# Questions tagged [strategy]

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

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### 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 ...
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313 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 ...
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### 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 ...
• 185
1 vote
327 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:...
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### 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 ...
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982 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. ...
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465 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. ...
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400 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 ...
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593 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 ...
• 928
1 vote
178 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 ...
• 801
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### 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 ...
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### 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 ...
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### 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
265 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 ...
832 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. ...
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### Think in a Odd way

You have been captured for the crime of making a rude comment on Puzzling Stack Exchange and sent to Puzzlcatraz, a special prison for perfectly logical logicians. The warden is fair and decides to ...
186 views

### The Island of Arbitrary Puzzles [closed]

One day, an eccentric billionaire who’s obsessed with puzzles decides that he needs to open a theme park based on them. After throwing money at the problem for a few years, he finally finishes. ...
1k views

### Shortest time to cook burgers

Attribution: I remember seeing this type of question some time ago but don't remember from where. So I have redesigned the question. Hope that is OK. You have 5 burger patties to grill. Each side ...
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738 views

### How to Divide 1,987 Gold Coins Among 40 Pirates?

There are 40 pirates, designated as P1, P2, ...... P40, respectively. They aim to divide 1,987 gold coins using a two-stage division scheme: In the first stage, P1 initially splits all the coins into ...
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### Drowning Squirrel

On a super foggy day, a squirrel falls from a tree into a swimming pool. Due to fog, it cannot see any bank of the pool, unless it touches the bank. It is aware that the swimming pool is in the shape ...
• 1,063
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### Catch the mouse (Easy)

A mouse is at the center of a square. There are 4 cats each on the mid-points of different sides of the square. Mouse is looking to escape to any corner of the square. Mouse and cats have the same ...
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329 views

### A safe with 4 locks

You are trying to open a safe. There are 4 locks and 4 keys (red, green, blue and yellow). When you insert the keys into the locks, the safe will make k beeps, where k is the number of keys that are ...
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708 views

### Attacking Hyenas

$N$ Hyenas are standing on a plane region in a forest. At $t=-1$, they see dead meat nearby. Being selfish, at $t=0$, each Hyena attacks the Hyena which is closest to it. All pairwise distances ...
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299 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 ...
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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. ...
909 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 ...
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419 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 ...
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317 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 ...
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244 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 ...
160 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 ...
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256 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.
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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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358 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 ...
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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 ...
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637 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 ...
297 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 ...
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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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662 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 ...
371 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", "...
226 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 ...
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596 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, ...
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797 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 ...
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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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338 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 $3^n$ ...
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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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234 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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