Questions tagged [strategy]

A puzzle whose solution is a methodological plan of action for realizing a specific goal.

Filter by
Sorted by
Tagged with
38
votes
5answers
13k views

Duel between the knight and the dragon

A dragon and a knight live on an island where the only sources of fresh water are a pond (containing ordinary water) and six wells, numbered 1 to 6. Each well's water is completely indistinguishable ...
5
votes
3answers
514 views

Foolproof double betting

Just made up a problem. Have ideas, but no proof yet – came here for professional help. Tonight an important match of Metagame (box/football/baseball/chess) takes place. Everyone is hyped. Everyone ...
8
votes
5answers
456 views

Two person game, choosing an integer between 1 and 30?

Suppose two players are playing a game. The first player chose an integer, n st. $n \in \left\{ 1,\ldots ,30\right\}$. The second player picks a different one. After that, a random integer x st. $x \...
6
votes
2answers
681 views

Crystal Maze totem pole puzzle

The UK game show "The Crystal Maze" features a puzzle based around a totem pole. The contestant has four different coloured blocks which can be stacked up to make a totem pole. The blocks may be ...
11
votes
1answer
423 views

Dim - A Game with Pebbles

Alice and Bob play a game with a pile of $n$ pebbles. They take turns, with Alice going first. On their turn, a player can remove any number of stones from the pile which is a proper divisor of the ...
3
votes
3answers
189 views

Optimal number of weightings in marble problem

Consider $N$ pieces of marble. The pieces of marble look identical to one another. One of the pieces is heavier than the other. In other words, out of the $N$ pieces, $N-1$ have the same weight and $1$...
14
votes
5answers
2k views

Church charity lottery

Suppose you've rigged the church charity lottery so that you cannot lose (what a swell guy you are). There are 10 drawings, and you start off with 10 dollars exactly. At each drawing, you must chose ...
4
votes
1answer
288 views

Variant to Minesweeper

The following game is a variant of minesweeper: There is a 7 by 7 grid of squares. Each square either has a skull or a number indicating the number of squares containing skulls surrounding that ...
25
votes
3answers
1k views

The lion and the zebras II: The lion with millimeter-long claws

This is a variant of this excellent question. The rules of the lion-zebra hunger games are exactly the same: The lion plays a deadly game against a group of 100 zebras that takes place in the ...
4
votes
1answer
207 views

Find the fake bar in 2 weighing [duplicate]

You are given 8 equal sized bars of silver labeled a to h. You know for a fact one of them is fake, and the only measurable difference is weight. However you do not know if the fake bar is heavier or ...
6
votes
1answer
504 views

Arranging cards in rows

This question appeared in an old math contest, and I seem to remember that the answer I had back when I first saw it was unsatisfactory. You have a deck of cards numbered from $1$ to $60$. First, ...
14
votes
7answers
2k views

Twelve balls on a scale, where one ball is lighter and another is heavier

Suppose you have twelve identical-looking balls. Ten of them are the same weight, but one is slightly lighter and one slightly heavier, in such a way that the weight of the lighter and heavier ball ...
-4
votes
1answer
294 views

What did the Wise Man Say? [duplicate]

An Arab sheik is old and must will his fortune to one of his two sons. He makes a proposition. His two sons will ride their camels in a race, and whichever camel crosses the finish line LAST will win ...
18
votes
4answers
3k views

A Tic-Tac-Toe type game

I found this interesting game with no name: You have a 1x11 grid, like this. The way you play is similar to Tic-Tac-Toe (aka Noughts and Crosses). Players take turns to place Xs and Os on the grid, ...
5
votes
3answers
275 views

Crazy queen in checkers

Checkers Checkers, also called draughts, is an interesting game. all pieces are placed on black tile and are all pawns at the start. When a pawn reach the final line, a powerful piece is created: the ...
4
votes
2answers
260 views

How many nodes in the network?

