Questions tagged [strategy]

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

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5
votes
3answers
287 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 ...
11
votes
3answers
1k views

Who wins the AI-game?

Anna and Isadora play a game by writing letters on the blackboard. In the first round, Anna starts by writing down the letter $A$ or the letter $I$. In the $n$-th round with $2\le n\le 999$, Anna ...
7
votes
2answers
1k views

The Great Houdini's awesome card guessing trick (3)

The Great Houdini is performing again! Houdini has built up lots of reputation by showing his great card guessing tricks in [predecessor puzzle-1] and in [predecessor puzzle-2]. Everybody wants to see ...
2
votes
3answers
230 views

Drawing squares

Anafenza and Zurgo are playing a game. They have a playing board of $23*92$ squares. The idea of the game is to put a square(of any size) onto the playing board. The one who can't put any more ...
8
votes
5answers
1k views

The Great Houdini's awesome card guessing trick (2)

The Great Houdini is performing again! Everybody wants to see the famous magician and the magic show is sold out. Today Houdini shows the following sophisticated trick: A guy from the audience ...
5
votes
3answers
906 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, $...
36
votes
6answers
3k views

The subtraction game

Alice and Bob play a game that starts by Bob picking a secret integer $N\ge100$. Then the game goes through several rounds. In every round, Alice picks an integer $x\ge3$. Every number can be picked ...
6
votes
2answers
399 views

Jewels in the box

Professor Egghead participates today in a local game show. There are six jewels (a diamond, an emerald, a moonstone, a ruby, a sapphire, and a topaz), and there are six boxes that carry the numbers 1,...
12
votes
2answers
695 views

What's the optimal score in the MU-game?

Mary and Ursula play a game by alternately writing letters into a $9\times9$ grid. In every move, the player picks an empty square and then writes her initial letter (M or U) into it. Mary has the ...
-2
votes
11answers
12k views

What's your price for the eggs? [closed]

I came across this problem some years ago in a book (which I won't mention, and request others to not mention if they know). The solution is quite elegant and difficult to arrive at by mere trial and ...
6
votes
3answers
1k views

Ten unspeakable words

I wrote the following puzzle a couple of years ago. Since I no longer remember the solution, I feel it's a good enough puzzle to share. On accusation of littering, you and your assistant are ...
-2
votes
2answers
509 views

Binary manipulation game

I made a (for now, 2 player) game once that deals with manipulating binary numbers on a single list. Here are the rules. Rules For now, take $n=5$. If possible, provide a solution for generalized $n$...
8
votes
3answers
3k views

Queen chasing a knight (chess pieces)

There is a player who controls only a queen, while his opponent controls a knight. Both pieces start from opposite corners of the board. The aim is to kill the knight, without having your queen killed....
6
votes
2answers
465 views

Placing dominoes on a 3x100 checkerboard

Alice and Bob play a game by alternately placing dominoes on a $3\times100$ checkerboard (3 rows, 100 columns). Alice has the first move. A move of Alice consists in placing a $1\times2$ (horizontal) ...
10
votes
1answer
2k views

20 coins on the table

Two boys , Brian and Gabe, decide to play a game. They lay 20 coins on the table. Each player took turns taking 1, 2, or 3 coins. Whoever took the last coin won. Brian thought if he went first, he'd ...
-4
votes
1answer
756 views

Connect 4 Infinite

"Attention everyone! It is the final game of the Connect 4 championship! Billy and Sarah have played perfectly so far during this tournament, so in efforts to prevent Player 1 from being able ...
21
votes
2answers
2k views

Rook game on chessboard

A rook stands in the lower left corner of an $m\times n$ chessboard. Alice and Bob alternately move the rook (horizontally or vertically, through any number of squares). As the rook moves, it leaves a ...
9
votes
3answers
1k views

n - archers and many arrows

Suppose there are n archers in a standoff and want to kill each other until there is just one archer remaining. However everyone's chance of hitting (and thus killing) another archer is not fair. ...
3
votes
4answers
2k views

