Questions tagged [strategy]

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

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6 votes
1 answer
330 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 ...
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3 votes
0 answers
193 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 ...
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3 votes
0 answers
136 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, ...
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3 votes
2 answers
641 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? ...
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  • 1,085
6 votes
1 answer
430 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/...
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12 votes
2 answers
535 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 ...
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  • 4,883
19 votes
9 answers
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 ...
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  • 4,883
1 vote
1 answer
276 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 ...
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  • 4,883
15 votes
2 answers
748 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 ...
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  • 4,883
22 votes
3 answers
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 ...
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  • 4,883
10 votes
2 answers
503 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 ...
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  • 1,085
3 votes
1 answer
123 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 ...
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9 votes
2 answers
806 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 ...
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5 votes
3 answers
739 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 ...
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1 vote
1 answer
139 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 ...
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7 votes
1 answer
226 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 ...
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2 votes
2 answers
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 ...
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3 votes
1 answer
358 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 ...
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  • 1,085
4 votes
2 answers
782 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, ...
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5 votes
2 answers
879 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 ...
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  • 285
2 votes
1 answer
145 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" ...
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  • 3,681
5 votes
0 answers
236 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 ...
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8 votes
1 answer
286 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 ...
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  • 3,681
2 votes
2 answers
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 ...
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6 votes
1 answer
306 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 ...
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4 votes
0 answers
209 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....
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27 votes
11 answers
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 ...
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1 vote
1 answer
182 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 ...
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  • 183
8 votes
2 answers
479 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 ...
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9 votes
0 answers
429 views

Can Alice form a unit square?

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 ...
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  • 4,883
9 votes
1 answer
833 views

Removing coins from a pile depending on the previous move

Alice and Bob play a game taking turns. There is one pile of $n\geq2$ identical coins on a table. Alice starts and with her first move she takes away at least one coin from the pile, but not all of ...
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2 votes
2 answers
373 views

Minimum number of questions?

This is an interesting puzzle which I've been racking my brain to solve for some time. I've found different variations of this puzzle but it does not seem like this one has been asked before. Here it ...
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11 votes
1 answer
802 views

Card game with equal piles

You and your friend have come up with a new two-player card game. There are 15 distinct cards numbered 1 to 15. The first player orders the cards in some order of his choice and places them face down ...
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7 votes
2 answers
644 views

Inferrence strategies for hidden pieces on a chessboard

This is a potentially off-topic question, however, the reason I'm asking it here is in the hope of gaining the perspective of puzzlers in tackling such a problem. That is, I am more interested in the ...
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1 vote
2 answers
124 views

Alice and Bob play neighboring sums game version 2

Alice and Bob are playing the neighboring game which is originally a single person game with the aim of getting the highest points at the end. You start with an empty 4x4 grid. At each turn, you can ...
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4 votes
0 answers
160 views

Police and Thieves

I played this game when I was young, but cannot find it online. It is played on a checkers board (e.g. the black squares of a chess board) between two players P and T. The game goes as follows: P ...
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  • 1,072
24 votes
13 answers
4k views

Can the cop catch the thief?

The cop and the thief, both mathematical points, live in an open interval $(0,1)\subset \mathbb{R}$. That is, their universe is a line segment of length 1 without the 2 endpoints. We know that both ...
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  • 4,883
6 votes
4 answers
283 views

Pawns and kings, what is the optimal play for white?

White to move. Source: wu riddles
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17 votes
1 answer
2k views

Blindfold Tic-Tac-Toe

You are playing the classic game of 3x3 Tic-Tac-Toe. You are blindfolded and you cannot see the grid, while your opponent can see it. When making a move you call out a cell. If that cell is taken you ...
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1 vote
3 answers
320 views

Egg drop problem for infinite floors [closed]

This is a modification of the infamous egg drop problem, which I have seen formulated as in the following manner: Given $e$ eggs and a building of $f$ floors, how can we find the lowest floor at ...
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  • 309
3 votes
1 answer
196 views

What is the most STAMINA-efficient strategy to escape the well?

You are roleplaying as an adventurer under the direction of a sadistic DM who has just thrown your character down a well. In order to escape, you have unlimited chances at a STAMINA check, difficulty ...
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  • 1,768
3 votes
2 answers
250 views

Three-player Nim

Suppose I'm forced to enter the game of nim with two players who are perfectly logical people. The rules is simple: We play a set number of rounds. In every round, a random number of marbles (between ...
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  • 31
4 votes
2 answers
455 views

Longest chain of checks and captures

On a standard size chessboard, with white to move, make a configuration of chess pieces and moves, so that with every move by white the black king repeatedly becomes checked. With every move black ...
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  • 6,596
12 votes
2 answers
853 views

Remove the magic from a 3x3 Magic Square

It's commonly stated that there is only one solution to the 3x3 magic square. This is simply because every variant found is simply a rotation, reflection or both of any other variant. Once such ...
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5 votes
3 answers
318 views

The Thieves and the Gold Bars II: Greed and Distrust

Two thieves, Bo and Jo, steal 7 gold bars and are driving away when their car is wrecked in an accident. They-and the loot- is intact. They are at Point A at 8 PM and must go to Point B which is 1 ...
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15 votes
2 answers
1k views

Scrabble with prime numbers!

How to Play Overall, gameplay is very similar to typical Scrabble; however, unlike typical Scrabble, you'll be using digits instead of letters (we'll cover your tile bag later). The objective is to ...
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3 votes
3 answers
273 views

Clearing the Snakes

While space was being cleared for a new building, a bunch of scitales came out of the water to munch on the worker's lunches, before falling asleep in the way of everything. You, having a knack for ...
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5 votes
1 answer
231 views

Can you destroy the kingdom without getting caught?

You are a shapeshifter that takes on the form of their victims and you've infiltrated the opposing kingdom's ranks, disguised as a lowly pawn . The opposing king has you presently assigned to the ...
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10 votes
2 answers
1k views

Strategies for Circuit Board Puzzle from NYT

The New York Times publishes a collection of variety puzzles each week, and new to the rotation recently is one called "Circuit Board". Here is an example of a puzzle (I added coordinates ...
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0 votes
1 answer
130 views

Catching the Vegetable-Goose [closed]

After an altercation involving giant bees, you have been sentence to some hard labour, specifically harvesting barnacle-lambs: a gourd-like fruit that grows geese in its shell While working, you get ...
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