossword. The clue is Injured person's mostly easy-going The (confirmed) cross-clues give C_S_A_T_. Normally I can guess at a part or at least the ...
4
votes
1answer
477 views

What is “A non-PC American woman overseas?”

I'm stuck on the last clue of a cryptic crossword. The clue is: A non-PC American woman overseas? (6) The cross letters are A_R_A_, confirmed by "check answers." Cryptic Crosswords iPhone app, ...

15 30 50 per page