Questions tagged [strategy]

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

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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 $3^n$ ...
834 views

Two Sheriffs and Eavesdroppers - 2

“The Two Sheriffs” puzzle was already discussed here Two Sheriffs and Eavesdroppers. This puzzle has only one difference: we have seven suspects instead of eight. Two sheriffs in neighboring towns ...
9k 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 ...
179 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 ...
496 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, ...
716 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 ...
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 ...
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 ...
120k views

Twelve balls and a scale

You are given twelve identical-looking balls and a two-sided scale. One of the balls is of a different weight, although you don't know whether it's lighter or heavier. How can you use just three ...
383 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 ...
199 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 ...
138 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, ...
649 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? ...
445 views

Solution or Origin of logic puzzle

This is not my puzzle and I do not know the solution. This was shared to me by a friend. Their former boss told them this riddle. I was told this question originated from Steven's Institute of ...
438 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/...
520 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 ...
547 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 ...
2k 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 ...
1 vote
282 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 ...
759 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 ...
11k 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 ...
1k 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 ...
312 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 ...
229 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 ...
3k views

A search game with 2016 numbers

Alice secretly chooses $2016$ integers $x_1,x_2,\ldots,x_{2016}$. Among these $2016$ integers, there are $2015$ that all have the same value, and there is only one number $x_k$ that takes a different ...
818 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 ...
128 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 ...
149 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 ...
746 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 ...
155 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 ...
1k views

How long can you survive at the devil's playground?

The devil has trapped you in his playground. The devil knows that you can't cross over the burning boundary of his circle, so he allows you to choose a position within the circle before he starts to ...
3k views

A two player game: Player who gets to 1000 or more first, wins

This is from the current weekly math challenge from the newspaper Le Monde. Alice and Bob play the following game, in turn: A number between $1$ and $10$ is written on a blackboard. At each of their ...
360 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 ...
790 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, ...
883 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 ...
869 views

The database of mini-facebook only has space for the data of 100 participants. These 100 participants want to establish as many mini-facebook friendships among them as possible. However, mini-facebook ...
9k views

Cutting circular pie into seven equal parts

your task is to cut this pie (shown below) into seven equal parts. What equal means by is size and shape you have only one knife of length equal to cakes diameter and a scale to ...
151 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" ...
686 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, you ...
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 ...
240 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 ...
287 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 ...
744 views

Two dimensional Mastermind

You have probably played the classic game of Mastermind with 4 pegs and 6 colours. It turns out that the codebreaker can always find the pattern in 5 moves or fewer. Now consider the 2D version of the ...
249 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 ...
210 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....
7k 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
1 vote
190 views

How can the princess escape the prince?

This is the story of the sister of the princess in this puzzle. I will shamelessly copy-paste some parts of this post. I have no reference to give for this version as I adapted a Computer Science ...
483 views

Form an equilateral triangle

Alice and Bob take turns to mark points in $\mathbb{R^2}$ (i.e. infinite 2D plane). Alice can only mark $1$ point on her turn, while Bob can mark $4$ points. They're free to mark their points anywhere ...
Alice and Bob take turns to mark points in $\mathbb{R^2}$ (i.e. infinite 2D plane). Alice can only mark $1$ point on her turn, while Bob can mark $N$. They're free to mark their points anywhere as ...