Questions tagged [strategy]
A puzzle whose solution is a methodological plan of action for realizing a specific goal.
100 prisoners and a secret number
There are 100 prisoners numbered from 1 to 100. They know their own numbers. There is an interrogation room with a table and an envelope. The envelope contains a secret number - an integer chosen ...
A three-way bet
Alice, Bob and Carole are playing a betting game. At the beginning, they have 20 chips in the common pot. They move alternatively in the order of Alice, Bob and Carole. In their move, a player ...
How should you bet?
Alice and Bob are playing a betting game. Each has 20 chips to start with. They move alternatively starting with Alice. In their moves, they name a number $n$ and toss a fair coin: if head, they get $...
How many pilots do they need?
I have just watched this old riddle video from Ted-Ed. It basically asks how can three pilots coordinate their flights such that the professor (one of the three pilots) can circumnavigate the earth. I ...
Survive the infinite zombie attack II
Zombies are back again. Same as last time, You're at the origin, and zombies occupy the points $(100𝑖,100𝑗)$ for all integers $𝑖,𝑗$ except the origin, as shown below: The ratio of your speed to ...
Even and odd game variant
You are playing a game with your friend on a $7$x$7$ grid board. In every turn, you begin by putting a $0$ (zero) on any empty square on the board, and then your friend puts a $1$ (one) on a different ...
100 Prisoners and 3-state clock
100 Prisoners and a clock seems far too easy on the prisoners, so the exact same question, except that they must change the clock by exactly 4 hours: There are 100 prisoners who are given a chance at ...
Adding up divisors of integers
Alice and Bob play a game, taking turns. Alice starts and writes an integer between 1 to 10 on a blackboard. Then Bob adds any integer between 1 to 10 to this number and writes it on the blackboard. ...
1 lion, with a zebra and a fixed enclosure
Background See the puzzle Variant of lion and 100 zebras from @ghosts-in-the-code which remains unsolved years after it was posted. Several times in the last couple of years I've started to write up ...
retsubkcolB Spelled Backwards
How would you enter retsubkcolB spelled backwards into the comment box below and press the "Add comment" button (nothing will happen, as there's only 11 letters) using at most 10 clicks in ...
Variation of 100 coins puzzle (no flipping) [closed]
You have 100 coins laying flat on a table, each with a head side and a tail side. 10 of them are heads up, 90 are tails up. You can't feel, see or in any other way find out which side is up. You ...
How did the king pay the worker? [duplicate]
A humorous king pays his worker with one inch gold bar everyday. He had a $31$ inches gold bar and he paid the worker $31$ days of a month cutting it in just $4$ places. How is this possible? Taken ...
What is the minimum number of helpers that an explorer need to cross the desert?
There is a desert which can be crossed only by walking and this takes six days. The explorers of the desert can carry at most four days' water and food. If they want, they can take helpers with them. ...
How did the criminals escape from the jail?
There are $72$ criminals in a jail in $8$ cells as shown in the picture above. There are $9$ criminals in each cell. There are $4$ guards. Each of them watch over the $4$ corridors. As there is a door ...
The Box of Tic-Tacs
You were kidnapped and had no way of escape. The kidnapper opens the lights, and in front of you is an opened box of Tic-Tacs. He claims that he ate from 0-5 Tic-Tacs, (with 60 from the newly-bought ...
Catch the fugitive
The fugitive is at the origin. He moves at a speed of 100. You have a guard at every integer coordinate except the origin. A guard's speed is 1. The fugitive and your guards move simultaneously and ...
Can you survive this infinite zombie attack?
You're surrounded by infinitely many zombies. You're at the origin, and zombies occupy the points $(100i,100j)$ for all integer $i, j$ except the origin, as shown below: You and the zombies move ...
Peg Solitaire variant: from 48 on an 8x8 board
Looking at David Ahl's Basic Computer Games, one of the programs that caught my eye was One Check. It's like Peg Solitaire, which I've figured, but it's on an 8x8 board with the 4x4 inner bit hollowed ...
Can you find and capture a shapeshifter?
A town was invaded by aliens, and some of its residents were kidnapped and replaced by shapeshifters. You're tasked with capturing one of the shapeshifters. Here's the setup: There are 7 residents of ...
One vs many. Can white force a draw?
On an infinite chessboard there's a single white king and N black kings. The nearest black king must be K moves away from the white king. Given N, white dictates the value of (finite) K, then black ...
Can the fugitive escape?
A fugitive is surrounded by N police officers, with the nearest one at distance 1 away. The fugitive and the officers move alternatively. In a fugitive move, the fugitive can travel no more than a ...
Best strategy for stick-taking game
Rules of the game: It's a two player game. Moves will alternate between players. There are N sticks on a table. A value M is defined at the start of the game such that 2 < M <= N. On their turn,...
Judgment-free construction of a playlist
Alice and Bob are planning a long car trip and need to come up with a playlist for it. For any given song, they have one of four opinions on it: "That's, like, my favorite song ever" (love), ...
Outmaneuver your opponents in the duel
A, B and C are in a three way duel. Starting with A, they rotate in the order of A-B-C, each firing one shot at a time. They stand close to one another, so that each can kill one of the others or ...
Two players alternately name dates
Two players alternately name dates. The winner is the player who names 31st December, and the starting date is 1st January. If a player names Xst of Y Month, the other player can name the first of the ...
