Questions tagged [strategy]

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

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6
votes
1answer
401 views

Checkers Against The King

The king has invented a new game called King's Checkers. The rules are simple, it's exactly like regular Checkers, the only difference? The king plays first and all his pieces are automatically "king",...
6
votes
2answers
719 views

Crystal Maze totem pole puzzle

The UK game show "The Crystal Maze" features a puzzle based around a totem pole. The contestant has four different coloured blocks which can be stacked up to make a totem pole. The blocks may be ...
6
votes
1answer
980 views

Frying Three Steaks

You invite your friend to the dinner. so you would like to prepare 3 fried steaks but you do not have much time to cook. You are trying to figure out how to cook all steaks perfectly (fried and ...
6
votes
2answers
489 views

Twilight Zelda Guardian Puzzle

I'm playing a game (see here), and in it is a puzzle, which I've made a TIKZ graph seen below for illustration: $\hspace{2.5cm}$ There is one player. The player ($\mathscr{L}$) moves from node to ...
6
votes
1answer
217 views

A mix of 2048 and Match 3

I was playing a game and thought of this problem: Rules There are 4 distinct tiles on a $6\times6$ grid. The game starts out with one block on the board. You can shift all the tiles in one of the ...
5
votes
7answers
665 views

The selling of the sheep [closed]

I do not know the answer to this puzzle, and I found it in some old files I had Many years ago, there was a shepherd with 3 children. One day, while talking to the owner of the herd, the shepherd ...
5
votes
5answers
458 views

Russian roulette

You are challenged to a game of Russian roulette. Your opponent places two bullets side by side in a six chamber revolver and spins the chamber. She explains that the game is single turn-based and ...
5
votes
2answers
759 views

A prime number game

Alice and Bob play the following game on a $9\times11$ chessboard. First Alice divides the chessboard into $33$ smaller rectangles of dimensions $1\times3$ and $3\times1$. Then Bob labels each of ...
5
votes
3answers
1k views

Hacking an electronic keypad v2

This is related to Hacking an electronic keypad. You are a spy trying to break into an enemy facility. The back door is protected by an electronic keypad lock. You know that this particular lock is ...
5
votes
3answers
2k views

Guessing a number game with a twist

Most of us have come across the problem in which a player chooses a number within a range $1-n$ and we have to guess that number by asking minimum no. of questions. That can be done by binary search(...
5
votes
5answers
549 views

Identify who is who between 3 persons who tell the truth and lie alternately

Dipsy tells the truth in 1 day and lies in the next day alternately. If today he tell the truth, tomorrow he will lying, 2 days later he will tell the truth, and so on. Lala tells the truth in 2 ...
5
votes
2answers
761 views

How much money can we make? v2

This is follow up question to How much money can we make? My five friends and I used to loan each other money all the time. But over the past several years we have moved apart. We don't trust ...
5
votes
3answers
1k views

Strategy for Modified Lights out

A friend of mine showed me a variation of lights out that they were interested in, and asked me if it would be possible to solve any given empty grid. This variation involves toggling not just the ...
5
votes
2answers
279 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 ...
5
votes
1answer
344 views

Another Secret Polynomial

Alice: Let's play a game, Bob! Bob: (sighing) What is it this time? Alice: I'm thinking of a polynomial $P$ with integer co-efficients. For any integer $n$, you can ask me what $P(n)$ is. Then, if,...
5
votes
1answer
16k views

What frequent patterns can be used to overcome Minesweeper obstacles?

Minesweeper, to those who do not know the strategies involved, is a difficult game. What patterns exist in the game which I can take advantage of? Meta-context: this question is an offshoot of ...
5
votes
2answers
201 views

Pick and roll and guess

The caretakers in a Home for the Golden Agers decided to have a guessing game for the old fellows. Two partner teams shall play the game and the winners shall have free access to the fridge for 1 week....
5
votes
3answers
297 views

Crazy queen in checkers

Checkers Checkers, also called draughts, is an interesting game. all pieces are placed on black tile and are all pawns at the start. When a pawn reach the final line, a powerful piece is created: the ...
5
votes
3answers
508 views

“Alien Love” Puzzle

There is a group of 10 aliens and each alien is either male or female. You don't know how many male or female aliens are in the group, but you know that exactly one of them is a "hybrid" male alien. ...
5
votes
3answers
963 views

The Great Houdini's awesome card guessing trick (1)

The Great Houdini is performing again! A guy from the audience arbitrarily chooses $52$ cards from a huge stack. He shuffles the cards and announces to Houdini that there are $a$ spades, $b$ hearts, $...
5
votes
2answers
136 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 ...
5
votes
2answers
598 views

Lead the murderers out

Imagine you are in a big hall. Except you, there are 20 other people. In the beginning, you have different pieces of paper: ...
5
votes
1answer
500 views

Optimal Building Strategy Puzzle

Suppose a general is in charge of a mining site with 5 workers and he has a total of 50 units of gold. Each worker is able to mine for him 40 units of gold per minute. The general is able to ...
5
votes
3answers
360 views

Playing the Square Chess

On an ordinary chess board (8x8) without any pieces on it as a starting position, two players will alternately place a pawn on any square (unoccupied) so that the first player that form a square (...
5
votes
3answers
526 views

Foolproof double betting

Just made up a problem. Have ideas, but no proof yet – came here for professional help. Tonight an important match of Metagame (box/football/baseball/chess) takes place. Everyone is hyped. Everyone ...
5
votes
4answers
508 views

Time traveler treasure Hunt

A time traveler is collecting treasures. He is using a space-time ship to transport between 5 different place-rooms. Each place has 1 precious treasure from the ancient times in each of 5 time zones. ...
5
votes
2answers
421 views

The Punic Wars are back!

