# Questions tagged [strategy]

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

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916 views

### Gold and silver coins in sealed envelopes

Alice has freely chosen to put either a gold coin or a silver coin in each of an infinite sequence of envelopes numbered 1,2,3,... Bob can open any number of envelopes and check the coins within, ...
366 views

### The game of 42: 10 cards to make 42

This is a game inspired by other recent questions. It is a 2-player game. The game is played with 10 cards numbered 1 to 10 and 2 positions or stacks. The game starts with all cards in stack 1. The ...
748 views

### Pole, rope, and chasm

You come across a chasm. It's perfectly smooth, 50m deep, and 50m across, and too wide to go around. You have a pole that is 40m long, and as much rope as you need. How do you get across the chasm? ...
2k views

### A Game of Phones

The Chaos Legion is an infamous criminal organization, responsible for every major disaster in history from the burning of the Library of Alexandria to the recent Sony hack. The Order of Seven is ...
2k views

### Winning chance in coins game with fixing

A player plays the following solitaire game. The game consists of as many rounds as are needed to produce a result. They have 20 fair coins, which may in any round be live or fixed; each coin starts ...
531 views

### Is it possible to fill an arbitrarily large hex grid completely given these rules? #2

Based off of this. Lets say you have two players, Red and Blue, that alternate filling an arbitrarily large hexagonal grid of tessellated hexagons with pieces of their color. Hexagons can either be ...
506 views

### Is it possible to fill an arbitrarily large hex grid completely given these rules?

Lets say you have two players, Red and Blue, that alternate filling an arbitrarily large hexagonal grid of tessellated hexagons with pieces of their color. Hexagons can either be filled or empty. A ...
3k views

### Two prisoners and twenty marbles

Two prisoners are planning their escape. Their cells are locked with a padlock that must be opened with a 5-digit code (numbers 00000 to 99999). Each prisoner knows the code of the other prisoner's ...
2k views

### 6 Water Glasses Upside Down

There are 6 water glasses as shown in the picture below: You need to turn all of them upside down with the rules below: You have to choose any 5 of them at every turn. Chosen ones need to be turned ...
520 views

### One vs many. Can white force a draw?

On an infinite chessboard there's a single white king and N black kings. The nearest black king must be K moves away from the white king. Given N, white dictates the value of (finite) K, then black ...
719 views

### The Alien Snails Experiment

Fictional Background Story (The Experiment): Two extremely fast and intelligent alien snails are randomly placed on two different points on an infinite plane, as an experiment by the cruel ruler of ...
153 views

### Dumb robot on chessboard [duplicate]

A robot is placed on the square A1 of a standard chessboard and has to reach H8. It understands orders Up, Down, Left, Right. On some squares, there might be a cement block; is such a case, the robot ...
930 views

### Anna tries to make triangles from broken sticks

Anna and Boris play a game with a red stick, a white stick and a blue stick, each of which is 1 meter long. Anna starts by breaking the red stick into three pieces. Then Boris breaks the white stick ...
2k views

### Determine whether the counterfeit coin is heavier or lighter in two weighings on a standard balance

To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you! ...
2k views

### Find the heaviest and the second heaviest coins

Each of 32 coins has a different weight. In 35 weighings on a standard balance, find the heaviest and the second heaviest coins. Clarification: Before you start to identify the heaviest and second ...
3k views

### Magic: the Gathering – Scry-sort

Let me start with a formulation of the problem for people who aren't familiar with Magic: the Gathering. You have a stack of distinct cards face-down. You can apply the following actions arbitrarily ...
442 views

### Magic: the Gathering – The end of time

Thanks to NeedAName and his latest Magic: the Gathering Challenge I actually noticed there is a magic-the-gathering tag. It was quite some time ago that I played Magic the last time, but nevertheless ...
753 views

### Optimal refueling strategy

On the way home from work, I want to refuel my car. There are 5 petrol stations along the way that all have a different price for petrol. I know that the prices will be in the range [A, B], chosen ...
4k views

### When do missionaries and cannibals problems have solutions?

In the Missionaries and Cannibals problem: Three missionaries and three cannibals must cross a river using a boat which can carry at most two people, under the constraint that, for both banks, ...
351 views

### Making an expression with the numbers 1 to 100 odd (or even)

Anna and Boris play a game with the numbers from 1 to 100 written in order in a row. Anna goes first, and turns alternate thereafter. In each move, a player puts one of the operation signs +, − and × ...
1 vote
60 views

### Change all eight numbers to 1 [duplicate]

A solitaire game starts with eight numbers arranged in a circle. Each is either 1 or −1, and the choice is arbitrary. In each move, one can multiply any three adjacent numbers by −1. Prove that one ...
198 views

### River crossing cats and dogs

A farmer and his $n$ cats and $m$ dogs are on one side of a river. There is a boat that can carry the farmer and at most $k$ animals at once. The boat doesn't move without a person operating it. The ...
859 views

### You have magic, but sometimes the spell backfires: how to win regardless? [closed]

This one is convoluted, and I’m not sure if there actually is an answer. For a character in a story. You have magic and want to rig a sporting event. However sometimes the spell will backfire. The ...
529 views

### Seven genuine and two fake coins

Seven genuine coins have the same weight. Two counterfeit coins also have the same weight. A counterfeit coin is heavier than a genuine coin. Identify the fake coins using a standard balance at most ...
1k views

