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# Questions tagged [strategy]

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

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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 ...
793 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 ...
1k 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 ...
813 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 ...
252 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 ...
541 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 ...
5k 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
172 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 ...
740 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 ...
324 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
578 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 ...
203 views

### Find the fake bar in 2 weighing [duplicate]

You are given 8 equal sized bars of silver labeled a to h. You know for a fact one of them is fake, and the only measurable difference is weight. However you do not know if the fake bar is heavier or ...
336 views

### Fake and genuine coins

There are 14 coins, numerated from 1 to 14, and presented as an evidence at the court. The first 7 are fake coins, and others are genuine coins. Fake coins have all the same weight and they are ...
198 views

### Rearranging Frogs [duplicate]

This is a small puzzle that I saw a lot as a kid but surprisingly haven't found on this site. Enjoy! You have six frogs arranged on seven lily pads in a line: three male frogs facing right on the ...
340 views

### How many subset intersections do you require?

Alice chooses a subset S of {A,B,C,D,E}. Bob makes a guess of any subset T and Alice tells him the number of elements in S$\cap$T. Bob has to continue making guesses until he can exactly determine S....
284 views

### Variant to Minesweeper

The following game is a variant of minesweeper: There is a 7 by 7 grid of squares. Each square either has a skull or a number indicating the number of squares containing skulls surrounding that ...
433 views

### The Lazy worker and the Punctual Boss

Before we start, idea blatantly stolen from this puzzle Tom has found another job, with another Boss who always arrives at the same time on weekdays. This boss, however, has a different policy. If ...
310 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 ...
261 views

### 100 prisoners' names in boxes, against smart warden

My question, which I do not know the answer to, concerns the classic 100 prisoners and 100 boxes puzzle, summarized below. The solution to this assumes the names are placed in boxes randomly, and gets ...
441 views

### Are there basic weighing puzzles requiring adaptive strategies?

Let us define a basic weighing puzzle as such: There are <number> identical balls, except one weighs <more/less/a different amount than the others> A balance scale may be used to weigh two ...
2k views

### When do missionaries and cannibals problems have solutions?

In the Missionaries and Cannibals problem: Three missionaries and three cannibals must cross a river using a boat which can carry at most two people, under the constraint that, for both banks, ...
114 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 ...
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 ...
1k views

### Coin division puzzle [duplicate]

You are blind and sitting at a table with 100 coins on it. You know exactly 50 coins are showing heads and the rest tails, and you can tell by feel where the coins are, but you are unable to see or ...
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 ...
518 views

### Get together to-get-her ;)

You are going to meet your school friends after four years. You are very excited about it. You have planned to gift everyone a chocolate. On the day of get-together you meet everyone and feel happy ...
1k views

### Dominating Furbles

This question was previously from the Haselbauer - Dickheiser Test For Exceptional Intelligence, a test that was previously available on the website www.highiqosociety.com, but was removed several ...
751 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, ...
670 views

### Battleship- Part 2

Mason is improving at the game Battleship. He's got this current game in the bag, or so he thinks. His opponent is Richard, whose method for placing his ships is completely random. Each side has 5 ...
326 views

### Rock-paper-scissors

Sheldon, Leonard and Wolowitz play a sizzling game of rock-paper-scissors for three players. In every round, each player simultaneously shows one of the three shapes. Rock beats scissors, scissors ...
582 views

### A variation of the poisoned bottle problem

Old story. The King has received X=950 bottles of wine, exactly one of which is poisoned enough to kill a man exactly 24 hours after ingestion. The King wants to feed some N prisoners some mix of the ...
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 ...
1k views

### The duck and the wolf [duplicate]

This is quite a famous one, I think, but hopefully not too famous. The phrasing is loosely taken from here. A duck finds itself alone in the centre of a round pond. On the edge of the pond stands a ...
795 views

### $\verb|Eight Circles|$

An entry in Fortnightly Topic Challenge #37: Rare and Endangered 1 Materials Pencil; Eraser; Blank A4 sheet of paper; and A ruler (also to use as a straightedge). Puzzle: Draw a square with a side-...
690 views

### Strategy for getting out of Hedge maze?

I often wonder: suppose I wake up one day and find myself in a maze of Hedges, like the one in "The Shining", what is the best strategy to get out of it? We can assume we have sunlight or a torch if ...
131 views

### Space saving dish washing

There are some stacks of dishes on the left side of the sink. There aren't any on the right side. A larger dish can never go on top of a smaller dish (this is valid for all stacks on both left and ...
338 views

### Classic 2 Guards But With 3 Doors Instead

So the rules are almost the same : You get to ask just one question to whichever guard you want to (just 1 guard; asking both guards is not allowed) There are 2 guards, one tells the truth and ...
613 views

### Monopoly Game Show: Is there a winning strategy?

We had left the TV on after the news finished and on came the Monopoly Millionaire's Club. I had no knowledge of its existence and watched some out of curiosity. The particular game in question was No ...
197 views

### $n$ buttons on a table

A generalization of Four buttons on a table: In a certain room there is a rotating round table, with 4 symmetrically located indistinguishable buttons. Each button can be either ”on” or ”off”, ...
186 views

### Optimal number of weightings in marble problem

Consider $N$ pieces of marble. The pieces of marble look identical to one another. One of the pieces is heavier than the other. In other words, out of the $N$ pieces, $N-1$ have the same weight and $1$...
345 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 ...
152 views

### Lattice hopping

A bunny is hopping around the plane. She must land on the following $25$ points on the main diagonal (multiples of 4): $(4, 4)$, $(8, 8)$, $(12, 12)$, $\ldots,$ $(100, 100)$, (The bunny can land ...
927 views

### Game against the Devil

While browsing through S.E you notice a spider crawl right out from under your keyboard! Startled, you twitch your hand and left clicked your mouse. You look up in shock as you notice that you just ...
230 views

### Another variation of the game of Nim

Two players set several piles of chips. The piles are arranged in a row from left to right. By turns each player takes one chip from one of the piles and adds at will as many chips as he/she wishes (...
319 views

This is an extension of the puzzle The Minotaur's Labyrinth which is inspired by the comments from histocrat. You are trapped (again) in a chamber at the center of the minotaur's labyrinth. There are ...
2k 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 ...
179 views

### How the best card can I choose?

Me and Varun playing a game of cards (standard deck of 52 cards). In which we distributed 5 cards to each other. Edit: We have seen each other's cards. We have to put the cards in a line one by one ...
656 views

### Optimal game of Bluff (not the wikipedia one)

Rules Basics 52 well shuffled cards are dealt equally to both players. Player 1 starts the first hand. The game consists of a number of rounds, which are played as follows. On each round, players ...
Stan (the clumsy coin flipper) is playing with his favorite toy: A set of $3n$ coins arranged in a circle, each one either heads up or tails up. He enjoys flipping these coins, but he's not very good ...