This tag is meant for questions about the mathematical principles behind games, riddles, or their possible solutions. If the answer is known to you please do not use this tag to "riddle" other users, but rather to ask about the correctness of a possible solution or ways to extend and improve an ...

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11
votes
5answers
294 views

Non-trivial “I know what number you're thinking of” [on hold]

Consider the following 'trick' (WARNING: very lame) Think of a number. Multiply this number by two. Add four. Divide the number by two. Subtract the number you were originally thinking of. I guess ...
4
votes
2answers
47 views

Meeting probability of two bankers: uniform distribution puzzle

Two bankers each arrive at the station at some random time between 5PM and 6PM (arrival time for each of them is uniformly distributed). They stay exactly five minutes and then leave. What is ...
4
votes
7answers
126 views

A logic riddle from “The Lady or the Tiger?” by Raymond Smullyan

Just to clarify, Case 3 and Case 4 must have flawed reasoning in order to reconcile my proof with the author's. I have been having a problem with a particular riddle from Raymond Smullyan and I can't ...
7
votes
0answers
102 views

5x5 Bingo Puzzle [Logical thinking problem]

5 people participate in a custom game. They are given blank cards, in which they have to fill numbers from 1-25 in a 5x5 table. Each card must contain all the numbers from 1-25 without repetition. The ...
6
votes
1answer
207 views

Why was I wrong about the monster-gem riddler

Every week I like to do the fivethirtyeight.com Riddler, an interesting and pleasantly challenging (at least for me) weekly math puzzle which comes out Fridays, with the answer and explanation to the ...
52
votes
10answers
22k views

Taking Seats on a Plane

This is a neat little problem that I was discussing today with my lab group out at lunch. Not particularly difficult but interesting implications nonetheless Imagine there are a 100 people in line to ...
2
votes
2answers
39 views

Awesome riddle including independence and exponential distribution [on hold]

The life cycles of 3 devices $A, B$ and $C$ are independent and exponentially distributed with parameters $\alpha,\beta,\gamma$. These three devices form a system that fails if not only device A fails ...
4
votes
0answers
46 views

Doing a magic trick with limited memory (from a problem solving course)

I got the following question in a problem solving course: There are four different objects lying on places 1, 2, 3, 4. A magician closes his eyes and someone from the audience comes. He switches ...
1
vote
0answers
72 views

Cat and a mouse on a circle

I hope this is the right plcae to post it as I'm not sure if the solution is mathematical. I saw this riddle on a board at the university and it seems that there's something I'm missing. It goes as ...
-1
votes
0answers
33 views

Need tools for this jigsaw-like problem [closed]

I would like to find a tool for this jigsaw-like problem. This one is to generate all possible planar graphs under some conditions on face labels/colors. As shown in the figure, there are 11 patterns ...
0
votes
1answer
28 views

Proof of coin and bag problem

There are 5 bags labeled 1 to 5. All the coins in a given bag have the same weight. Some bags have coins of weight 10 gm, others have coins of weight 11 gm. I pick 1, 2, 4, 8, 16 coins respectively ...
2
votes
2answers
920 views

Sudoku Puzzles and Propositional Logic

I am currently reading about how to solve Sudoku puzzles using propositional logic. More specific, they use the compound statement $\bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p(i,j,n)$, ...
1
vote
1answer
56 views

2048 Logic Puzzle

I thought up this logic problem related to the 2048 game. If all 16 tiles on a 2048 board all had the value 1024, how many ways are there to get to the 2048 tile? Here is what I am talking about in an ...
1
vote
2answers
748 views

Basic probability : the frog riddle - what are the chances?

A few days ago I was watching this video The frog riddle and I have been thinking a lot about this riddle. In this riddle you are poisoned and need to lick a female frog to survive. There are 2 frogs ...
21
votes
3answers
718 views

Sudoku with special properties

Sudoku is a puzzle, with the objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the grid (also "sudoku-blocks") contains all of ...
2
votes
4answers
1k views

the time at which the hour & minute hands in a clock becomes straight?

