Skip to main content

Questions tagged [puzzle]

For questions about the mathematical principles behind puzzle, games, riddles, or their possible solutions. Questions that are not strictly mathematical in nature should be asked on Puzzling Stack Exchange.

Filter by
Sorted by
Tagged with
0 votes
1 answer
62 views

Probability of 3 darts landing in the same half of the board [duplicate]

Problem: Find the probability of 3 randomly thrown darts landing in the same half of the board. More generally, if $n$ points picked uniformly randomly on a disk, find the probability of them lying in ...
Hex1729's user avatar
  • 81
4 votes
1 answer
151 views

Creative Algebra Net Problem Solving Question

I came across a problem that I found pretty tedious and difficult to answer and I would appreciate any views or solutions for this question. The diagram shows the net of a cube. On each face there is ...
Jonathan Xu's user avatar
-2 votes
0 answers
46 views

A hypothetical question about probability in a scenario of chicken and clay

I was watching a video on facebook where this chinese merchant sells chicken and clay in a wrappers, the wrappers all looks the same, each bets takes 10 dollars. Assuming that all the customer wanted ...
Guan Li's user avatar
4 votes
1 answer
72 views

Expected Number of Letters Typed Until MOO is Typed When Letters Are Typed Randomly

I'm failing to see the mistake in my reasoning for this problem. Here is the problem: Problem A man can only type two letters: M and O. He types M with probability $.4$ and types O with probability $....
Goku241's user avatar
  • 138
0 votes
3 answers
81 views

If the ends of a mile-long bar are pressed $1$ foot closer together, then how high will the midpoint rise?

Years ago, I read an arc-length vs chord length puzzle something like the following: A bar is $1$ mile in length. If you press the ends towards each other, allowing the center to rise, how high is ...
tejloro's user avatar
0 votes
1 answer
52 views

Question 4.31 Heard on the Street - Probability/Game Theory Question

The Question: Two players A and B play a marble game. Each player has both a red and a blue marble. They present one marble to each other. If both present red, A wins \$3. If both present blue, A wins ...
Connor Brown's user avatar
0 votes
0 answers
97 views

Gear Math Puzzle

The puzzle has 4 gears with 8 ends each, at each end it is randomly labelled with numbers 1-8. The gears are arranged in an 2 by 2 grid and the goal of the puzzle is to match the ends in between each ...
Vinn's user avatar
  • 1
0 votes
1 answer
60 views

expected value of high-low guessing game

Assume a number between 1-100 (inclusive) is chosen randomly. You then attempt to guess the number. On each guess, if you didn't get the exact number, you're told whether the guess is higher or lower ...
james's user avatar
  • 15
2 votes
1 answer
52 views

Relationship of the Egg Riddle solution to bisection and $\log(N)$ function?

I stumbled upon the video "Can you solve the egg drop riddle? - Yossi Elran" on the TED-Ed YouTube channel. What I found interesting is that in the solution, given that the triangle numbers ...
trojj's user avatar
  • 21
1 vote
0 answers
63 views

Generation of abstract reasoning puzzles

I'm trying to automatically generate abstract reasoning puzzles. My problem is, that I want to ensure that they "make sense", i.e. there is only one logical correct solution. Suppose, that ...
DasArchive's user avatar
2 votes
0 answers
47 views

Dividing $N$ coins into at most $K$ groups such that I can get any number of coins by selecting whole groups

Problem Inspired from Dividing $100$ coins into $7$ groups such that I can choose any number of coins by selecting whole groups . I am interested in the number of possible ways we can get such a split....
EnEm's user avatar
  • 1,181
1 vote
1 answer
69 views

Dividing $100$ coins into $7$ groups such that I can choose any number of coins by selecting whole groups

The problem goes somewhat like this: Let's say that we have 100 coins. Now, I have to split these 100 coins into seven different groups such that I can choose any number of coins only by selecting ...
user avatar
0 votes
1 answer
38 views

