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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1
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2answers
33 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
52 views

A clown, a robot, a cowboy, and a mathematician are traveling through the woods when they come to a river they need to cross. [on hold]

A clown, a robot, a cowboy, and a mathematician are traveling through the woods when they come to a river they need to cross. There is a boat at shore that can only hold two people or one robot. ...
2
votes
1answer
48 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 ...
19
votes
0answers
117 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) ...
4
votes
3answers
63 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 ...
1
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0answers
66 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, ...
6
votes
0answers
86 views

Separating Heavier from the Lighter Balls

Classic Case I think we are familiar with the classic problem where we need to find one heavier ball among the rest identical lighter $n$ amount of balls using a scale and the minimum number of ...
1
vote
6answers
248 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 $33$. $$1+4=5$$ $$2+5=12$$ $$3+6=21$$ $$8+11=?$$
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2answers
25 views

Is it possible to decompose a triangle into quads without splitting edges?

By quads I mean four sided shapes. You can add vertex anywhere inside the triangle, but you can not add vertex onto existing edges, i.e., splitting them. I tried but currently it appears to be ...
8
votes
2answers
101 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 ...
5
votes
3answers
189 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 ...
-2
votes
2answers
49 views

Guess/Find a formula just given input and output. [closed]

I am looking a formula that given the three inputs, gives the output: $$(7,8,9)=7 \\ (1,3,3)=2 \\ (65,30,74)=56 \\ (9,9,7)=8 \\ (999999999, 999999998, 1000000000 )=999999998 \\ (775140200 ,616574841 ...
-2
votes
0answers
49 views

Prisoners and hats variation

Five prisoners are arrested for a crime. However, the jail is full and the jailer has nowhere to put them. He eventually comes up with the solution of giving them a puzzle so if they succeed they can ...
1
vote
1answer
61 views

An interesting puzzle from Jiří Matoušek's book

There is an interesting puzzle from Jiří Matoušek's book Invitation to Discrete Mathematics, problem 1.2.8, which confused me lots of time. Divide the following figure into $7$ parts, all of them ...
0
votes
1answer
48 views

How many tables needed

We invite $N$ person to a wedding, each new guest has to sit at a friend's table or at an empty table if he has no friend. If each couple of persons $\binom{N}{2}$ has a probability $p$ to be ...
3
votes
1answer
50 views

Number of vertices of a random convex polygon

Take $n>2$ random points, chosen independently with uniform probability on $[0,1]\times[0,1]$. What is the probability $P(n,k)$ that the convex hull of these points is a polygon with exactly ...
0
votes
0answers
20 views

Interrelated sets or numbers

Consider the ordered collection of digits base $10$ of length $m, A=a_1a_2a_3...a_m$. Let us look at some forms of inter-relation in these numbers. Here is an example of interrelation. Let vicinity of ...
3
votes
2answers
316 views

Solve 6 simultaneous equations for 8 variables puzzle

How to solve this puzzle? The image was sent to me with a caption in Chinese (解了一天了 帮帮忙吧… - googling leads to some solutions) and blank spaces where I have added letters. Separating each row and ...
1
vote
0answers
26 views

Solvability if two pieces of the fifteen puzzle are identical?

It's known that only half of all the permutations in the fifteen puzzle can be solved (in the sense of recovering the sequential order of numbers, with the empty slot in the lower right corner), for ...
2
votes
0answers
46 views

Candy Crush as an integer programming problem

I'm trying to model the basic version of a match-three game, where the player (has a maximum number of swaps) must swap any two adjacent gems (no diagonals) in an 8x8 grid of gems in order to match ...
2
votes
5answers
180 views

Puzzle About Cubes (from the book thinking mathematically)

I want to confirm my solution to the given problem (solutions were not available in the book) I have eight cubes. Two of them are painted red, two white, two blue and two yellow, but otherwise ...
1
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2answers
57 views

Clock Problem of logic [closed]

There is an analog clock that runs 90% of the normal speed of a clock.This clock will show the correct time exactly two times a day. Prove the following.
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votes
5answers
97 views

How To Combine 1,2,3,4,5 into 333? [closed]

I am trying to figure out how it is possible to combine 1,2,3,4,5 into 333. Apparently there exists some way that makes this work, but I am not sure how. 1,2,3,4,5 can only be used once, and I am ...
2
votes
1answer
55 views

Probability of prime numbers

Say we use the Euclidean construction for prime numbers and take a set $S$ solely containing prime numbers, so that $p_n$ is the greatest prime within S. What is the probability that $1+p_1 \cdots ...
1
vote
5answers
80 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 ...
9
votes
1answer
104 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 ...
0
votes
1answer
86 views

Probability Riddle

I was told a puzzle recently, and I can't figure out how to solve it. It went like this: You are a prisoner. You play a game with the guard many times a day. This game has a unique probability ...
1
vote
2answers
71 views

Loaded revolver puzzle.

This was a puzzle asked in one of the interviews. It goes like : There are 3 consecutive bullets in a revolver barrel (total out of 6), so 3 are empty. Now you roll the barrel so you don't know which ...
0
votes
3answers
70 views

Sailor's weather riddle

I'm stuck with this problem and right now I have no clue how to solve it. Maybe someone here might have an idea that could help solve this problem. I am not asking for a spoon-feed type of answers, I ...
2
votes
1answer
69 views

Mathematical puzzle on the coordinate planes.