10 friends play a number game

You and 9 friends are playing a game, is there a way to force a win, if so, how, if not, what is the most optimal strategy? Gameplay: Each player can have a turn, or if he/she wishes, 2 turns. Each ...
18
votes
1answer
1k views

The Delayed Guessing Game

This is a similar but harder version of 6 Tries to Guess a Number Between 1-100. You friend gives you $n$ tries to guess an integer $x$, $1\le x\le 100$. Your guesses must be of the following type: ...
3
votes
1answer
389 views

$N_{max}$ balls in 3 weightings

This is a small generalization of well known 12 balls puzzle: You are given two-sided scale and some number of balls. All balls have the same weight but one. It is of a different weight, although ...
11
votes
7answers
2k views

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 ...
8
votes
2answers
624 views

Middle weight puzzle

There are 100 white and 101 black balls. All the balls have different weights. Balls of the same colour look the same. White balls are numbered from lighter to heavier (from 1 to 100). The same is ...
4
votes
1answer
581 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 ...
3
votes
0answers
114 views

Magical election of novices in a monastery [duplicate]

In a monastery, there is a special rite to elect new novices. All candidates (we're talking of a huge number, so let's assume an infinite amount) gather together in one hall that gets locked, so that ...
27
votes
10answers
3k views

One prize, infinitely many choices

Having reached the final stage of a game show, you face an endless row of doors labelled $1$, $2$, $3$, ... The game show host has selected a whole dollar amount, and has put this exact amount as a ...
6
votes
5answers
1k views

A mouse, Two mousetraps, Eight houses

You are chasing a mouse living in a row of eight houses. Every night the mouse moves from the house it is in, to an adjacent house, and stays there the whole day. Apart from this, you have no a-priori ...
5
votes
1answer
495 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 ...
2
votes
0answers
959 views

Strategy for solving many-clue detective puzzles [closed]

There are some puzzles that require sorting out many possible clues, such as The SErial Killer's killer and Mysterious Murder Mystery 3. They are often mysteries. What is a good way to organize ...
11
votes
2answers
388 views

No-Connecting-4

Imagine a game of connect 4 where Player1 wins by Player2 connecting 4, and Player2 wins by forcing the board into a filled board without any 4-in-a-rows. A tie happens if Player1 connects 4. Now Let'...
8
votes
4answers
2k views

How do we get those dang Illuminati?

The Illuminati just stole our office They shot JFK and have committed numerous crimes against humanity (not really) but we usually let that slide. But for stealing our offices, we have decided to ...
8
votes
3answers
2k views

A puzzle of trust and lies, allies and spies

Here is a puzzle involving distrust and asymmetric knowledge. (It was inspired by, but not exactly following, the board game The Resistance: Avalon.) There are ten resistance fighters trying to ...
8
votes
2answers
1k views

Entangled physicists

The anti-intellectuals have won the war, and under the iron rule of emperor Nonotin anyone who has been deemed too smart for their own good has been brought to labour camps. But most of the science ...
-3
votes
6answers
1k views

The Maze With An Unknown Size

You awake in the middle of a maze. You do not know how large the maze is. You do not know how many paths there are. How can you assure you get out in the shortest amount of time? This assumes the ...
15
votes
1answer
2k views

Elegant solution to the Magic Hexagon problem

The Magic Hexagon Problem A magic hexagon of order $n$ is an arrangement of close-packed hexagons containing the numbers $1, 2, ..., H_{n-1}$, where $H_n$ is the $n^{th}$ hex number such that the ...
5
votes
2answers
411 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 ...
6
votes
1answer
2k views

What is the lowest you can get in 2048? [duplicate]

What is the lowest score you can get in 2048? Creating high numbers is obviously bad, but what about not matching numbers? What is the chance of getting this lowest score?
8
votes
1answer
376 views

How to deal with conjugate-pair pseudocycles when solving Sudoku

In single-solution regular Sudoku puzzles, sometimes you may encounter a combination of possible cell solutions such as: {2,7} in A1 and A7 (same row) {2,7} in A7 and B8 (same box) {2,7} in B8 and E8 ...