Russian roulette with re-spin intuition for asymmetric solution

Suppose we have a 2-player Russian Roulette game where the barrel is re-spun after every trigger pull. There is 1 bullet in a 6-chamber revolver. Should you choose to be first or second? I am confused ...
Decaf Custom's user avatar
0 votes
0 answers
19 views

A 2D circle (cake) is cut randomly with straight lines n-times. What's the expected number of pieces? [duplicate]

This is a Jane Street puzzle, and I will provide my working so far: I defined my 'random' cut as two numbers randomly selected from the range 0-2π mapped to the circumference of the circle, with a ...
Oscar Prestidge's user avatar
4 votes
0 answers
98 views

Which abelian groups and odd integers lead to a well-posed weights puzzle?

Consider the following puzzle (which I quote from here): In a collection of 101 balls, each ball weighs a whole number of pounds. If any one is removed from the collection, the remaining balls can be ...
Tim Seifert's user avatar
  • 2,243
0 votes
1 answer
47 views

Counterfeit Coins II (green book)

There are 5 bags with 100 coins in each bag. A coin can weigh 9g, 10g, or 11g. Each bag contains coins of equal weight, but we do not know what type of coin each bag contains. You have a digital scale ...
Connor Brown's user avatar
0 votes
1 answer
65 views

Logic Puzzle with truths & lies to questions

Puzzle : We are at a crossroad of 2 paths. One path leads to a swamp and one path leads to the treasure. At the crossroad we meet 2 people , of whom we know that 1 is always telling the truth and 1 is ...
Root Groves's user avatar
0 votes
1 answer
38 views

Achieving parallel wires with 180-degree rod rotations in an interconnected node system

We have 5 nodes on the left and 5 nodes on the right. You can imagine it this way: the nodes are on parallel rods and are connected with wires so that initially the wires are all parallel. We'll call ...
H-a-y-K's user avatar
  • 729
0 votes
2 answers
37 views

Seeking Book and Online Resource Recommendations for Problem-Solving

I'm looking for recommendations for books or online resources that emphasize problem-solving. While I don't mind if relevant theory is introduced along the way, I'm not looking for materials that ...
FieldHouser's user avatar
1 vote
1 answer
101 views

Generous Banker

You are at the bank and it is your lucky day. The banker is going pick random positive integer and you are too. You are both allowed to determine the probability distribution on the positive integers ...
Harsh's user avatar
  • 378
1 vote
1 answer
70 views

Game - two players take turn moving a marker to an adjacent square in a 9x9 grid

A marker is placed in the centre of a $9$x$9$ grid. Ann and Beth take turns moving the marker to one of the adjacent squares (one sharing a side) provided that this square has never been occupied by a ...
Abhinav Sood's user avatar
0 votes
1 answer
63 views

Minimum number of weighings

Akbar has four golden crowns that he can wear. He does not know their exact weight but knows that all of them are an integral number of grams. Birbal has a balance that displays the difference of ...
Harsh's user avatar
  • 378
1 vote
0 answers
40 views

Number of paths with $m$ good pairs of moves [duplicate]

Consider the set $S$ of all paths from $(0, 0)$ to $(n, n)$, formed by sequences of $2n$ moves of the form $(a, b) \rightarrow (a, b + 1)$ or $(a, b) \rightarrow (a + 1, b)$, such that at any point $(...
Harsh's user avatar
  • 378
2 votes
0 answers
75 views

Smallest number of groups

Eighty-four developers sign up to contribute to a public open-source project. You need to divide the developers into $n$ subteams such that each contributor is on exactly one team. Their personalities ...
Harsh's user avatar
  • 378
0 votes
1 answer
84 views

Largest collections of subsets [closed]

I need to find largest collection of subsets of $\{1,\ldots, 84\}$ such that each subset has size 5 and any two distinct subsets have exactly one element in common. Any help is appreciated, Thanks
Harsh's user avatar
  • 378
2 votes
1 answer
75 views

Are there instances of the "Lights Out" puzzle that can be solved faster with the square-root-of-NOT?