Recently, I come across this quite interesting mathematical puzzle: Consider the ten points $(0,0)$, $(1,2)$, $(3,3)$, $(4,1)$ and $A, B, C, D, E, F$ on the coordinate plane. It is known that if any ...
2
votes
0answers
60 views

Is Einstein's riddle an example of a combinatorial design?

I have just learned a bit about combinatorial designs (BIBDs, constructing a ($b,v,r,k, \lambda$)-design, necessary conditions for a design, cyclic designs) and it reminded me a lot of Einstein's ...
5
votes
1answer
101 views

Game: two pots with coins

Rules of the game with two players. First player puts any number of coins in the first pot. Then second player, knowing that number, puts any amount of coins in the second pot. Then they in turns ...
0
votes
1answer
38 views

Odds of nonconsecutive number draw

What are the odds that you will randomly draw 10 non consecutive numbers from a deck of 40 cards (i.e. numbered 1-40)? (answer should be in a X:1 format, with X representing the average # of drawings ...
0
votes
2answers
93 views

Is my answer to this math riddle correct, and is there an easier method of solving it?

I've been given the following riddle by my boss, and while I think I might have figured out the answer, I'm not entirely sure how to check that it's correct since I kind of cheated and wrote a python ...
3
votes
3answers
104 views

Random Walk of a drunk man

Problem Statement: From where he stands, one step toward the cliff would send the drunken man over the edge. He takes random steps, either toward or away from the cliff. At any step his probability ...
10
votes
1answer
240 views

How many spheres can fit in this box?

HASELBAUER - DICKHEISER TEST #15: What is the maximum number of one inch-diameter spheres that can be packed into a box ten inches square and five inches deep? My attempt to solve this: If i ...
1
vote
1answer
47 views

Cars in Traffic [closed]

There is a very long, straight highway with some number of cars (N) placed somewhere along it, randomly. The highway is only one lane, so the cars can’t pass each other. Each car is going in the same ...
0
votes
0answers
29 views

Minimum gems required to make a garland containing all permutations, with uniqe colored gems, of size n, where we have infinite gems of N colors.

What is the minimum number of gems required to make a garland (circular) which contains all permutations, with unique colored gems considered as a valid permutation, of size n, when we have infinite ...
2
votes
1answer
56 views

Number of ways of getting from a certain point to another point.

Calculate the number of ways of getting to the pizza without stepping on bombs (you can move up and right) My solution was to calculate the number of ways of getting from the snail to the pizza ...
2
votes
1answer
29 views

Finding the $M^{th}$ person from randomly chosen $S^{th}$ out of $N$ people in a circle?

$N$ people are sitting in a circle, numbered clockwise from $1$ to $N$. Person number $S$ is chosen at random, and we count $M$ people starting from him, and proceeding clockwise, going back to $1$ ...
2
votes
1answer
85 views

Puzzle: Each entry in a number grid is the average of its neighbors

I'm trying to solve the following puzzle: Each number should be the average of its four neighbors. For example, $x$ should be equal to $\frac{1}{4}(4+10+y+z)$. I don't know how to make a formula ...
1
vote
3answers
60 views

Which box is heavier

There are 2 identical boxes (cubes). First one contains 27 big identical marbles and second one contains 64 small identical marbles. The marbles are made by steel. Supposing that in each box the ...
3
votes
2answers
51 views

Which of these two methods provides the correct answer for this probability riddle?

First, I know this riddle has been asked (many times) before. The question I want answering is why is a tree diagram not a correct method for determining the probability in this case. There are ...
5
votes
2answers
91 views

Logic puzzle: the rich man and the 1000 casks of wine

I recently came across an interesting logic puzzle during a challenge at a programming competition. Neither of the people on the two-person team completing that challenge could figure out an answer ...
9
votes
1answer
195 views

Obscuring squares of Rubik's cube

This is a combinatorial question related to Rubik's cube $3\times3\times3$ (and, in the end, its generalizations $n\times n\times n$). I assume that the readers are familiar with this puzzle. Let's ...
19
votes
5answers
507 views

How to arrange these 10 digits to make a correct equation?

My daughter brought home the "problem of the week" last night and it was explained to me as this: Given the following digits: $$1\ \ 1\ \ 2\ \ 3\ \ 3\ \ 4\ \ 5\ \ 6\ \ 6\ \ 7$$ Arrange them ...
3
votes
1answer
89 views

(Green/blue)-eye logic puzzle. Statement validation

There is a logic puzzle aiming on freeing same-color-eyed people from an island. The thing is that they must be certain of their own eye color so that they can leave. For that reason an external party ...
1
vote
2answers
590 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 ...
0
votes
1answer
38 views

Defective coin weighing problem and ternary representation when number of coins is not a power of 3

We are given $N$ coins and a set of scales. We are told that there is a defective coin and we know whether it is lighter or heavier than the others. Our goal is to identify it in as few weighings as ...
1
vote
1answer
127 views

The three-coin-flip riddle

Is the following true (It seems obvious to me that it's not... but... a PhD in physics, Derek Abbott, seems to think others explanation at end of post): Someone flips 3 coins on the table, they are ...