Flashlight and 8 batteries
Source: this TED-Ed video. A flashlight requires 2 AA-type batteries to operate. Both these batteries need to be charged for the flashlight to provide light. We happen to have 8 batteries, but 4 of ...
Sorting 6 boxes by selecting 3 boxes each time
There are 6 boxes, each containing a distinct number. You can select 3 boxes and the Oracle will tell you which box has the smallest number and which has the largest number of the three selected boxes....
What type of puzzle is "Room to Grow"?
I saw this game on Steam. They have a demonstration of the game in video form here, and here's the GIF I generated from that video (that's lower in quality and shortened due to the maximum 2 MB ...
Determine minimal number of moves to find cells on a square table 10×10 in which a treasure is hidden
In a 10x10 square table, two neigbouring 1x1 cells contain a hidden treasure. John needs to guess these cells. In one move he can choose some cell of the table and can get information whether there is ...
Playing tic-tac-toe by submitting your moves in advance
Suppose that, instead of playing in your turn, you have to submit in advance, an ordered list of the 9 board positions. Then a computer plays for you by using, whenever it is your turn, the leftmost ...
How to find the 2021st integer co-prime to 15
I recently saw a puzzle where you were to find the 2021st positive integer co-prime to 15 (it was phrased in terms of a game but this is the mathematical core). I wrote code to find the answer but can’...
Recover the answers of a test with n yes/no questions
Given a test with 𝑛 yes/no questions, a candidate is able to submit multiple solutions. For a given solution, the candidate gets feedback on the number of correct answers. The goal is to recover the ...
How to open the lock from this safe?
The puzzle is as follows: The figure from below shows a lock mechanism used to store sensitive data microfilms from a certain lab. This mechanism is magnetic and consists in numbered buttons which ...
100 boxes, only 50 attempts [duplicate]
There are 100 boxes in the room. In every box there is a note with some number from 1 to 100 (no repetitions).Person A comes into the room and checks all the boxes and notes inside them. He can (doesn'...
Is a fake coin lighter or heavier? [closed]
There are 16 coins, 3 of which are slightly heavier or lighter than the others. The counterfeit coins have the same weight but it is not known whether they are heavier or lighter than the genuine ones....
Outsmarting a Con (sales) man
During a fun filled golf event vendors have set up stalls offering different things to participants like golf gear, food, clothing etc. Participants can also win gifts in putting contests, drives and ...
Helping a team guess a correct number without prior knowledge [duplicate]
I am new here and would like to request your explanation for a riddle I saw. It is quite interesting but I don't understand it and would like your assistance to understand what's going on, how to &...
Variation of 100 prisoners [duplicate]
There are 100 prisoners, each prisoner is given a number between 1 and 100 without knowing which number, the number can repeat and not all of the numbers must be given. Each prisoner in his turn can ...
Holiday Madness: Draw a line through all the gifts
Can you collect all the gifts? The rules: Start from the star At each intersection are arrows. You can only move through the intersection in accordance with the direction of the arrow. (e.g If you ...
Looking for a strategy for assembling a Minesweeper grid knowing only the tiles but not their positions
This puzzle consists of 36 tiles. Each tile has a digit and may or may not have a mine. The goal is to assemble a 6×6 Minesweeper grid — in other words, each digit must equal the number of mines ...
Strategy for solving a 3D maze
Given enough time, you can solve a large 2D maze by simply following a wall. Is there any similar strategy for solving a 3D maze that can be used (no marking/memorizing places you've seen in the maze ...
Optimal Strategy for Matching Pairs
I found a reality TV show recently that I thought would make a fun puzzle. On the show are 10 men and 10 women that have been "matched by experts" (ie. randomly paired). Their goal is to ...
Social Distancing Colors - A New Type of Puzzle? [closed]
I think I just thought of a new type of puzzle: Social Distancing Colors. Each of the colors in the rainbow represents at least how much one has to distance by: Red is 6m, Orange is 5m, Yellow is 4m, ...
Another coin weighing puzzle, now including shifty coins!
You are, as you have been many times before, in some place that has a balance scale and 12 coins. 11 are all "normal" and stay normal, but one of these coins, however, is shifty -- as soon ...
10 Rats and 10 bottles, find one non poisonous bottle with least rats killed [closed]
There are 10 bottles of liquid, out of which 9 bottles are poisonous and one bottle of liquid is non-poisonous. The rats are to be fed this liquid one bottle at a time and rats die instantaneously. ...
Save the person in 14 moves on a cross
A person was trapped in a building, and you have to save him. You are a police officer and you will arrive at the building at 7 o'clock in the morning. The building looks like this: Every 2 minutes, ...
Optimal refueling strategy
On the way home from work, I want to refuel my car. There are 5 petrol stations along the way that all have a different price for petrol. I know that the prices will be in the range [A, B], chosen ...
Save the poor Gingerbreadmen!
The poor gingerbread men want to survive to Xmas (they don't mind being eaten afterwards). If at least one of them doesn't guess his hat correctly, they will all be cruelly eaten before Xmas. This is ...
Variation of 100 Prisoners' names in boxes
100 Prisoners' Names in Boxes The following puzzle is a variation of the above puzzle. Names in Boxes The names of 4 prisoners are placed in 4 wooden boxes , one name to a box, and the boxes are ...
Crossing a river with bonds and beefs
Here is a river crossing puzzle (note that whenever I use the term "colors", I mean the squares): Yellow and Red are on one side of the river, while Pink, Blue, Green and Black are on the ...