The Roman Empire is at war with Carthage. Hannibal's army is composed of $a$ archers, $b$ ballistae, $c$ cavalrymen, $d$ dart-shooters, $e$ elephants and $f$ fighters. In each round of the battle, ...
5
votes
2answers
423 views

Land claim staking

It was traditional during the times of the Oregon Trail and the gold rush that men founding new towns were allowed to stake their claim on land upon arriving to the west coast. Suppose a man is ...
5
votes
2answers
222 views

How do I choose between letter possibilities for 2- and 3-letter words in a cryptogram?

I've tried to begin solving a cryptogram by making educated guesses from the context: position of punctuation, the presence of single-letter words, or assumptions about the frequency of the letter E, ...
5
votes
1answer
582 views

What will be the last Sudoku number to be filled?

When I am completing a Sudoku puzzle, there are always two last numbers to fill. Maybe it is just my puzzle solving approach or maybe it is inherent to Sudoku. I got wondering, would everyone who ...
5
votes
3answers
311 views

Dots and Boxes Part 2- Best Move in Given Position

This is a follow-up to my first Dots and Boxes question. It is just a little bit harder than the first one. Each one I post will be a bit harder than the previous one, and they will all be from games ...
5
votes
2answers
207 views

Simple game of dice - what is the optimal strategy?

The game is pretty simple, whoever reaches 50 first wins, but there are a few important details: 2 players, one die. Players take turns. Rolled values are simply added up If you roll a 6, however, ...
5
votes
2answers
221 views

Arranging a long line of cards

Annie has a very long line of cards, numbered from 1 to $n$, such that every odd card is face-up and every even card is face-down. The only way she can modify the line is by taking any segment of ...
5
votes
2answers
563 views

The Unknown Prison of Unknown Size

Inspired by The Circular Prison of Unknown Size by @MikeEarnest (Great puzzle, by the way!) The rules are almost same, so I won't waste time by rewriting them all here. (They're still valid, though.) ...
5
votes
1answer
289 views

Find k defective balls out of n balls

There are $n$ balls out of which $k$ are defective, where $k<n/2$. All defective balls have the same weight $w$, and all non-defective balls have the same weight $v$ with $v<w$. Determine all ...
5
votes
3answers
337 views

Strategy game on a blackboard

Adam and Bob play a game on a blackboard. A number $n>1$ is initially written on the board, and alternately they replace the number $k$ currently written with one of these: A) A positive divisor ...
5
votes
2answers
5k views

Is there an algorithm for the Rubik's 360?

Is there an algorithm to help me solve the Rubik's 360? Usually I just do it at random, but I rarely succeed.
5
votes
1answer
227 views

Answered it badly…on purpose?

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 ...
4
votes
2answers
942 views

Five Card Magic Trick with $N$ card Deck

Last week, I saw a magic show, and was the volunteer for climactic act. The magician introduced this act by talking about the Fitch-Cheney card trick, but then explained that she was going to do an ...
4
votes
5answers
2k views

Coin flipping game

An $8\times8$ checkerboard is filled with two-sided coins (that are blue on one side and red on the other side). The following picture shows three examples of a cross (multiplication sign): the five ...
4
votes
6answers
847 views

Best strategy to get all heads/tails from three coins

Your friend has 3 fair coins: a dime, a nickel, and a quarter. She places them on a table behind you. She can arrange then in any pattern of heads and tails as long as they are not all the same. You ...
4
votes
2answers
276 views

How many nodes in the network?

I don't actually have a solution in mind for these, but it seemed puzzly enough to bring to the table. Seems as though someone must have come up with this before, but if so, I couldn't find it when I ...
4
votes
3answers
555 views

Dr. G's Interesting Theorem on Playing Cards

Dr. G has spent his last weekend with analyzing $n$ number of cards which are numbered from $1$ to $n$. He has a fair shuffling machine for his cards and while playing and drawing some cards, he uses ...
4
votes
4answers
583 views

Rapunzel and the Prince

This is a simple mathematical puzzle, which I decided to improve a bit one year after posting. Some of the answers below consider slightly different, but equivalent setting of the problem. Rapunzel ...
4
votes
3answers
6k views

Is there any way to 'trap' my opponent on Connect Four?

I am trying to find out if there are any 'optimal' moves in the game, so as to trap my enemy to put his pawns in the place where I need them
4
votes
1answer
178 views

Turn based Number game

You and a friend take turns saying positive integers greater than one. You can't say a number that is a multiple of previous numbers or a sum of multiples of previous numbers. For example, if A says 3 ...
4
votes
2answers
995 views

Clock puzzle using 3 hands [duplicate]

I'm quite familiar with "clock puzzles", but only when the puzzle is such that all 3 hands start at 12:00. I recently tried this one: Over a 12 hour period, how often are AT LEAST 2 of the 3 hands of ...
4
votes
4answers
329 views

Limited functions calculator

There's a calculator with 10 functions exp, square, sin, cos, tan and their inverses. We need to convert 0 to 1 to 2 to 3 to -3. Note: Addition, subtraction, multiplication and division are not there
4
votes
2answers
397 views

Perfect strategy for the 2nd player in 'The coins on a table game'

I've just seen this and looked at the duplicate post it directs me to. I'm interested in a point raised in one of the comments in the answer, although it wasn't resolved in that question. It is ...
4
votes
1answer
618 views

Which one is the lightest marble?

There are 8 marbles that one of them is lighter than the others, and all other seven marbles have the same weight. There is a balance scale that you can use it twice or once. Is there any way to find ...