# Questions tagged [strategy]

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

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### The Troll, the dwarves and the gloves

A group of $N$ dwarves are caught by an evil Troll. As usual the Troll gives the dwarves a chance to escape if they solve a puzzle he created just for the occasion. Tomorrow morning each dwarf will ...
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909 views

### Unbalanced weight of boxes

You are given a traditional balance scale with two pans (no reading) and 6 boxes with the following properties: 1) the weight of each box is a positive integer number 2) if you put any number of boxes ...
• 11.8k
460 views

### Is Oh Tetris Oh! always a draw?

Alice and Bob were playing Oh-Tetris-Oh!, when they decided that every game must be a draw (played intelligently). Can you prove this? (Oh yes, the rules: A $10\times10$ grid, you can pick any ...
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471 views

### Wizard's Labyrinth

A thief has snuck his way into the wizard's castle. After traversing a plethora of magical traps and illusory walls, he finally spies the wizard's hidden stash of gems beyond the end of a long ...
• 1,580
1 vote
1k views

### The missing number

The integer numbers from 1-30 are mutually communicated to you one by one in a random order (one number about every 5 seconds). However exactly one of those numbers is not communicated. What is a ...
• 11.8k
435 views

### Quantum tic tac toe strategy

Most of us learn tic tac toe early in our life. Also, it is easy to find an optimal strategy for playing. How about Quantum tic tac toe? What is the optimal strategy for playing it? Rules On a ...
• 4,344
163 views

### How to effectively hide an earth rebooter thingy [The Good Place Season 4 spoilers]

This puzzle is unsolved. I don't know if there is a solution or how to solve it. I'm also not sure what type of puzzle this would be, so if anyone wants to correct the tags, feel free. Imagine you ...
• 133
557 views

### Crossing the desert

There are explorers that want to go as far in the desert as possible. One explorer can carry water for himself for 10 days. If they would all stick together, they would have enough water to go 5 days ...
• 121
2k views

### Find two coins using a balance scale

You are given 20 identical coins. 18 of those coins have a weight of 10g each, 1 coin has 9g and 1 coin has 11g. You are given a traditional balance scale with two pans (no reading). What is the ...
• 11.8k
507 views

### A flower-shaped robot-control puzzle

The goal of this puzzle is to find a sequence of max 5 commands that will move the triangle through the maze and visit all colored squares. Three types of commands can be used: F0 makes the sequence ...
• 685
3k views

### How to get a bowl with one liter of water

You are given a rectangular bowl with size 5 x 30 x 40 cm and you should put exactly one liter of water into the bowl. You go to your kitchen, where you can put the water directly into the bowl from ...
• 11.8k
165 views

### Find the lowest floor from which Venus eggs break [duplicate]

Venus gave you two eggs because she wants to test their strength. She lives in a 100 floor building and she wants to find the first floor above which the eggs break when thrown out of the window. ...
• 5,102
304 views

### Maximizing Product of Selected Cards

Jennifer is playing a game. The Ace through King of spades are taken from a standard playing deck and laid out facedown on the table. At any time, Jennifer can select two cards and reveal them, and ...
• 608
329 views

### A Bored Jailer and His Number Game

A bored jailer tells a prisoner that if he can guess a secret number he will be set free. The rules are given that the number will not be more than three digits in length and the prisoner may guess ...
672 views

### United States Towns/States Traversing by Name Puzzle

I’m new to puzzle solving in a structured way, so please go easy on me, but I thought the following was interesting (sorry if it’s not or seems like grunt work). I came up with this while staring ...
145 views

### Another how to kill 7 submarines

7 submarines are placed on an x, y grid - 0 to 111. They are located on whole numbered locations. Each submarine starts from any selected location with a given fixed speed and fixed direction, ...
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370 views

### Russian Roulette (Redux!)

You are challenged to a game of Russian roulette with a six-chamber revolver, but you and your opponent are allowed to change the outcome of the game in different ways. Here's how the game will ...
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196 views

### How to kill 7 submarines

7 submarines are placed on an x, y grid - from negative infinity to positive infinity. They are located on whole numbered locations. Each submarine starts from a location with a given fixed speed and ...
• 2,229
1k views

### 30 fake coins out of 99 coins v2

Follow up question to my other question, but totally different methodology required. You are given 99 coins which consists of 30 fake ones. You also have a digital balance scale with perfect ...
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2k views

### Can you catch the thief?

This was a puzzle I recalled from university a couple of years back. I don't know what the original puzzle is but if someone knows it, please let me know so I can credit the source. You are a police ...
• 223
2k views

### Find number 8 with the least number of tries

You and your friend plays a game. In this game, there are numbers written on the cards from 1 to 12 on one side (so 12 cards in total). The other side is blank. You can write anything on the blank ...
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972 views

### Line segments inside a square

A set of line segments inside or at the edge of a square with side length 1 should be positioned in such a way, that any straight line going through the square must touch or intersect at least one of ...
• 11.8k
2k views

### Three knights searching for a princess in a castle

There is a castle with rooms arranged in a 4x4 square grid. The princess living in the castle sleeps in a different room each night, but always one adjacent to the one in which she slept in the ...
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415 views

### Two knights searching for a princess in a castle

There is a castle with rooms arranged in a 3x3 square grid. The princess living in the castle sleeps in a different room each night, but always one adjacent to the one in which she slept on the ...
• 29.7k
242 views