The "Lights Out" puzzle is a simple solitaire game played on an $m\times n$ grid of light bulbs and corresponding switches. Conventionally by flipping a switch at row $i$, column $j$, that ...
Mark S's user avatar
  • 432
0 votes
1 answer
38 views

Is there a technique for solving magic square-style puzzle using matrices on pen and paper?

The cells (in the puzzle below) must be filled with integers in {1,2,...,12} and they must all be distinct. The numbers on the outside indicate the sum of the cells. For example, the 1st row's cells ...
lightyourassonfire's user avatar
0 votes
0 answers
38 views

Finding a basis for an unknown-weights-and-balance puzzle?

I have a collection of unknown integer weights $w_1, \ldots, w_n$. I have a balance which I can use to weigh some pile of weights against some other pile to see which is heavier. Suppose I've done $n$...
user326210's user avatar
  • 17.7k
0 votes
3 answers
63 views

A crew needs to divide oranges [duplicate]

A boat sinks in the ocean and the 5 survivors each jump into a different lifeboat. They agree to meet on the deserted island pointed out in the distance. The next morning, the first castaway walking ...
whyu's user avatar
  • 19
0 votes
0 answers
52 views

Cinema Hall Seating Problem [duplicate]

There are n people in line to enter a cinema that own n seats. Each of the n people have an allotted seat in the cinema hall where they are supposed to sit. The first person forgets his/her seat ...
WizardGamer44's user avatar
0 votes
0 answers
34 views

Maximum Line Segments in an n × n Grid Without Loop formation

Exploring Proof for Maximum Line Segments in an (n * n) Grid Without Loop Formation Hello Math SE community, I am investigating how to maximize the number of line segments in an $(n * n)$ grid ...
omkar tripathi's user avatar
5 votes
3 answers
333 views

Point $D$ inside $\triangle{ABC}$ such that $\angle{ABD}=\angle{CBD}=6^{\circ}$,$\angle{BCD}=12^{\circ}$,$\angle{ACD}=18^{\circ}$, $\angle{BAD}=?$ [closed]

Point $D$ is in $\triangle{ABC}$ such that $\angle{ABD}=\angle{CBD}=6^{\circ}$,$\angle{BCD}=12^{\circ}$,$\angle{ACD}=18^{\circ}$, $\color{red}{\angle{BAD}=?}$ Can we find a pure elementary geometric ...
Adventitious Angles Qs Poster's user avatar
0 votes
1 answer
50 views

Calculating the minimum number of moves for an N*N number puzzle where you can swap any two tiles in one move

I've seen similar posts on the classic 8 or 15 number puzzles, where they have a blank tile and you can swap it with any orthogonally adjacent tile in a single move, but the puzzle I'm thinking of ...
AimeeJay's user avatar
2 votes
1 answer
139 views

Cutting one 2021-inch-long piece of wood into 2021 1-inch-long pieces using the fewest cuts

A 1x2021 plank is to be cut into 2021 unit squares. In each move, we can either cut through a single plank, dividing it into two (not necessarily equal), or through a stack of planks of equal length, ...
Jacob Phan's user avatar
-1 votes
1 answer
90 views

A Probablity puzzle on exiting from doors. [closed]

A person enters at $A $(see fig.), and after reaching the point of intersection, he chooses a direction randomly (including the possibility of turning around). If the person reaches an exit then he ...
Leibniz-Z's user avatar
  • 1,009
2 votes
0 answers
66 views

A first course in abstract algebra Fraleigh 8th ed Section 5 Exercise 65

Cracker Barrel Restaurants place a puzzle called “Jump All But One Game” at each table. The puzzle starts with golf tees arranged in a triangle as in Figure 5.29a where the presence of a tee is noted ...
점시맙's user avatar
2 votes
2 answers
140 views

Game of Pigeons - Probability Puzzle

The Problem: Alice and Bob take turns drawing a pigeon from a sack which initially contains $W$ white and $B$ black pigeons. The first person to draw a white pigeon wins. After each pigeon drawn by ...
Devansh Agarwal's user avatar
35 votes
4 answers
3k views

Mathematical justification of this "34" array trick

Frequently my son's teacher will show him fun little math "tricks." I usually take this as a moment to show him what's really underlying the trick (e.g., why two consecutive squares will ...
Randall's user avatar
  • 19.2k
3 votes
1 answer
82 views

You pick $N$ positive integers between $1$ and $M$ without replacement. If you add another number, what is the probability the maximum hasn't changed?

