Questions tagged [strategy]

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

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7
votes
4answers
526 views

'Companion Planting' Logic Puzzle - Is there an elegant solution?

Problem: You're a vegetable gardener planning to plant out seedlings in a new garden bed, however your farmer's almanac has outlined a system of rules about what plants can and cannot be placed next ...
4
votes
1answer
273 views

Practical Strategy to beat the casino over the long haul [duplicate]

This is another iteration of beat the casino. That question did not require a practical, implementable strategy, whereas this one does. The rules are the same and I list them below. However, the OP ...
11
votes
1answer
3k views

Deceptive dice game

You must create a set of 6-sided dice and play a game with an opponent. The dice are like regular dice, but you can change the numbers on the dice. For example, regular dice have sides ...
15
votes
9answers
3k views

A search game with 2016 numbers

Alice secretly chooses $2016$ integers $x_1,x_2,\ldots,x_{2016}$. Among these $2016$ integers there are $2015$ that all have the same value, and there is only one number $x_k$ that takes a different ...
16
votes
1answer
583 views

Let's make Mango Orange Apple Juice!

Annie recently took a temp job at the famous juice shop, All About Juice. As is the case with most juice shops, creative mixtures are the norm, but the store's most famous product is still its ...
8
votes
3answers
864 views

Forty-six genuine and two fake coins

Inspired by this puzzle. In the country Dragonia, there are only two types of coins: genuine ones and fake ones. All genuine coins have the same weight, and all fake coins have the same weight. It is ...
6
votes
1answer
973 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
5answers
404 views

101 special numbers

There are 101 special positive integer numbers (1,2,3...) you need to find for this question. What is the minimum value of the biggest number of these 101 numbers that provides all sums of any two ...
11
votes
6answers
750 views

Lots of Gold Stacks and a Balance Scale

You are given X amount of stacks of golden coins, each stack consisting of ten (10) golden coins and a digital balance scale with perfect precision that shows how much difference between weights you ...
1
vote
2answers
539 views

Roulette tournament?

You have been invited to play in a French Roulette tournament. The tournament-specific rules are as follows: You start with 100 tokens Play lasts for 5 rounds Minimum bets based on color, low/high (1-...
15
votes
3answers
2k views

A way to beat the system?

I and my friend have always had an interest in gambling. Every week, we each have $£100$ to spare, and we like to bet it on football games at the bookmaker’s. In the long term, we (unsurprisingly) don’...
20
votes
4answers
1k views

Strategy to beat the casino over the long haul

$A$ and $B$ are attempting to beat the casino again, and the rules are the same: Each round, $A$, $B$, and the casino simultaneously decide to show a $0$ or a $1$. If all three numbers match, $A$ ...
5
votes
2answers
213 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 ...
3
votes
3answers
1k views

Sorting 4 numbers using “maximum” & “minimum” between 2 numbers

I'm having some trouble solving this thing. You're given an unlimited number of "black boxes" which will return the maximum or the minimum between 2 inputs. The goal is to compare/sort 4 numbers ...
35
votes
1answer
5k views

Say 100 and win

Our good friends that like games, Alice and Bob, play a game called "Say 100 and win". The rules are: In the beginning they use one regular 6 faced die to get a random number between 1 and 6. Let's ...
16
votes
1answer
2k views

A game with 330 pebbles

Anastasia and Barnabas play a game that starts with $330$ pebbles in a bowl. The game consists of two phases. The first phase looks as follows: First Anastasia announces an integer $A$ with $2\le A\...
14
votes
5answers
2k views

Three riders, two horses

We have three riders which need to travel some distance (say, 13.5km) through a rough terrain (no running, no skiing etc., only walking or horse trot), but they have only two horses. The speed of a ...
35
votes
5answers
2k views

Strategy to beat the Casino

Two players, $A$ and $B$, and the Casino play a game. It involves showing zeros or ones: each player picks $0/1$ and also the Casino picks $0/1$. If the Casino and both players $A$ and $B$ show the ...
7
votes
1answer
335 views

Minimum number of tries to find the balance!

There are 8 distinct weights and a two-pan equal arm balance scale, and you know the weights' weight order: the lightest is numbered as 1 and the heaviest is numbered as 8 and the rest accordingly. ...
7
votes
2answers
659 views

A matchstick game

On the table there is a $9\times9$ grid made of matchsticks, so that each of the $81$ little squares is bordered by exactly four matchsticks. Alice and Bob play the following game. Alice and Bob move ...
5
votes
3answers
395 views

Removing green marbles from the table

Alice and Bob play the following game that starts with $N\ge3$ green marbles on the table. Alice and Bob move alternatingly. Alice makes the first move. In this first move, Alice removes $x$ green ...
1
vote
1answer
622 views

How many doors are there? [duplicate]

You wake up in the center of a large, homogeneous, nearly-circular room. Along the edge of the room, are many doors, each looks identical to the last. When you stand at one door and look across the ...
8
votes
1answer
283 views

Two players playing the SET game

The SET game works with a deck of $81$ cards. Each card contains a set of symbols with four attributes: color (red, green, purple), shading (empty, striped, or solid), shape (oval, squiggle, or ...
6
votes
3answers
425 views

Guessing a number with 250 divisors

Alice and Bob play the following number guessing game. First Alice picks an integer $n$ with exactly $250$ positive divisors. These divisors include $1$ and $n$, and are denoted as $1=d_1<d_2<...
0
votes
5answers
678 views

One Hundred Prisoners and a Rubik's Cube

Say there are 100 perfectly intelligent prisoners (who don't have incredibly good memories) who are jailed for life (and also live eternally). The warden decides to play a game with them. There is a ...
10
votes
3answers
1k views

