Questions tagged [strategy]
A puzzle whose solution is a methodological plan of action for realizing a specific goal.
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Equilibrium of differences
There is a subtraction equation written on the board, with three digits minus three digits, and the first digits both fixed. Alice and Bob need to fill in the remaining 4 digits (A~D below) using 4 ...
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100 prisoners and a secret number (potential solution) [closed]
Please ignore this question
I came across the brilliant 100 prisoners and a secret number and have a potential solution which I can't find any flaw with. Can you please let me know what I'm missing.
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7
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5
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Colorblind Mastermind
This puzzle is part of the Monthly Topic Challenge #7: Board games.
Inspired by the incident, I created a variant of Mastermind, although it wasn't actually intended for colorblind people. The main ...
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A bit complicated 20 card games v2
this is follow up question of A bit complicated 20 card games.
As the person who determines the order of the cards without changing the numbers on them, you want to make it more difficult for the ...
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A bit complicated 20 card games
In the game of 20-card games, the objective is to select a card or pass on it at every turn, with the goal of maximizing the sum of the numbers on the chosen cards. You have knowledge of the numbers ...
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Good and bad numbers of remaining mines
You've been tasked with finishing solving this Minesweeper board:
"How many mines remain?", you ask. "I'm just choosing that now, actually. Tell you what: I was going to consider every ...
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1
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Coin weighing - heaviest or lightest
I have 6 coins
Each coin has different weight
I can weigh as many coins at a time on a scale (for example I can weigh 3 vs 2)
I want to determine which coin is second heaviest or second lightest in ...
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Ball weighing - second heaviest
Let's say we have 6 balls, where all of them have different weight.
Find and describe the least weighings you need on scales to find second lightest ball and second heaviest ball.
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Hat and Earring Guessing Puzzle, with penalty for passing
You are in the final round of a game show with 3,999 other conteseants.
Here is the game: The host has blindfolded you at put a red, green or blue hat and red, green or blue earrings (not necessarily ...
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Trapping the Adventurer: the Value of a Gambling Game
An Adventurer is standing on the first of eight sequential platforms, ready to advance. But a Booby-trapper is positioning a trap to catch them in a game played over several rounds.
Each round, the ...
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Beyond earth and countries fighting for land
Consider 2 countries, A,B that have discovered a new planet, the size of Earth.
They have decided to split the planet into regions of minimum area $10^3 m^2$ and maximum area $10^5 m^2$, with borders ...
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Prisoners, apples & oranges - revisited
You are one of twelve prisoners, and the warden has a game to play with you.
In a room, there are twelve boxes, four of them contain two apples, four contain two oranges, and the rest one of each, but ...
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2
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Prisoners, apples & oranges
You are in a group of sixty prisoners, and the warden has a game to play with you.
In a room there are sixty boxes. Each box can contain either two apples, two oranges or one of each, but you don't ...
- 509
6
votes
3
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More Genuine and Fake Coins
I have 36 identical coins of which four, all weighing the same, are known to be fake. Fake coins are either all heavier than genuine coins, or all lighter.
At most how many weighings on a balance ...
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An overconfident grandmaster 2
The same grandmaster from An overconfident grandmaster decides to avenge his loss and prepares for rematch. He ends up in a winning position once again. He decided to place a bet again. He gives the ...
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Labyrinth of Teleporters
You find yourself in an empty room, with a few distinctly numbered elevated platforms on the floor; your only possession is a pebble that can easily be picked up and placed down. You step on one of ...
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Get the treasure from an island of knights and a joker
You've learned that there's treasure buried somewhere on a small island, but not exactly where. The island is a perfect circle with a radius of 25 meters. There are 15 islanders there, one of whom is ...
3
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2
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Dethy Mafia: Solved on the first day
Consider the game Dethy Mafia. The full rules can be found here, but this is all you need to know to solve this puzzle:
Each of the five roles "Sane Cop", "Insane Cop", "...
3
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1
answer
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Conclusively solving the extreme gerrymandering puzzle
This is the source of the following puzzle: CMU puzzle 20
When I look at the official solution though, I feel that the proof is not comprehensive. First the question (slightly rephrased to improve ...
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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, ...
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Decision Paralysis
This puzzle is part of the Monthly Topic Challenge #1: Restricted Title: xkcd 1xxx and is based on https://xkcd.com/1801/.
Protip: If you ever need to defeat me, just give me two very similar options ...
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3 blindfolded people dividing 9 coins
3 people are blindfolded and placed in a circle. 9 coins are distributed between them in a way that each person has at least 1 coin. As they are blindfolded, each person only knows the number of coins ...
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Generalization of twelve balls and scale problem
This problem is a generalization of Twelve balls and a scale problem. So I can solve and understand how things are going if we have 12 balls or 9 balls but how do I generalize? If say we have $3^n$ ...
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Guess the secret number
I'm thinking of a 2-digit secret number XY, where X is the first digit (non-zero) and Y is the second digit. You can make guesses to find it. If your guess is correct then the game finishes. Otherwise ...
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How to be bad at Wordle [closed]
There are many sites that help with solving Wordle, including some that use Information Theory to find an optimal solution There is also a New York Times app called Wordle Bot (behind their paywall ...
