# Questions tagged [strategy]

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

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### Blindfolded tic-tac-toe with a twist

You're playing tic-tac-toe and you're blindfolded. The objective is to never lose, winning when given the chance under the classic ruleset of the game. Furthermore, an observer who is only aware of ...
225 views

### Strategy for solving "Hypatian Enigma" puzzle (all lines add to 38)

The "Hypatian Enigma" puzzle consists of 19 hexagonal blocks numbered 1 through 19. The blocks are arranged in 5 rows. The first and last rows have 3 blocks, the second and fourth row has 4 ...
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### How fast can you win this (very stupid) game?

You and I get together to play the following (dumb) game: Two positive integers N and K are fixed from the outset. We both start the game with N coins and proceed to play some number of rounds like ...
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### Prisoners and warden game, again?

Source: There are 100 prisoners in a prison. As usual, there is a warden who loves to play games, hence offers the prisoners a chance to free themselves. He says There is a room with a whiteboard, ...
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### The Merchant's coin weighing [duplicate]

You're a merchant in the old medieval times, and a customer has come to you to buy something for 13 coins. You know him of course, like everyone in town, and you know he's a sketchy guy. Someone who ...
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### Rats & Snakes: Avoid being eaten, escape unharmed

I'm trying to create a puzzle for an RPG that involves a classic lever puzzle. It is presented as follows: There are four rooms, you start in the southern-most room (S). In this room are two closed ...
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### The Room Of Tiles

You are stuck in a room with 100 floor tiles, and a magic button which you can carry with you. There are three types of tiles: real, fake and nopey. There are at most 49 fake tiles, and there is at ...
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### Guess the Permutation

Let $p$ be a prime. I chose a secret permutation $a_0,a_1,...,a_{p-1}$ of $0,1,...,p-1$ unknown to you. Now, you can ask the following types of questions to me: Type $1$: Tell me two integers $i,j$ ...
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836 views

### More Catching of Cats

After my first puzzle on this theme was solved relatively quickly, here is a (trickier) follow up question in the same vein! The setup is similar - you are in a room with an infinite line of boxes, ...
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### Catching a Cat on an infinite Line

Upon entering a (very) large room, you are faced with an infinite line of cardboard boxes that are labeled, in order, by the nonnegative integers. In one of these boxes, a cat is hiding, but you do ...
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### Communicate square on a 3-by-3 grid by flipping precisely one of 13 coins

A coin is placed on each of the $13$ squares in the following diagram: Each coin may be showing heads or tails arbitrarily. An adversary points to a square in the $3\times 3$ grid. You must ...
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### Keys and Locks Puzzle

Let $a,b,n$ be positive integers in which $a,b\le n$. You are locked in a room, with $n$ distinguishable keys and $n$ distinguishable locks in it. You know that each lock can be unlocked by a unique ...
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### The game of 42: 10 cards to make 42

This is a game inspired by other recent questions. It is a 2-player game. The game is played with 10 cards numbered 1 to 10 and 2 positions or stacks. The game starts with all cards in stack 1. The ...
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### Pole, rope, and chasm

You come across a chasm. It's perfectly smooth, 50m deep, and 50m across, and too wide to go around. You have a pole that is 40m long, and as much rope as you need. How do you get across the chasm? ...
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### Winning chance in coins game with fixing

A player plays the following solitaire game. The game consists of as many rounds as are needed to produce a result. They have 20 fair coins, which may in any round be live or fixed; each coin starts ...
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### Is it possible to fill an arbitrarily large hex grid completely given these rules? #2

Based off of this. Lets say you have two players, Red and Blue, that alternate filling an arbitrarily large hexagonal grid of tessellated hexagons with pieces of their color. Hexagons can either be ...
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### Is it possible to fill an arbitrarily large hex grid completely given these rules?

Lets say you have two players, Red and Blue, that alternate filling an arbitrarily large hexagonal grid of tessellated hexagons with pieces of their color. Hexagons can either be filled or empty. A ...
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### Two prisoners and twenty marbles

Two prisoners are planning their escape. Their cells are locked with a padlock that must be opened with a 5-digit code (numbers 00000 to 99999). Each prisoner knows the code of the other prisoner's ...
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### The Alien Snails Experiment

Fictional Background Story (The Experiment): Two extremely fast and intelligent alien snails are randomly placed on two different points on an infinite plane, as an experiment by the cruel ruler of ...
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### Anna tries to make triangles from broken sticks

Anna and Boris play a game with a red stick, a white stick and a blue stick, each of which is 1 meter long. Anna starts by breaking the red stick into three pieces. Then Boris breaks the white stick ...
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### Determine whether the counterfeit coin is heavier or lighter in two weighings on a standard balance

To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you! ...
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### Find the heaviest and the second heaviest coins

Each of 32 coins has a different weight. In 35 weighings on a standard balance, find the heaviest and the second heaviest coins. Clarification: Before you start to identify the heaviest and second ...
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### Magic: the Gathering – Scry-sort

Let me start with a formulation of the problem for people who aren't familiar with Magic: the Gathering. You have a stack of distinct cards face-down. You can apply the following actions arbitrarily ...
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### Making an expression with the numbers 1 to 100 odd (or even)

Anna and Boris play a game with the numbers from 1 to 100 written in order in a row. Anna goes first, and turns alternate thereafter. In each move, a player puts one of the operation signs +, − and × ...
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### Dumb robot on chessboard [duplicate]

A robot is placed on the square A1 of a standard chessboard and has to reach H8. It understands orders Up, Down, Left, Right. On some squares, there might be a cement block; is such a case, the robot ...
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1 vote
60 views

### Change all eight numbers to 1 [duplicate]

A solitaire game starts with eight numbers arranged in a circle. Each is either 1 or −1, and the choice is arbitrary. In each move, one can multiply any three adjacent numbers by −1. Prove that one ...
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### River crossing cats and dogs

A farmer and his $n$ cats and $m$ dogs are on one side of a river. There is a boat that can carry the farmer and at most $k$ animals at once. The boat doesn't move without a person operating it. The ...
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### You have magic, but sometimes the spell backfires: how to win regardless? [closed]

This one is convoluted, and I’m not sure if there actually is an answer. For a character in a story. You have magic and want to rig a sporting event. However sometimes the spell will backfire. The ...
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### Seven genuine and two fake coins

Seven genuine coins have the same weight. Two counterfeit coins also have the same weight. A counterfeit coin is heavier than a genuine coin. Identify the fake coins using a standard balance at most ...
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### Can you beat random?

It is known that one cannot beat a truly random player in Rock Paper Scissors. Here you will play a variant of the game. In this variant you are not allowed to play the same shape twice in a row. So ...
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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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### 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 ...
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1 vote
352 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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### 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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### 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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423 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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### 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
206 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 ...
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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
302 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 ...
858 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 ...
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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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### 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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### 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 ...
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