I don't actually have a solution in mind for these, but it seemed puzzly enough to bring to the table. Seems as though someone must have come up with this before, but if so, I couldn't find it when I ...
5
votes
3answers
1k views

Hacking an electronic keypad v2

This is related to Hacking an electronic keypad. You are a spy trying to break into an enemy facility. The back door is protected by an electronic keypad lock. You know that this particular lock is ...
5
votes
2answers
748 views

How much money can we make? v2

This is follow up question to How much money can we make? My five friends and I used to loan each other money all the time. But over the past several years we have moved apart. We don't trust ...
17
votes
10answers
1k views

Communicating Information about Cards

Seven cards, numbered $1,2,3,4,5,6,7$, are distributed randomly among three people: Rand gets one of them, Deusovi gets three of them, and Gareth gets three of them. All three know what the seven ...
18
votes
3answers
7k views

Can you Turn MI to MU?

Using the letters M, I, and U, which can be used to create words. Can you turn MI into MU using in each step one of the following rules: Insert a U to the end of a word ending in I. e.g: MI becomes ...
1
vote
0answers
280 views

Can a group of professors determine their average salary without learning any information about each other's? [duplicate]

A group of at least 5 jealous professors are locked in a room. There is nothing else in the room but pencils and one tiny scrap of paper per person. The professors want to determine their average (...
25
votes
4answers
2k views

Lions and Zebras on a Chess Board

The black knight is our lion chasing 8 white bishop zebras which can't capture. Can the zebras evade the lion forever, if team zebra positions all the pieces and has the first turn? Rules: The game ...
8
votes
4answers
2k views

The Greedy Box (Or: Another crazy guard offering his prisoners freedom)

Two prisoners, in separate cells, are watched over by one eccentric and whimsical guard. One day he (inevitably) decides to give the prisoners a chance to earn their freedom by playing a game with ...
15
votes
2answers
2k views

10 prisoners and 10 lists of numbers [duplicate]

10 prisoners are held captive by a cruel warden. One day he gathers them in the prison hall and tells them about a new game he wants to play: "Tomorrow, I will assign each one of you a random ...
6
votes
3answers
389 views

Guessing game with infinity coin flips

Evan and Ollie are going to play a game as a team. The two friends placed in separate rooms, and then a coin is flipped infinitely many times*. Evan is told the results of the even numbered flips, ...
15
votes
4answers
35k views

Is it possible to use one sequence of moves to solve the Rubik's cube from any position?

Is there a sequence of moves that can be repeated over and over again which can solve any legal position the Rubik's Cube? If so what is it, and if there's more than one, what's the shortest? If not, ...
5
votes
1answer
337 views

Another Secret Polynomial

Alice: Let's play a game, Bob! Bob: (sighing) What is it this time? Alice: I'm thinking of a polynomial $P$ with integer co-efficients. For any integer $n$, you can ask me what $P(n)$ is. Then, if,...
8
votes
3answers
419 views

Gettings most jewels in a square 5x5

Playing an online game I came across a small puzzle (a mini-game in game). The game is about getting jewels in a row - a player needs to get 5 in a row / column or a 5-square-diagonal. Let me show you ...
64
votes
3answers
4k views

A secret polynomial

Alice has a secret polynomial $P$ with positive integer coefficients. When Bob gives Alice a positive integer $n \neq 2016$, Alice replies with the value of $P(n)$. After doing this several times, Bob ...
8
votes
1answer
2k views

99 chips into more chips

You are at a casino in Vegas and you have earned 99 chips by playing poker! While you are checking out a slot machine, someone comes to you and congratulates you that you have a chance to make more ...
7
votes
2answers
438 views

99 chips into more chips V2

This is follow up question of 99 chips into more chips, which is originally: You are at a casino in Vegas and you have earned 99 chips by playing poker! While you are checking out a slot ...
44
votes
7answers
6k views

The Circular Prison of Unknown Size

You are the president of a secret society of mathematicians with $n$ members, including yourself. No one in the society knows what $n$ is. The dictator of the world, in an effort to erase mathematics ...
40
votes
7answers
5k views

Amnesiac in a ring shaped palace

Related: Turn off all lights in a ring-shaped palace Your boss has trapped you inside a ring-shaped palace, and all you know about the palace is that there are some number* of identical rooms, each ...
6
votes
3answers
399 views

The Alchemist's brew

I'm an Alchemist and I want to prepare Universal Panacea. That's a precious thing and I will be able to sell it for good money. The complete recipe for the Panacea is of course very complex (and ...
7
votes
1answer
795 views

A Strategy Game Involving Conquering of Regions

This is a game that I saw in a book long ago. Unfortunately I cannot find the book now, and even if I can as I recall it does not provide a strategy. I will be very grateful if you can provide me a ...
7
votes
4answers
544 views

'Companion Planting' Logic Puzzle - Is there an elegant solution?