At what time exactly does the minute hand and the hour hand in a clock becomes straight between 7O'clock & 8O'clock. Iam getting the time is in between 7:05 and 7:10 but what after that. can it be ...
1
vote
0answers
42 views

Position games: how to fill a matrix with dominos? [duplicate]

Dominos of size $2 × 1$ can be placed on a $m × n$ board so as to cover two squares exactly. Two players alternate placing dominos. The first one who is unable to place a domino is the loser. I can ...
1
vote
0answers
60 views

Twisty Puzzle Solving Program

I'm writing a program to help me solve a twisty puzzle. In this case it's the face-turning octahedron. I'm representing the puzzle as a group with face twists as generators. The facelets are in a list ...
-2
votes
0answers
47 views

Number of Holes in a Number [closed]

In a recent puzzle I was working on, it asked to find the number of holes in a given number as a string. I was wondering if there was a mathematical solution to this rather than creating a list of ...
-1
votes
2answers
71 views

Random Room changing in the Hilbert hotel. [closed]

Let's say you have a Hilbert's grand hotel full occupancy. Assign each occupant a new room select randomly without regard to whether the room is assigned to someone. i.e. empty rooms, multiple ...
0
votes
0answers
59 views

Generalization of classic 3 roll die game to $n$ rolls

I am trying to generalize the following well-known 3 roll die problem: "We roll a single die no more than 3 times. We can stop immediately after the first roll, immediately after the second roll, or ...
6
votes
0answers
142 views

Separating Heavier from the Lighter Balls

This was posted Here and received a good answer, solving the general questions in either $n$ or $n+1$ moves, which is by just half a move on average "less good" than my manual solutions here. ...
2
votes
1answer
432 views

Counting the number of cubes in an isometric view

I had seen questions in a sample aptitude test, where an isometric view of an object made up of cubes was given, with some of the cubes removed. We were supposed to count the number of cubes present ...
2
votes
6answers
3k views

Proof that a common brain teaser is wrong (Burning Rope)

There is a common brain teaser that goes like this: You are given two ropes and a lighter. This is the only equipment you can use. You are told that each of the two ropes has the following property: ...
23
votes
6answers
6k views

100 prisoners and a lightbulb

100 prisoners are imprisoned in solitary cells. Each cell is windowless and soundproof. There's a central living room with one light bulb; the bulb is initially off. No prisoner can see the light bulb ...
13
votes
1answer
572 views

Cookie Clicker Chocolate Egg strategy

Introduction Cookie Clicker is a silly Javascript based web game. Here is a brief description of what you do: (description taken from this question: Explain a surprisingly simple optimization result) ...
6
votes
2answers
67 views

Monty Hall Problem extended

After seeing the popularity of the standard $3$ door problem, Monty thought to put a twist in the story. There are $N$ doors, $1$ car, $N-1$ goats. We need to choose any one of the doors. After we ...
1
vote
5answers
90 views

$3$ children riddle, compute the ages based on information given

A man has $3$ children such that their ages add up to some number $x$, and whose ages multiply to some number $y$, such that $xy = 756$. What are the ages of the $3$ children? Letting the ages be ...
0
votes
1answer
25 views

How to decide what numbers to show in a sudoku grid so that it's solvable?

Let's assume I've generated, from an empty board, a complete and valid sudoku board by some means. Borrowing from this question, let's say that board is: ...
4
votes
1answer
38 views

When are all pairwise sums consecutive?

What finite ascending sequences of integers $(a_1, \cdots, a_n)$, with $a_1 = 0$, are such that the sequence obtained by sorting all the pairwise sums $a_i + a_j\;\;(j > i)$ consists of ${n \choose ...
4
votes
1answer
925 views

Prove that there is only one way to make a square using all six tangram pieces

I am pretty sure there is only one way to make a square from the six tangram pieces: How can I prove this is the only way respecting all symmetries?
0
votes
0answers
43 views

An Interesting Variation to the “Pebbling a Checkerboard” Puzzle

Pebbling a Checkerboard (or chess board) was a puzzle proposed by Maxim Kontsevich in 1985, which was very interesting and fun to try, and you can find a great video on it at: ...
0
votes
0answers
70 views

100 people standing in a circle.

