Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness.

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9
votes
3answers
4k views

Is my sibling a sister [duplicate]

A male friend of yours wants to test if you are ok at Math and logical thinking, he says I am one of two children of my parents, and asks you to find out the probability that his sibling is a sister, ...
9
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3answers
2k views

How to cheat at cards

I have a deck of 52 cards on the table in front of me, in random order, each one randomly facing either up or down. I place one joker at each end, each of these again randomly facing either up or down,...
9
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5answers
1k views

How long will my money last at roulette?

I'm at the casino, standing next to a roulette table with a \$10 minimum bet. I want to stay here as long as possible, so I'm going to repeatedly make the minimum bet until I run out of money. I'm ...
9
votes
2answers
433 views

How to beat Count Dracula, part 3

This is a follow-up to "How to beat Count Dracula" and to "How to beat Count Dracula, part 2". Abraham Van Helsing and Jonathan Harker play a game against Count Dracula. The three players agree on ...
9
votes
3answers
422 views

A box full of unfair coins

Lolek and Bolek are arguing on whose turn is to take out the trash. They have a box with $n$ coins. when the coin $i$ is thrown, the probability that it lands on heads is $p_i$. They decided to make ...
9
votes
4answers
455 views

Number exchange game

Inigo and Vizzini are to have a battle of wits to the death. The rules are: Inigo is given two independent random numbers uniformly distributed between 0 and 1. Inigo chooses one of the numbers to ...
9
votes
3answers
1k views

A first choice die

You and your friend have met to play a game of dice. This is a very simple game where both players roll a die at the same time, and the player with the lower score pays a coin to the other player. In ...
9
votes
5answers
319 views

Find the optimal strategy for this dice game

You are playing a game: You have $6$ standard 6-sided dice that are all rolled at the start of the game. The sum of dice values is your score. Each turn, you can take any (or none) dice and reroll ...
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 ...
9
votes
2answers
675 views

What is the probability that all the bullets will be destroyed?

A gun shots bullets with different speed each second. The bullets form a straight line. The bullets keep their speed (not getting slower or faster). But if 2 of the bullets collide, 2 of them are ...
9
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3answers
657 views

Generalizing the “shooting puzzle”

Inspired by this puzzle. You have $n$ shooters having a duel, labeled $1, 2, ... n$. Each shooter has an accuracy of $k_n$, with each $k_n$ some probability in $(0,1]$, with $k_1 < k_2 < ... &...
9
votes
2answers
210 views

What are the odds that there is no solution on a given Set board?

I was playing a game of Set with a group. We had the usual twelve cards out and all agreed that there was no set. We then increased the number of cards to fifteen and were still unable to find a set....
8
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6answers
5k views

100 pieces 1 opportunity, choose wisely!

Say you have a cake that is cut into 100 pieces. One of the pieces has a hidden prize. 100 people take turns, each taking a piece in sequence hoping to find the prize. Note: I slightly modified (...
8
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7answers
2k views

Mr. Gardner's dessert

Mr. Gardner is facing the choice of dessert at his favorite restaurant The Erratic Chef. The cook tends to prepare great desserts, but is not very consistent. Mr. Gardner hates it when his choice for ...
8
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2answers
2k 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 ...
8
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7answers
1k views

7 Numbered Balls Game

You are walking on the street and notice a guy gambling with some other guys and you start to watch. The game principle is pretty easy. There are 7 balls in a pouch and you have 3 balls to draw ...
8
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2answers
409 views

Kangaroo on a square

A kangaroo is jumping around on the corners of the square ABCD. The kangaroo starts at corner A. In each jump it moves to one of the two adjacent corners, with a probability of exactly 1/2 for each. ...
8
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2answers
1k views

Keypad Door Lock

Your progress is barred by a locked door, it is clearly controlled by a keypad. with 10 digits (0-9) plus a button for ENTER and a button for CANCEL. You know several things about this lock: This ...
8
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4answers
982 views

Social Engineering (The Birthrate Problem)

The distant country of Toomalia has a birthrate of 67 boys for every 33 girls. In an effort to restore a 50:50 gender ratio in the country, Toomalian policymakers institute a mandatory new social ...
8
votes
2answers
842 views

Wait, it is worth it?

You went to a Casino, and saw a quite interesting stall. The cardboard besides the stall says: You first pay \$$5$ You have to toss the fair coin. If it lands heads, you can ...
8
votes
2answers
514 views

The asymmetric coin game

After finding a coin in her farm, Alice proposes the following game to Bob: Alice will flip the coin $n$ times. Bob will then flip the coin $2n$ times. If Bob manages to get the same amount of ...
8
votes
1answer
265 views

Mission: Impossible 2

Ethan Hunt is tied to a chair and can't get up. The super-villain Matt Fillimore stands in front of him. There's a gun. There's the barrel of the gun, six chambers, all empty. Fillimore is putting two ...
8
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3answers
797 views

The tile-flipping game

The tile-flipping game uses 6 tiles that have a white side and a black side. It starts with the tiles arranged in a line with their white side facing up. $$\circ \circ \circ \circ \circ \circ$$ We ...
8
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4answers
519 views

Circle inside circle

Here's a fun little math problem I made(by fun I mean no complicated methods needed at all.) You have a large circle with radius N with a cross in it to seperate the 4 quadrants(so that the figure ...
8
votes
1answer
305 views

Frog in the Well [duplicate]

A frog is trapped in a well, just 1 meter below the lip. On sunny days, the well is dry, and the frog is able to climb up 1 meter. On rainy days, the well is wet and the frog slides down 1 meter. If ...
8
votes
5answers
581 views

Two person game, choosing an integer between 1 and 30?