Problem: You're a vegetable gardener planning to plant out seedlings in a new garden bed, however your farmer's almanac has outlined a system of rules about what plants can and cannot be placed next ...
2
votes
1answer
171 views

Taming a Bomb Puzzle (Part 3 of 3)

The part 1 can be found here: Taming a Bomb Puzzle (Part 1 of 3) The part 2 can be found here: Taming a Bomb Puzzle (Part 2 of 3) The Mechanics Ampera Bridge, the famous landmark of Palembang City ...
5
votes
3answers
491 views

“Alien Love” Puzzle

There is a group of 10 aliens and each alien is either male or female. You don't know how many male or female aliens are in the group, but you know that exactly one of them is a "hybrid" male alien. ...
2
votes
1answer
148 views

Taming a Bomb Puzzle (Part 2 of 3)

The part 1 can be found here: Taming a Bomb Puzzle (Part 1 of 3) The Mechanics Ampera Bridge, the famous landmark of Palembang City is in danger! A terrorist has sticked a bomb in the middle of ...
7
votes
2answers
321 views

Taming a Bomb Puzzle (Part 1 of 3)

The Mechanics Ampera Bridge, the famous landmark of Palembang City is in danger! A terrorist has sticked a bomb in the middle of Ampera Bridge. The bomb cannot be removed and it can explode anytime. ...
4
votes
1answer
350 views

Fake and genuine coins

There are 14 coins, numerated from 1 to 14, and presented as an evidence at the court. The first 7 are fake coins, and others are genuine coins. Fake coins have all the same weight and they are ...
3
votes
2answers
185 views

How the best card can I choose?

Me and Varun playing a game of cards (standard deck of 52 cards). In which we distributed 5 cards to each other. Edit: We have seen each other's cards. We have to put the cards in a line one by one ...
3
votes
5answers
1k views

Dominating Furbles

This question was previously from the Haselbauer - Dickheiser Test For Exceptional Intelligence, a test that was previously available on the website www.highiqosociety.com, but was removed several ...
5
votes
3answers
1k views

Strategy for Modified Lights out

A friend of mine showed me a variation of lights out that they were interested in, and asked me if it would be possible to solve any given empty grid. This variation involves toggling not just the ...
13
votes
1answer
514 views

Hiding Cat Puzzle on a Grid

The Youtube channel MindYourDecisions posted a video about the "Hiding Cat Puzzle". In the puzzle, you have a line of five boxes, one of which contains a cat. You don't know where the cat is, and your ...
1
vote
2answers
276 views

The Monster and the Chessboard [duplicate]

You have a standard checkerboard with 64 squares and a coin in each square, randomly facing heads or tails up. There is an evil monster in the room with you and he arbitrarily selects some square and ...
10
votes
7answers
1k views

Prisoners and minority voting

Disclaimer: this is a scenario that I came up with on my own, and I do not actually know if there is a possible solution. The reason for posting is to see if the combined intellect of PSE can help to ...
-3
votes
4answers
324 views

If 27 x 147 = 3969 What is its square root WITHOUT using complex / long calculationx [closed]

Basically what you have to do is find √3969 without using complex /long calculations
0
votes
1answer
83 views

Taking a ball from basket challenge [duplicate]

I have 10 red balls, 10 blue balls, and 2 baskets. You are free to choose the numbers of red balls, and the numbers of blue balls to put to the first basket. Then you have to put rest of the balls to ...
18
votes
10answers
4k views

How to get voters to vote against themselves [closed]

On an island far away, there are people. They have an ancient law which states that anyone can propose a new law. However, new laws must be voted upon immediately after proposal (i.e there is no time ...

1 2 3 4 5 11