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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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7
votes
6answers
997 views

Single-pile Nim with Three Players

Three perfectly rational logicians (Alice, Bob and a Quetzalcoatlus) are playing a game. (Charlie couldn't make it, so he asked the Quetzalcoatlus to fill in for him.) The rules are very simple: ...
7
votes
2answers
633 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
2answers
990 views

Find the term which does not fit into the series given below

C4T, F10R, I20P, L43N, O90L It can be easily seen that the first letters are 3rd, 6th, 9th, 12th, 15th and the last ones are 20th, 18th, 16th, 14th, 12th. But I cannot understand the logic of numbers ...
7
votes
3answers
2k views

Is it always safe to click first in the lower lefthand corner of a Minesweeper puzzle?

I always start a Minesweeper puzzle in Windows by clicking the cell in the lower left corner. Even though I have never seen a bomb there, how sound is this strategy? Is it possible that some time in ...
7
votes
3answers
1k views

Surviving Captain Nefarious

Captain Nefarious has captured you and two of your friends, Alice and Bob. Being a villain, he has a natural desire to monologue, so he sits you down (guarded, of course by his Largely Incompetent ...
7
votes
3answers
806 views

Dinosaur Egg Drop v2

This question is a little different and kinda follow-up version of Dinosaur Egg Drop 1- You have 100 story building and 6 Apatosaurus dinosaur eggs. 2- You have 81 story building and 3 ...
7
votes
1answer
833 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 ...
7
votes
3answers
406 views

Writing differences on a blackboard

The numbers 25 and 36 are written on a blackboard. At each turn, a player writes on the blackboard the (positive) difference between two numbers already on the blackboard, if this number does not ...
7
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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 ...
7
votes
3answers
580 views

The Ebbozonian coin weighing puzzle

In the country of Ebbozonia, there are only two type of coins: light coins and heavy coins. The weights of these coins satisfy the following properties: All light coins have the same weight $L$. All ...
7
votes
4answers
654 views

Higher or lower?

The game “Higher or Lower” is a simple one in which playing cards are drawn randomly from a deck, and the player has to guess whether each subsequent card will be higher or lower in value than the ...
7
votes
2answers
720 views

A generalization of Tyler Seacrest's “Three voting prisoners” puzzle

The following is a straightforward (but nonetheless not completely trivial) generalization of Tyler Seacrest's great puzzle "Three voting prisoners". There are $n\ge2$ prisoners that have a brief ...
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 ...
7
votes
2answers
257 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 ...
7
votes
2answers
829 views

Rational Smuggling

Archie, the archaeologist, has discovered 50 valuable gold coins, which he needs to ship to Zurich. Using an insured courier is expensive, costing $50\%$ of the shipment value. On the other hand, ...
7
votes
2answers
706 views

Solitaire Chess- Round 2

This is another Solitaire Chess puzzle like this earlier puzzle. Rules: Pieces move as in regular chess Every move must be a capture When there is only 1 piece left, you win.
7
votes
2answers
434 views

99 chips into more chips V2

This is follow up question of 99 chips into more chips, which is originally: You are at a casino in Vegas and you have earned 99 chips by playing poker! While you are checking out a slot ...
7
votes
2answers
676 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 ...
7
votes
1answer
360 views

Another 'Find the Path' Puzzle

Based on user477343's Find the Path puzzle I have produced a slightly larger puzzle based on a similar mechanic. Goal is as follows: Draw a continuous path between the two red dots. The path must ...
7
votes
1answer
534 views

Connect 4 Recursive

Here is a variant of the standard connect 4. There are seven connect 4 grids (size 6 by 7) numbered 1 to 7. Each grid has the columns numbered 1 to 7. The person who starts selects any one of the ...
7
votes
2answers
310 views

Taming a Bomb Puzzle (Part 1 of 3)

The Mechanics Ampera Bridge, the famous landmark of Palembang City is in danger! A terrorist has sticked a bomb in the middle of Ampera Bridge. The bomb cannot be removed and it can explode anytime. ...
7
votes
1answer
820 views

Tic Tac Toe Recursive

Related: Connect 4 Recursive We have a mega tic tac toe grid. Each of the nine cells of the mega grid has a smaller tic tac toe grid. In total we have 81 cells that can be filled. (Maybe imagine a ...
7
votes
1answer
634 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 ...
7
votes
1answer
233 views

Domino Tiling Game

Two players are presented an $n\times n$ grid. They take turns placing a piece on the board until no more moves are possible. The last player able to make a move is the winner. The pieces are $2\times ...
7
votes
1answer
462 views

