Questions tagged [strategy]

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

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10 votes
1 answer
241 views

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 ...
  • 654
-1 votes
1 answer
92 views

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. ...
7 votes
5 answers
854 views

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 ...
2 votes
2 answers
398 views

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 ...
  • 29.5k
3 votes
1 answer
292 views

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 ...
  • 29.5k
2 votes
1 answer
216 views

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 ...
-1 votes
1 answer
147 views

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 ...
  • 149
3 votes
2 answers
238 views

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.
  • 149
-1 votes
1 answer
145 views

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 ...
3 votes
1 answer
161 views

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 ...
  • 199
7 votes
3 answers
1k views

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 ...
  • 189
2 votes
1 answer
330 views

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 ...
4 votes
2 answers
425 views

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 ...
6 votes
3 answers
315 views

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 ...
3 votes
1 answer
284 views

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 ...
  • 1,270
14 votes
4 answers
2k views

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 ...
  • 243
7 votes
4 answers
632 views

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 votes
2 answers
356 views

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 votes
1 answer
208 views

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 ...
10 votes
0 answers
555 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, ...
  • 5,279
13 votes
2 answers
771 views

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 ...
  • 15.3k
24 votes
9 answers
5k views

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 ...
1 vote
1 answer
206 views

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 $3^n$ ...
  • 613
6 votes
1 answer
409 views

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 ...
3 votes
0 answers
219 views

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 ...
  • 139
3 votes
0 answers
161 views

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, ...
3 votes
2 answers
665 views

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? ...
  • 1,270
6 votes
1 answer
458 views

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
14 votes
4 answers
1k views

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 ...
  • 5,279
21 votes
9 answers
3k views

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 ...
  • 5,279
1 vote
1 answer
295 views

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 ...
  • 5,279
15 votes
2 answers
823 views

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 ...
  • 5,279
22 votes
3 answers
2k views

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 ...
  • 5,279
10 votes
2 answers
601 views

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 ...
  • 1,270
3 votes
1 answer
139 views

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 ...
10 votes
2 answers
827 views

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 ...
6 votes
3 answers
752 views

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 ...
2 votes
1 answer
152 views

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 ...
8 votes
1 answer
244 views

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 ...
2 votes
2 answers
167 views

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 ...
  • 5,182
3 votes
1 answer
368 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 This problem is based on a similar concept ...
  • 1,270
4 votes
2 answers
805 views

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, ...
5 votes
2 answers
900 views

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 ...
  • 337
2 votes
1 answer
185 views

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" ...
  • 6,724
5 votes
0 answers
256 views

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 ...
9 votes
1 answer
304 views

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 ...
  • 6,724
2 votes
2 answers
268 views

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 ...
7 votes
1 answer
389 views

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 ...
4 votes
0 answers
226 views

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....
28 votes
12 answers
12k 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 ...

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