### The game with cookies on a red and a blue plate

Aabzaari and Basharat play a game, alternating turns with Aabzaari going first. At the start of the game, there are 20 cookies on a red plate and 14 cookies on a blue plate. A legal move consists in ...
5k views

### Can you beat random?

It is known that one cannot beat a truly random player in Rock Paper Scissors. Here you will play a variant of the game. In this variant you are not allowed to play the same shape twice in a row. So ...
13k views

### What's the optimal strategy for Wordle?

Wordle is a game by Josh Wardle in which you try to guess a 5-letter word in at most six attempts. After each guess, the letters which are not in the word are highlighted in grey, the letters which ...
365 views

### Press The Grue Button

[This puzzle is inspired by the webpage https://apparenthorizons.com/2017/10/12/the-grue-problem-and-deep-learning/] 55 workers have got a chance to double their pay, as said by their boss. So, the ...
369 views

### The Monty Hall loot box

Everyone sufficiently competent in probability knows that in The Monty Hall problem as most commonly presented, switching doors wins you the car $\frac23$ of the time. I have come up with this ...
1k views

### Two Trains, One Track

Two trains are heading towards each other on a track. One train is blue, the other is green. Each train has a locomotive hauling nine wagons. Each locomotive is 10 meters long, and each wagon is also ...
1 vote
345 views

### SEVEN-COUNTERS GAME

This simple puzzle is from the 1908 book “A Scrap-Book of Elementary Mathematics” by William F. White. Required to place seven counters on seven of the eight spots in conformity to the following rule:...
997 views

### Sliding crosses in a 4x4 grid

You are given a 4x4 grid with 3 crosses as shown below. Each turn, you can select a cross and slide it along horizontally or vertically. It will continue sliding until it hits another cross or a wall. ...
2k views

### Sliding crosses in a 5x5 grid

Well you probably already knew that this was coming after the last two puzzles :) I believe this is the most beautiful one. You are given a 5x5 grid with 3 crosses as shown below. Each turn, you can ...
474 views

### Sliding crosses in a 3x3 grid

You are given a 3x3 grid with 3 crosses as shown below. Each turn, you can select a cross and slide it along horizontally or vertically. It will continue sliding until it hits another cross or a wall. ...
675 views

### A game of 101 stones—win at (not quite) all costs

In the land of Humilia, a tournament game is played between two players with 101 stones in a pot between them. On each turn, a player may take up to five stones from the pot (and must take at least ...
421 views

### 1000 Batches, 1 Poisoned, 4 Mice, Minimized Costs

You work at a pill factory that recently produced $1000$ batches, each with ample samples. Your boss has just discovered that exactly one batch is entirely poisoned, and just one pill from it will ...
448 views

### Escape the labyrinth

Devise a concrete winning plan for White. The title will help. En passant is not possible. FEN: 7k/8/6p1/3p1pPp/p1pPp1p1/PpPpPpPp/1P1B1P1B/3NRKQN w - - 0 1 Hint: Hint 2:
605 views

### Minimum K for detecting fake pearls in one weighing

There are 10 boxes, each with the same number of pearls (represented by K). Genuine pearls weigh 30g each, while fake pearls weigh 29g each. Each box is either all genuine or all fake, and any number ...
1 vote
199 views

### Two Sheriffs and Eavesdroppers - 3

“The Two Sheriffs” puzzle was already discussed here. This puzzle has only one difference: we have six suspects instead of eight. Two sheriffs in neighboring towns are on the track of a killer, in a ...
2k views

### Poison ivy chess: Can the king get to safety?

The king is on a chessboard filled with poison ivy bushes. Can the king get to safety? Details: The king is initially located at the top left-hand corner square of the chessboard. The finite ...
593 views

### Game of the glasses on the windowsill

The windowsill above the sink is where my wife and I place our dirty wine glasses. And while both of us love each other, neither of us love loading the dishwasher. As a result, these dirty glasses ...
6k views

### The Mexican Standoff

There are three cowboys in a Mexican standoff against each other, named Juan, José, and Jorge. Juan is the straightest shooter in the West, and can hit his target 100% of the time. José, who has a ...
231 views

### Wounded Soldiers/Crossing a Bridge Puzzle - checking a solution

I am working on a Prolog university assignment, where we have to determine what the shortest time is for 4 wounded soldiers to cross a bridge to safety. This seems to be a variation of the more common ...
1 vote
290 views

### Fox and rabbit on a circle

There are five holes in a line. One of them is occupied by a rabbit. Each night, the rabbit moves to a neighboring hole, either to the left or to the right. Each morning, a fox gets to inspect a hole ...
3k views

### Using a balance scale the minimum number of times, find the median weight person

There are 15 person with different weights. What is the least number of tries required to find the middle (median) weight person? How? The only tools you have is your brain and a balance scale with ...
4k views

### Red and Blue in the Chocolate Fountain Room

Where: Hackanoogie Prison. When: Who cares? The Master Key Keeper had had a really good day and in a fit of insanity and niceness decided to let all the inmates to go free if they manage to carry ...
22k views

### Learning to Solve a River Crossing Puzzle

I have seen many variations of the following puzzle: Once upon a time, a farmer went to the market and purchased a fox, a goose, and a bag of beans. On his way home, the farmer came to the bank of ...
855 views

### How did she do that?

The King wants to test his 2 very smart advisors Sadin and Lena. In the courtyard he sets up 4 closed wooden boxes on a table. All are the exact same size. In front of each box there is a name plate. ...