I've got this problem on my Graph algorithms exam and I still can't solve it!Here is the problem: At first there are 100 people sitting at a round table and neither one is enemies with their ...
0
votes
0answers
19 views

Convert Levenshtein Distance to percents

This is my first post here so please bare with me. I would like to ask if is possible to convert Levenshtein Distance to percents? There is similar question on StackOverflow which does have several ...
3
votes
4answers
179 views

Multiplication without figures

I have taken the 12th problem of this pdf, do you know any way to resolve it without using brute force? Simply I have to replace '*' of this multiplication below with correct digits, in order to have ...
9
votes
1answer
117 views

Place each number from 1 through 10 in a box…

The puzzle is: Place each number from 1 through 10 in a box. Each box must contain a number that is the difference of two boxes above it, if there are two above it. The ten boxes are ...
-2
votes
1answer
90 views

Puzzle: Players $A,B,C,D$ are in a line

Players $A,B,C,D$ stands in a line. Players $A, D$ do not move. round $1:$ player $B$ moves one distance closer to the midpoint of $A$ and $C$ round $2:$ player $C$ moves one distance closer to ...
4
votes
1answer
156 views

General approach to puzzles such as the “$6$ books puzzle”

Six different books $(A,B,C,D,E,F)$ of identical size are stacked as in the figure. We know $A$ and $D$ are not touching. $E$ is between two books which are both vertical or both horizontal. $C$ ...
0
votes
1answer
40 views

Does the first player have a winning strategy?

Two players play a game where they alternatively cross out a number from the numbers written on the board ($1-21$). They stop when two numbers are remaining. If thie sum of these two numbers is ...
5
votes
4answers
977 views

Puzzle about six travellers going through bridge above canyon with an oil lamp

There is a dark night and there is a very old bridge above a canyon. The bridge is very weak and only 2 men can stand on it at the same time. Also they need an oil lamp to see holes in the bridge to ...
22
votes
8answers
3k views

There is a subset of positive integers which no computer program can print

It's said that a computer program "prints" a set A ($A \subset \mathbb N$, positive integers.) if it prints every element in A in ascending order (Even if A is infinite.). For example, the program can ...
1
vote
2answers
53 views

Optimization with a Probability

Imagine two points in $ℝ^2$ at $(-1, 0)$ and $(1, 0)$. You would like to walk from one point to the next in the shortest distance possible. However, there is a line segment coming from the origin to a ...
2
votes
1answer
54 views

A puzzle concerning the axiom of choice and the reals

Recently I was told the following riddle: Let $A=(a_1,...a_n,...a_{2n},a_{2n+1})$ a 2n+1-tuple of real numbers with the following property: Whatever number $a_i$ is removed from $A$ the remaining 2n ...
4
votes
3answers
64 views

Time-and-Work and Motorcycle Tyres

A problem about motorcycle tyres, related to Time-and-Work or rate-of-work methods. This is not a homework question, nor, as far as I know, a contest question. It is intended as a challenge for Year ...
20
votes
0answers
143 views

Painting the plane red and blue: Is it possible for each unit circumference to contain exactly $n$ blue points?

I recently stumbled upon the following problem: Consider the plane: You may color each point either red or blue. Is there a way to color it such that each unit circumference (centred anywhere) ...
5
votes
2answers
196 views

Riddle similar to the 100 prisoners riddle, but different

The riddle goes like this: $\qquad$ There are $100$ prisoners standing in line, each with a number on their back. The numbers are all different, and range from $1$ to $101$ (i.e. one number is ...
1
vote
0answers
71 views

Will the boy outwit the teacher in this way? [duplicate]

In the book, Solving Mathematical Problems: A personal perspective (written by Terry Tao), he discusses a problem named (on Analytic Geometry Chapter, page 79): Problem 5.4 (Taylor 1989, p. 34, ...
11
votes
3answers
232 views

Smallest integer $k$ so that no Sudoku grid has exactly $k$ solutions

Inspired by this question, consider hints on a Sudoku board. A regular puzzle has a unique solution. It is clear that there are puzzles with 2 or 3 solutions, and therefore, I guess, puzzles with say ...
8
votes
1answer
112 views

Can this puzzle be solved without brute force?

Consider positive integers $a$ and $b$, where $a \ge b$ and the sum $\frac{a+1}{b}+\frac{b+1}{a}$ is also an integer. Find the sum of all $a$ values less than $1000$ that meet this criteria. For ...
1
vote
6answers
265 views

What's the solution to this puzzle? [closed]

I saw this on Instagram with no solution and was wondering what the answer is. I got $33$. $$1+4=5$$ $$2+5=12$$ $$3+6=21$$ $$8+11=?$$