Questions tagged [strategy]
A puzzle whose solution is a methodological plan of action for realizing a specific goal.
722
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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 ...
2
votes
2
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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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1
answer
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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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2
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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 ...
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1
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1
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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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4
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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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31
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3
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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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8
votes
3
answers
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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. ...
9
votes
3
answers
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A game of 101 stones—win at (not quite) all costs
In the land of Humilia, a tournament game is played between two players with 101 stones in a pot between them. On each turn, a player may take up to five stones from the pot (and must take at least ...
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9
votes
5
answers
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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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3
votes
1
answer
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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
Hint:
Hint 2:
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5
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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 ...
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1
vote
1
answer
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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
...
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12
votes
1
answer
2k
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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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16
votes
1
answer
565
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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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19
votes
4
answers
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6 Water Glasses Upside Down
There are 6 water glasses as shown in the picture below:
You need to turn all of them upside down with the rules below:
You have to choose any 5 of them at every turn.
Chosen ones need to be turned ...
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16
votes
4
answers
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The Mexican Standoff
There are three cowboys in a Mexican standoff against each other, named Juan, José, and Jorge.
Juan is the straightest shooter in the West, and can hit his target 100% of the time.
José, who has a ...
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votes
2
answers
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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 ...
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1
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1
answer
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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 ...
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13
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7
answers
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Using a balance scale the minimum number of times, find the median weight person
There are 15 person with different weights.
What is the least number of tries required to find the middle (median) weight person? How?
The only tools you have is your brain and a balance scale with ...
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17
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9
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Red and Blue in the Chocolate Fountain Room
Where: Hackanoogie Prison. When: Who cares?
The Master Key Keeper had had a really good day and in a fit of insanity and niceness decided to let all the inmates to go free if they manage to carry ...
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32
votes
4
answers
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Learning to Solve a River Crossing Puzzle
I have seen many variations of the following puzzle:
Once upon a time, a farmer went to the market and purchased a fox, a goose, and a bag of beans. On his way home, the farmer came to the bank of ...
5
votes
1
answer
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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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4
votes
2
answers
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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 ...
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1
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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. ...
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11
votes
2
answers
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Bicoloured 2048
I made a new puzzle game that you can play here. It is a variant of 2048 where there are tiles of two colours. You need to merge tiles of the same colour and value to increase your score. In more ...
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2
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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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6
votes
4
answers
739
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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 ...
- 1,063
14
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2
answers
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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 ...
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6
votes
2
answers
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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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2
answers
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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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3
votes
2
answers
330
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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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11
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How can one solve a Rubik's cube without relying on guides/algorithms?
I am wondering who is able to solve Rubik's cube just by thinking without knowing the rules behind it. As far as I know the inventor Ernő Rubik was professor of architecture and he intended to help ...
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votes
4
answers
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How many rolls on average to get N dice to all show the same value?
So for example:
if $N = 3$
I roll and get -> $1,2,3$
I re-roll the $2$ and $3$ -> $1,4,4$
I re-roll the $1$ -> $2,4,4$
I re-roll the $2$ -> $4,4,4$
In this case, it ...
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10
votes
1
answer
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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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4
votes
2
answers
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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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7
votes
5
answers
911
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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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9
votes
3
answers
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Block the snake from reaching points
Solution for Version 2 pending....
There is a $100\times 100$ grid. The upper left corner has coordinates $(1,1)$ and bottom right corner has $(100,100)$.
A 'snake' starts by occupying a single cell ...
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votes
1
answer
108
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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.
...
2
votes
2
answers
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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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3
votes
1
answer
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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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1
answer
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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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votes
3
answers
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Judgment-free construction of a playlist
Alice and Bob are planning a long car trip and need to come up with a playlist for it. For any given song, they have one of four opinions on it: "That's, like, my favorite song ever" (love), ...
CommunityBot
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7
votes
4
answers
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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 ...
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0
votes
1
answer
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Nine lemons, find the one that is different [duplicate]
You have 9 lemons, which all look exactly same. Same height, same color... There is no visible difference between any of them.
All lemons weigh the same amount, except for one, which weighs a little ...
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votes
7
answers
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Flashlight and 8 batteries
Source: this TED-Ed video.
A flashlight requires 2 AA-type batteries to operate. Both these batteries need to be charged for the flashlight to provide light.
We happen to have 8 batteries, but 4 of ...
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15
votes
2
answers
925
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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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votes
1
answer
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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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3
votes
2
answers
257
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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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votes
1
answer
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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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