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Strategies better than brute force for solid-color areas of a jigsaw puzzle, where the pieces have the same general shape?
I have a jigsaw puzzle that I've been working on for a while where I have somewhat stalled out because the remaining pieces/areas are all solid black (or if there are color variations between them, ...
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Fastest way to helpmate
What is the fastest way to checkmate/helpmate white(A helpmate is a type of chess problem in which both sides cooperate in order to achieve the goal of checkmating Black/White) in this given position? ...
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Find the best plan for White
Here is a chess position to be solved. It is technically illegal, but for the sake of the puzzle, we'll ignore that. Find the plan for White that wins the game, with proper reasoning.
FEN: 1rkr1b1b/...
- 1,270
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4
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The mower's challenge
Weeds have taken over the roads. If mowed, they don't grow back, but unmowed weeds spread at speed 1 along the road. What's the minimum speed of the mower to get rid of all weeds? Roads are connected ...
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Catch the invisible and omniscient thief
The thief has stolen two powerful artifacts: the Cloak of Invisibility and the Glasses of the Oracle. Now they're equipped with both. The cop at the bottom, not knowing where the thief is, is trying ...
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Can you escape from two lions?
You're at the center of a circular arena. A pair of lions are at the border, planning to catch you. One of them moves as fast as you, but the other moves slower than you. The three of you are confined ...
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Can the lion protect the sheep from the wolves?
In a closed arena, three wolves are on the vertices of an equilateral triangle at the border. The sheep and his lion friend are at the center.
The wolf eats the sheep if their distance is $0$, and ...
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Dividing a piece of land
Alice and Bob try to divide a piece of land $D$, shaped in a perfect closed disk of radius 1.
Alice moves first to mark some finite (at least one) number of points in $D$.
Bob then draws any number of ...
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An overconfident grandmaster
Suppose you are playing a grandmaster with the White pieces and you are on the verge of losing the game.
The overconfident grandmaster offers you a bet: You will make two consecutive moves with White ...
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votes
1
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Sliding balls and stars on a 4x4 grid
You are playing a game on the following 4x4 grid. It contains balls, stars, empty cells, walls (solid blue squares) and target cells (T). Each turn you can slide all the balls and all the stars into ...
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Sliding balls on a 5x5 grid
You are playing a game on the following 5x5 grid. Each turn you can slide all the orange balls into one of four directions: left, up, right or down. A ball will continue sliding along a direction ...
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Sliding balls on a 4x4 grid version 2
You are playing a game on the following 4x4 grid. Each turn you can slide all the orange balls into one of four directions: left, up, right or down. A ball will continue sliding along a direction ...
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1
answer
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Sliding balls on a 4x4 grid
You are playing a game on the following 4x4 grid. Each turn you can slide all the orange balls into one of four directions: left, up, right or down. A ball will continue sliding along a direction ...
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1
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O princess, where art thou?
In the highest tower of her castle, a princess has N bedrooms which are arranged in a circle. She never sleeps in the same room on two consecutive days. Every morning she moves to another room by ...
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2
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Twenty (or fewer) questions to solve a three-digit code
In an episode of Odd Squad, the squad are left with five yes/no questions to get a three digit code out of a villain. Luckily for them, they have sufficient questions to guess the first number by ...
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1
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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
This problem is based on a similar concept ...
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votes
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Tic-Tac-Collatz
Have you ever heard of the Collatz conjecture? Just in case you haven't, I'll summarize it for you! Take any positive integer $n$, if it is even then simply divide it by $2$; however, if it is odd, ...
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Sand Castle Builder Glass Ceilings Puzzle
Disclaimer: This is not mine but taken out of the game Sand Castle Builder, but I can't find it anywhere in a distilled version and it's a nice puzzle :)
You are given N (6 is a good start) coins ...
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1
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No-Luck Riomino
Kris Burm's Riomino (or Tashkent Domino) is played with 25 identical dice that look like this:
The actual rules are as follows.
Each player rolls 12 dice that then serve as their "dominos" ...
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0
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The Jumbled Jaunts of Jormungandr
Jormungandr, the Snakebot of Doom has left New York. The world's armies and air forces have been decimated and cannot stop it. It has moved on from New York, and has flattened the following North ...
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1
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Be Paired or Be Square
8 white and 8 black dots are drawn on a piece of paper. Parcly and Tori take turns drawing edges, always between white and black dots not already adjacent (so the graph is always bipartite); the first ...
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How to solve sitting arrangement questions with 100% accuracy?
There are questions of sitting arrangement like persons sitting in a circular arrangement facing inward/outward or both, or a linear arrangement or box arrangement etc.
Sometimes a few data points are ...
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The Resistor Game Show
You were one of $n$ contestants chosen to participate in a game show. Each of you will secretly select a resistor of your choice, with a resistance between 0.01 and 10,000,000 ohms. Once everyone has ...
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By what rules are they changing the switch?
First of all, I don't know the answer to this question; I have some ideas, but nothing rigorous. Apologies if it's not on-topic. I have solved the puzzle now.
Suppose there is a light switch in a room....
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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 ...