Suppose two players are playing a game. The first player chose an integer, n st. $n \in \left\{ 1,\ldots ,30\right\}$. The second player picks a different one. After that, a random integer x st. $x \...
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2answers
595 views

Help! I lost my marble(s)!

Tomorrow is the annual meetup for the Northwest Region Marble Lovers Association. The days festivities will include various marble games, admiring collections of marbles, a guest speaker who will talk ...
8
votes
1answer
105 views

Black-hat/white-hat logicians with a bell and a meal

At the 2020 yearly black- and white- hatted logician gathering, the following fun activity is organized. $N$ logicians will sit around a table, each wearing a black or a white hat the color of which ...
8
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2answers
318 views

Expected value of a milion dollar (equal?) division

I've heard this riddle a while ago and it is quite interesting. Say I've got two sons and one million dollars to spare. Each boy gets one dollar as a start and from there I give them dollar by dollar ...
8
votes
8answers
608 views

Five Haberdashers

This is yet another hat puzzle, but not one of the usual ones! Key differences/commonalities between other hat puzzles are emphasized. Five friends are going to go on a game show. When the game ...
8
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4answers
442 views

Which gun is Alice's best choice?

Alice, Bob and Charles are involved in a deadly three way duel game. Before the game starts, the referee prepares three guns for the players to choose from. She randomly picks three guns from a very ...
8
votes
1answer
258 views

Maximizing Product of Selected Cards

Jennifer is playing a game. The Ace through King of spades are taken from a standard playing deck and laid out facedown on the table. At any time, Jennifer can select two cards and reveal them, and ...
7
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9answers
7k views

Card probability problem [duplicate]

You have three cards in a hat. One is white on both sides, one is red on both sides, the third is white on one side and red on the other. You pull a card out of the hat and lay it down. The face is ...
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
436 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, ...
7
votes
1answer
250 views

Coin with two heads [closed]

I was at a job interview and got a question. You have a bag with 100 coins. One of these coins has two heads, other coins are regular. You get one coin from this bag, put it on a table and see head. ...
7
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5answers
2k views

Three 50/50 guesses

Three friends enter a quiz-show as a team, the final round of the show is all or nothing, they only get their prize if they can win this round. Three boxes labelled 1, 2 and 3 are placed in a room, ...
7
votes
3answers
2k views

No two heads in a row

Suppose I toss a fair coin a 100 times. What is the probability of not getting two heads in a row?
7
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2answers
1k views

Clash of arrows

During the last country fair, you have seen a weird arrow-shooter machine. Its shape is a regular polygon with $N$ sides of length $1$ and it fires one bolt from each vertex at the same time. The ...
7
votes
2answers
2k views

Find Coin's unfairness with only 4 tosses

There is a unfair coin and you want to find out its actual probability, to find the exact probability is actually not an easy task, you need to toss it many many times to get the close to actual ...
7
votes
3answers
631 views

Building the ideal Scrabble dice set

This is a genuine question and I don't know the "correct" answer to this. I'm also of two minds if it is really on-topic on the site. Finding the answer is surely "a puzzle" (if ...
7
votes
2answers
736 views

What are the chances you lost a nickel?

Yesterday you had 50 coins totaling exactly one US dollar in value. Somehow you lost one of those fifty coins on the way to the vending machine. Assume the likelihood of losing each coin (regardless ...
7
votes
2answers
207 views

Searching for the Covid vaccine

You have 1000 possible Covid vaccine candidates. You need to test them and find out if one works as quickly as possible. The test is to apply a small drop of a vaccine candidate to a sample, and ...
7
votes
1answer
655 views

Will You (Yes, You) Decide The Election? [closed]

You are the only sane voter in a state with two candidates running for Senate. There are N other people in the state, and each of them votes completely randomly! Those voters all act independently and ...
7
votes
2answers
340 views

Where the water is hotter

There are two perfectly identical boilers containing the same amount of water, switched on and working in identical environments. Both are setup so that the heating starts when the temperature of ...
7
votes
4answers
768 views

Born to lie, to live, to die

There is a race which has a truth gene. It consists of 3 alleles, namely T, F and O. A person inherits one allele from each of his parents, hence he/she has always exactly two alleles. For example, if ...
7
votes
1answer
167 views

Guessing the coin flips [duplicate]

Two prisoners, Alice and Bob, are captured by a dragon and placed in separate, isolated cells. The dragon then flips an infinite number of fair coins, and tells the outcomes of odd throws to Alice and ...
7
votes
3answers
169 views

Playing Chess Game of Chance

I still enjoy playing chess at the age of ninety four.Those contemporary opponents I used to play with have all passed away without me even getting even scores with any of them. On my spare time I ...
7
votes
1answer
165 views

The Attack on Fort Alpha

I made this puzzle up in 1999 when I was a student. Fort Alpha, on your border territories, was attacked by The Enemy. You don't know if it fell, or repulsed The Enemy's vicious onslaught. A totally ...
7
votes
1answer
194 views

The sadistic chieftain and the lethal truel game

In an adventure to a remote island, you get caught by the xenophobic locals and are about to be executed. But the tribe chieftain, known for his sadistic taste, suddenly changes his mind. "I'll ...

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