### A short but stimulating robot-control puzzle

The goal of this puzzle is to find a sequence of max 4 commands that will move the triangle through the maze and visit all colored squares. Three types of commands can be used: F0 makes the sequence ...
• 685
613 views

### Marbles on a Mancala Board

I would like to introduce an ancient African board game I've just invented. Until someone comes up with a better name, it's called Marble Mancala. The rules are pretty simple: There are two ...
• 72.4k
1 vote
205 views

### Don't Fail MY Exam [duplicate]

A professor decides the following grading scheme in his class. After the final exam is graded, he keeps all the papers upside down on his table in a random order so that no student can recognise his ...
• 61
316 views

### The Wires Underground [duplicate]

There are ten wires that run underground across a river. Thus on each of the banks, there are ten ends of the wires. Unfortunately, given an end of a wire on this bank, one doesn't know which end on ...
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321 views

### 12 balls 1 scale with 4 groups

So, we all know the famous 12 balls 1 scale riddle. It has been here repeated many times, however, the provided solutions always start with splitting the twelve balls into three groups of four. This ...
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181 views

### Sleeping Beauty Study at the Institute of Mad Science [closed]

You've been approached to assist in the furtherance of SCIENCE as a research subject at the Institute of Mad Science (local branch)! The experiment you'll be involved with is called the Sleeping ...
• 696
184 views

### Positioning cards labeled with numbers from 0-9

Ann and Bob play a game. On a table there are 10 cards which are labeled with number from 0 to 9 each. Bob is allowed to change the position of the cards with a sequence of his preference. When he is ...
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182 views

### A pile of chips involving powers of 2

Ann and Bob play alternately on a pile of chips. On each play, any number of chips, which is a power of 2 (including 1=$2^0$), can be removed from the pile. Obviously the number of chips to be removed ...
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209 views

### A pile of chips involving primes

Ann and Bob play alternately on a pile of chips. On each play, either 1, 2 or 3 chips can be removed except if the number of chips is a prime number. In that case either 1, 2, 3, 4 or 5 chips can be ...
• 11.8k
395 views

### Reverse dots and boxes – Guess the last move

Alice and Bob are playing a game of reverse dots and boxes. The players take turns adding one horizontal or vertical line of size 1 in one free spot on the grid (marked with light gray lines ...
• 71k
248 views

I'm sure this has been asked before, but I tried searching and couldn't find it. I don't know the solution, and it is possible there isn't one. There is unsavoury pirate and an unscrupulous merchant....
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1 vote
168 views

The Square Spin series of puzzles is a bit abstract. There is quite a lot for newcomers to digest and getting started may be daunting. Even if you thoroughly read the rules and intend to attempt one ...
• 2,897
739 views

### Reverse dots and... cubes? - Snowflake edition

A Reverse dots-and-boxes puzzle inspired by @jafe Albert and Robinson are playing a game of reverse dots and boxes. The players take turns adding one plane in one free spot on the grid (...
• 21.6k
874 views

### Reverse dots and boxes, swastika edition

Alistair and Roberta are playing a game of reverse dots and boxes. The players take turns adding one horizontal or vertical line in one free spot on the grid (marked with light gray lines in ...
• 71k
844 views

### Reverse dots and boxes

Alice and Bob are playing a game of reverse dots and boxes. The rules are simple: The players take turns adding one horizontal or vertical line in one free spot on the grid (marked with light ...
• 71k
2k views

### Where are the Wazirs?

A wazir is a fairy chess piece that moves like a rook, but can go only one square.                   &...
• 131k
263 views

### I'm a Proper Divisor

Ann and Bob are playing a number game. Ann starts with the number 60. Then she subtracts a proper divisor of 60 from it. Bob then takes the number Ann made and subtracts one of its proper divisors ...
• 2,275
345 views

### 3D Chess - Stale NBA (kNight-Bishop Assault)

This is my very first chess puzzle. Any constructive feedback is more than welcome. Thanks! Introducing 3D Chess! To make things simple for the first time, we are using a $3\times3\times3$ ...
• 21.6k
594 views

### Red and White Squares

There are two grid boards with the dimension of 9x9 and 14x14, consist of all white squares. You are supposed to color some squares with a red color on the conditions below: In a board, if two square ...
• 29.9k
244 views

### You Sign Me Right Round (Extended Edition)

I wanted to ask more questions about variations on This Problem. If you hadn't seen that one, check it out. It's required reading (and probably more fun). In the original problem, these were the ...
• 3,552
285 views

### You Sign Me Right Round

This is a 9x9 grid, with a sign in the center cell like shown. You can add signs to this grid one at a time following these rules: Each sign placed must point to the next sign placed Placed signs ...
• 3,552
370 views

Teacher: You got a 0. Miles Morales: Is that...failed? Teacher: Listen. If you answer all questions on a multiple choice test randomly, you would get a 25%. This means the only way for you to ...
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489 views

### A programming puzzle without code

The goal of this puzzle is to find a sequence of max 5 commands that will move the triangle through the maze and visit all colored squares. Three types of commands can be used: F0 makes the sequence ...
• 685
135 views

### Leveling up and Getting Items! v2

This is follow up question to Leveling up and Getting Items! You are playing an online RPG game with 9 friends of yours (10 people in total) and in the game, there is a 2-player dungeon where you ...
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1k views

### 10 coins, 3 of them are fake

Inspired by some great weighing puzzles here (This being one of my favorites), I just made another weighing puzzle - I'm not quite sure how difficult or easy this one is. You are given 10 coins, 7 of ...
• 2,595