The Expedition Into The Ancient Cave

You are a archeologist and have taken 8 of your students on a expedition trip to a ancient cave to try and find ancient treasure. After you and your team entered the cave, you travel as a group ...
7
votes
1answer
620 views

Bottles of wine, poisoned with time

You are the ruler of a medieval kingdom. This time, you've decided to throw a royal party with 10,000 bottles of wine, rather than just 1,000. You remember the problems the courtier gave you with the ...
3
votes
2answers
154 views

Stakes on a table [duplicate]

Two men sat at a square table, each with a very large number of stakes. They had entered a contest of wits, or so they called it. The winner of the contest would be the last person to place a stake ...
21
votes
6answers
2k views

A game with 52 cards

Alice and Bob play the following game with two (identical) standard decks of $52$ cards. First Alice secretly arranges one deck of $52$ cards in a long row on the table. All cards are face-down, and ...
20
votes
2answers
1k views

Titanicker Tic-Tac-Toe

This is something of a follow-on to Hugh Meyer's enjoyable "Titanic Tic-Tac-Toe." Fortunately, our intrepid heroes Xavier and Oliver have wrested away a bit of wreckage that some fellow named Jack was ...
35
votes
1answer
1k views

Titanic Tic-Tac-Toe

Xavier and Oliver were playing tic-tac-toe on the Titanic using a wooden board and metal X's and O's. As the stern of the ship sank lower and lower they found, to their annoyance, that the pieces ...
7
votes
3answers
1k views

Sliding 10 coins to make them alternate

You have 10 coins: five heads, then five tails, all in a row. HHHHHTTTTT (H is for heads and T is for tails.) In each move, you can take two adjacent coins and ...
13
votes
2answers
2k views

The Finger Game

There's a game called the finger game. It's played by two players who each start with one finger on each hand up. The players take turns using one of their hands to tap one of their opponent's hands. ...
10
votes
4answers
1k views

Find the minimum number of guesses

Your friend will pick a 4-letter word and you will make guesses in order to find it. -A word can contain only the letters A, B, C, and D, and they can be used more than once. (AAAA-DDDD). -In your ...
17
votes
4answers
2k views

Two prisoners and the prison ward

Two prisoners are imprisoned at opposite ends of the prison. They cannot meet, nor exchange any kind of information. However, one day they are brought together by the ward who tells them: "I shall ...
13
votes
2answers
1k views

Empty one pile of balls and win

There are two piles of balls. One contains $5$ balls and the other contains $18$ balls. $A$ and $B$ are playing the following game: In each round, a player has to move balls from the larger pile to ...
11
votes
3answers
1k views

The game with cookies on a red and a blue plate

Aabzaari and Basharat play a game, alternating turns with Aabzaari going first. At the start of the game, there are 20 cookies on a red plate and 14 cookies on a blue plate. A legal move consists in ...
10
votes
3answers
223 views

The game of Shafiqa and Habibi

Shafiqa chose a positive integer number $X\le100$, and Habibi is trying to guess the number. Habibi can select two natural numbers $M$ and $N$ less than $100$ and ask about the greatest common ...
3
votes
2answers
648 views

Put the colours back in order

Background I wrote up a web-based sketchpad that lets the user pick from a series of colours, and tracks the recently selected colours for ease of use. I randomly had this idea as a personal puzzle, ...
2
votes
1answer
438 views

Another 2016 coins and a balance

This continues the puzzle "2016 coins and a balance". Again, there is a balance with two pans on the table. Again, the display on the balance tells the difference between the weight in the left ban ...
7
votes
2answers
629 views

2016 coins and a balance

On the table, there is a balance with two pans. The display on the balance tells the difference between the weight in the left ban and the weight in the right pan (measured in gram). There are also $...
7
votes
1answer
829 views

Heaps of marbles

Alice and Bob play the following game with two heaps of $10,000$ and $20,000$ marbles. Alice and Bob move alternatingly. Alice makes the first move. In every move, the active player may (i) either ...
13
votes
9answers
3k views

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 ...
22
votes
2answers
3k views

The Dwarves' Test

One day, the chief of the dwarves decided he wanted to test his tribe. So that night, he told the dwarves that he would paint on each dwarf's back a dot colored either red or blue. Each dwarf will ...
63
votes
3answers
4k views

A secret polynomial

Alice has a secret polynomial $P$ with positive integer coefficients. When Bob gives Alice a positive integer $n \neq 2016$, Alice replies with the value of $P(n)$. After doing this several times, Bob ...
6
votes
2answers
179 views

Ranking soccer teams

Louis van Gaal has compiled a list of 20 soccer teams, ordered by how good he thinks they are, but strictly refuses to share the ranking. Alex Ferguson knows the names of the 20 teams, but does not ...
14
votes
2answers
1k views

Removing chips from the table

Alice and Bob play the following game with $n\ge2016$ chips on the table. Alice and Bob move alternatingly. Alice makes the first move. In every move, the active player removes $k$ chips from the ...
15
votes
1answer
1k views

Clear board in Othello (Generalisation)

Based on Clear board in Othello If we have an $2m\times 2n$ Othello board ($m\geq n\geq 2$), and the centre $4$ squares have the usual starting position, then for what all values of $m$ and $n$ ...
10
votes
1answer
844 views

Clear board in Othello

Is there a valid set of moves in Othello that allows a win score of 64-0 for either player? And is there record of any such game in the past?
27
votes
7answers
2k views

23 Clones and Two Lightbulbs

Rise and shine, Mister Bond. James awoke to find himself yet again imprisoned by an evil genius. At least, that's what he presumed. He was alone in a room with a strange device: it consisted of a ...