You initially start with all the integers between $1$ and $M$. You then pick $N$ of them randomly, without replacement, to generate a new set of $N$ non-repeating numbers. The maximum of this set is $...
Reasonable_Task's user avatar
3 votes
1 answer
124 views

Given 99 bags of red and blue sweets, is there a selection of 50 bags containing at least half of each type of sweet?

Assume you have 99 bags containing sweets of two kinds, say blue and red. Is it always possible to pick out 50 bags such that you have at least half the total of red sweets and half the total of blue ...
donvmax 's user avatar
1 vote
0 answers
77 views

How can i find the way to escape robot?

A scout robot is trapped at the center of a square with side length 1km. The scout robot can move at a speed of 3km/h. A guard robot is located at a vertex of the square, and patrols the boundary of ...
sorksnrnro's user avatar
2 votes
1 answer
61 views

A long-form mathematics books tetris questions

I am currently trying to solve the problem 1.4 from the book Proofs: A long-form mathematics textbook. This problem is about tetris, and it requires to prove that it is impossible to cover a 4x5 chess ...
pdaranda661's user avatar
1 vote
2 answers
145 views

Simple solution to random walk

The final score of a football match was 4:3 in favour of the home team. How many ways could the result have gone if there was a period of the match when the away team was leading? I have learnt of a ...
user555076's user avatar
1 vote
2 answers
66 views

Expected payout riddle: How to keep signature collectors from forging?

I made up this riddle, but I don't know how to solve it. Marissa owns a company that collects signatures. Marissa can only hire perfectly rational self-interested agents (as defined in game theory), ...
Jesse Lee's user avatar
  • 149
1 vote
2 answers
64 views

Puzzle: variant of Identify the counterfeit bag

You have 10 bags of 100 coins, and in all of them except for one, every coin weighs exactly 10 grams. However, in the counterfeit bag, all coins weigh either 9 or 11 grams. You need to identify the ...
Cidatama 0's user avatar
1 vote
1 answer
70 views

How to build a $6\times 6\times 6$ cube using 4-unit T-shaped pieces?

I am trying to solve a 3D block puzzle. It consists of 54 T-shaped pieces, each made up of 4 units, shaped as follows: $$ \square \\ \square\square\square $$ The goal of the puzzle is to build a $6\...
Evyenia Coufos's user avatar
2 votes
1 answer
114 views

Turning black-and-white boxes in a $4\times4$ grid to all-white with two operations

One of my friends and I do maths problems sometimes, but this one has had us stumped and we don't know what to do to solve it. A magic lock is made of a $4\times 4$ grid. The colour of each box on ...
edwardo's user avatar
  • 37
0 votes
5 answers
2k views

Robot Capture the flag

Two robots, Aaron and Erin, have made it to this year’s final! Initially they are situated at the center of a unit circle. A flag is placed somewhere inside the circle, at a location chosen uniformly ...
bigstreet's user avatar
  • 125
4 votes
1 answer
145 views

Formalising the problem and create a proof for the game "Waffle"

Waffle is an online game at https://wafflegame.net/daily. It consists in moving letters (swapping them) to recreate the original words. While you have 15 moves, it can be done in 10. I usually try to ...
user's user avatar
  • 1,125
1 vote
1 answer
54 views

General solution to a weighing puzzle

A specific form of this puzzle looks like this: There are $N$ piles of stones. Each pile contains stones that weigh the same. The possible weights are $1$ or $2$. The task is to determine the weight ...
Victor Lo's user avatar

1
2 3 4 5
67