Clearing the Robot Museum

The grand opening of the Collapsible Robot Museum is just 1 week away in the robot nation of Robotia. The museum is unique because shortly after the museum closes, the building collapses into a flat ...
7
votes
4answers
538 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 ...
7
votes
2answers
799 views

Cooperative guessing against an evil god

Following this: Cooperative guessing game: A standard deck of 52 cards is shuffled and split into two piles of 26 cards each. Two players cooperate, they must score as many tricks as possible. ...
7
votes
1answer
784 views

A Strategy Game Involving Conquering of Regions

This is a game that I saw in a book long ago. Unfortunately I cannot find the book now, and even if I can as I recall it does not provide a strategy. I will be very grateful if you can provide me a ...
7
votes
3answers
378 views

A game of Connect 4++

This is an entry to the 17th fortnightly topic challenge. Alice and Bob are playing connect four. Bob is tired of losing all the time, so he suggests changing the rules. He wants to drop 2 pieces ...
7
votes
1answer
394 views

The Robostanchion Exam (a puzzle about game-graph connectedness)

The St. Čapek Crowd Control Academy, June, 2115. Commander Gall is worried. On one hand, the graduating class this year is the most promising in the institution's history, every cadet's reasoning ...
7
votes
1answer
3k views

Additional solving techniques to diagonally symmetric Nonograms

Dear Reader: This question assumes you know what a Nonogram is. If you do not, I recommend reading the Wikipedia entry first. Nonograms have many solving techniques. One of the lesser used ones - ...
6
votes
3answers
3k views

Impossible 100 Balls Game

You are trying to make an impossible game where there are $100$ balls numbered from $1$ to $100$ and ordered in the worst case and put next to each other. The player is supposed to order the balls ...
6
votes
5answers
7k views

River Crossing Puzzle

There is a family which contains 4 members: Dad, Mom, Son, Daughter. They have a boat which carries only 100 kg at a time. Mom and Dad weigh 100 kg each, while Son and Daughter weigh 50 kg each. ...
6
votes
2answers
6k views

Strategy for solving Flow Free puzzles

There is an app on the app store called Flow Free. Basically, there is a grid with a few sets of colored dots, and you need to connect each dot to the other dot of the same color, filling up the ...
6
votes
2answers
716 views

Block the snake

On a $9\times10$ checkerboard with $90$ squares, a game proceeds as follows: First, you place $x$ rocks on the board. Each rock occupies a single square. No rock may touch the edge of the ...
6
votes
3answers
27k views

Solving Rubik's cube with one algorithm [duplicate]

I was wondering if it's possible to solve a Rubik's cube just iterating a single algorithm. It doesn't matter how complex the algorithm is (as long as it is less than 1 million moves), nor the time ...
6
votes
4answers
1k views

Filling the board with 0s and 1s

You are given a $9\times9$ grid board. You have 40 "$1$"s and 41 "$0$"s. You can put these numbers wherever you want on the board. After that, you will take the sum of the numbers in each row and ...
6
votes
3answers
273 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 ...
6
votes
5answers
4k views

Dots and Boxes- Best Move in Given Position

In the following game of Dots and Boxes, it is your move. Your opponent is a computer who will play perfectly. What is the best move, and why?
6
votes
3answers
428 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<...
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 ...
6
votes
3answers
373 views

Guessing game with infinity coin flips

Evan and Ollie are going to play a game as a team. The two friends placed in separate rooms, and then a coin is flipped infinitely many times*. Evan is told the results of the even numbered flips, ...
6
votes
5answers
280 views

Halve or diminish, and race to unity!

Alice and Bob are playing a game. In the beginning, the integer $9172016$ is written on a blackboard. In a move, a player, can: either decrease the number on the board by $1$ (i.e., replace $n$ by $n-...
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?
6
votes
2answers
265 views

“Balls in Boxes in a Sack” Weighing Problem

This puzzle is based on a competitive programming problem in SG NOI 2019. Let's assume there are $100$ balls with some labels (e.g. with $100$ different marks on them) having different weights of ...
6
votes
2answers
182 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 ...
6
votes
1answer
716 views

2 bishops versus a lone king

There are 4 pieces on the board, the white and black kings, as well as 2 white bishops (on differently colored squares). The only way a stalemate occurs is if the black king is not in check, but ...
6
votes
1answer
13k 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 ...
6
votes
2answers
146 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 ...
6
votes
5answers
408 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 ...