Questions tagged [strategy]

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

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18
votes
3answers
7k views

Can you Turn MI to MU?

Using the letters M, I, and U, which can be used to create words. Can you turn MI into MU using in each step one of the following rules: Insert a U to the end of a word ending in I. e.g: MI becomes ...
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 ...
19
votes
11answers
48k views

6 Tries to Guess a Number Between 1-100

After every time you guess, you're told if you're right, too high, or too low. Is there a strategy you can use to guarantee you'll get it on your 6th attempt (or lower)? I know a strategy to get it ...
13
votes
7answers
2k views

Faulty computers

You have $99$ computers in a LAN room, and you know that at least $50$ are working. The others can be faulty. The only thing you are allowed to do is to ask computer $i$ the question "Is computer $j$ ...
-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 ...
34
votes
1answer
6k views

Coins on a table

John and Jane are playing a game. They both go to the bank and get 1000 euros in 2 euros. So each of them has 500 euros at stake. They then find a large rectangle table and decide who wins the ...
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 ...
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 ...
9
votes
2answers
3k views

Color the Table

Color each cell of the table with following rules: Yellow and Orange cells are adjacent, but Red and Black are not. Cell with number 3 is White, Green, Blue or Red and the cell with number 5 is not ...
4
votes
1answer
582 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 ...
20
votes
3answers
6k views

The lake monster

You are on a rowboat in the middle of a large, perfectly circular lake. On the perimeter of the lake is a monster who wants to eat you, but fortunately, he can't swim. He can run (along the perimeter)...
6
votes
1answer
501 views

Arranging cards in rows

This question appeared in an old math contest, and I seem to remember that the answer I had back when I first saw it was unsatisfactory. You have a deck of cards numbered from $1$ to $60$. First, ...
12
votes
2answers
1k views

How to survive, with statistics

You are kidnapped and your offender plays a game with you. In front of you are 2 boxes, containing a total of 50 white balls and 50 black balls. The kidnapper will pull out a ball from one of the two ...
4
votes
3answers
342 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....
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 ...
8
votes
2answers
627 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 ...
12
votes
2answers
3k views

A two-player game

This is from the current weekly math challenge from the newspaper Le Monde. Alice and Bob play the following game, in turn: A number between $1$ and $10$ is written on a blackboard. At ...
14
votes
5answers
2k views

Church charity lottery

Suppose you've rigged the church charity lottery so that you cannot lose (what a swell guy you are). There are 10 drawings, and you start off with 10 dollars exactly. At each drawing, you must chose ...
3
votes
1answer
390 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 ...
14
votes
7answers
2k views

Twelve balls on a scale, where one ball is lighter and another is heavier

Suppose you have twelve identical-looking balls. Ten of them are the same weight, but one is slightly lighter and one slightly heavier, in such a way that the weight of the lighter and heavier ball ...
4
votes
3answers
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
29
votes
7answers
110k views

Clever ways to solve Mastermind?

Is there any specific way to solve Mastermind? Apart from the first step that is pure chance, is there any way to continue based on the colors that you think are correct?
0
votes
1answer
229 views

Is there any specific way to play Solitaire?

I am interested in finding out if there is any specific way (algorithm) to play solitaire (not the card game)
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.
84
votes
7answers
18k views

Why does this solution guarantee that the prince knocks on the right door to find the princess?

I found this puzzle online: On the top floor of a castle lives a princess. The floor has 17 bedrooms arranged in a row. Each bedroom has doors connecting to the adjoining bedrooms as well as to the ...
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?
11
votes
1answer
9k views

How do I approach a “stuck” game of minesweeper?

I've played many a-game of minesweeper, and I frequently reach positions in which there is no logical, deterministic way to come to a conclusion about how I should solve the puzzle. How should I ...
5
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 ...
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 ...
0
votes
1answer
976 views

How could I have avoided this mistake in Minesweeper?

The puzzle grid pictured below is a prime example of the classic rush to judgment: I was so sure of my decision, but when I double-clicked to clear more cells, the cell to the left of the one I had ...
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 ...
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 ...
12
votes
5answers
27k views

Of these five approaches to starting a jigsaw puzzle, which one is fastest?

Of the following 5 strategies for getting started assembling a jigsaw puzzle: Assembling the border and connecting other pieces to it Working your way out from one corner Trying to assemble faces ...
5
votes
2answers
212 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, ...
53
votes
9answers
78k views

Twelve balls and a scale

You are given twelve identical-looking balls and a two-sided scale. One of the balls is of a different weight, although you don't know whether it's lighter or heavier. How can you use just three ...
15
votes
4answers
31k views

Strategy to solve the Missionaries and Cannibals problem

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 and ...
9
votes
3answers
2k views

Sliding Bolt Puzzle - fastest solution (time-wise)

This is a follow-up question for the Sliding Bolt Puzzle. If you have not solved it yet, you might want to head there first, as the extended discussion of its solution in this question will contain ...
50
votes
3answers
5k views

Sliding Bolt Puzzle

You are in a room with two adjacent doors locked by four sliding bolts. The bolts are movable and block only one door at a time; however, you do not know which bolt currently is blocking which door. ...
41
votes
4answers
4k views

Which switch goes to which bulb?

You are in a room with three switches, labeled $A$, $B$, and $C$. Initially, each switch is in an off state. In an adjoining room, there are three incandescent light bulbs. Your task is to ...
27
votes
4answers
17k views

Learning to Solve a River Crossing Puzzle

I have seen many variations of the following puzzle: Once upon a time, a farmer went to the market and purchased a fox, a goose, and a bag of beans. On his way home, the farmer came to the bank of ...