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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2
votes
1answer
39 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 ...
6
votes
0answers
71 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 ...
4
votes
3answers
61 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 ...
17
votes
0answers
97 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
3answers
180 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
62 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
225 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
2answers
98 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
237 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 $33$. $$1+4=5$$ $$2+5=12$$ $$3+6=21$$ $$8+11=?$$
0
votes
2answers
24 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 ...
-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 ...
9
votes
5answers
3k views

How to perform a fair coin toss experiment over phone?

I was recently asked this question by my friend. Suppose the two individuals participating in a toss are not near each other, but could communicate over a telephone. How does one construct a fair coin ...
-2
votes
0answers
48 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 ...
2
votes
5answers
179 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 ...
8
votes
5answers
621 views

The frog puzzle

So here's the puzzle. You're poisoned in the jungle and the only way to save yourself is to lick a special kind of frog. To make matters worse, only the female of that species will do. Licking the ...
9
votes
1answer
101 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 ...
17
votes
1answer
2k views

Given a set of digits, what is the biggest number we can make using exponentiation - numberphile noodle quiz

The question is motivated by a question on a can of number noodles. Each item is a digit between $0$ and $9$. Clearly, if you form a string and consider it to represent a base $10$ integer, then ...
65
votes
14answers
34k views

Dividing 100% by 3 without any left

In mathematics, as far as I know, you can't divide 100% by 3 without having 0,1...% left. Imagine an apple which was cloned two times, so the other 2 are completely equal in 'quality'. The totality ...
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 ...
1
vote
2answers
577 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 ...
3
votes
1answer
47 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
1answer
47 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
2answers
309 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 ...
0
votes
0answers
19 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 ...
4
votes
2answers
140 views

Does there exist a tool to construct a perfect sine wave?

For example, a perfect circle can be constructed using a compass and a perfect ellipse can be constructed using two pins and a piece of string, because a circle can be defined as the locus of points ...
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
1answer
414 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 ...
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 ...
-1
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
0answers
45 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
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 ...
1
vote
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.
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 ...
0
votes
4answers
520 views

How to solve 4 variables

I received the below puzzle today (via whatsapp): We tried to solve this, but we can't solve. We think that this puzzle is wrong. Can this be solved? Or is this a wrong puzzle?
3
votes
2answers
295 views

Magic Squares with Lucas and Fibonacci Numbers

I am quite curious about can we construct magic squares using only Lucas and Fibonacci numbers(of course not repeating them? If yes, how can we construct them? And if not , what is the proof?
10
votes
3answers
695 views

Explain a surprisingly simple optimization result

The following optimization problem came to my attention as an idealization of the silly browser game Cookie Clicker, but is representative of a range of strategy games: You have an initial ...
0
votes
1answer
85 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 ...
10
votes
1answer
239 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 ...
4
votes
1answer
807 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?
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 ...
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 ...
4
votes
2answers
720 views

A puzzle about a sum and product of two numbers

The Gray Man wants to test The Hardy Boys. He says to them, "I've selected 2 positive integers, both bigger than one." He then proceeds to reveal their total and product to Frank and Joe ...
19
votes
1answer
407 views

What Rubik's Twist configuration has the lowest visible surface area?

The Rubik's Twist has been a fun time sink. From the wiki page, [It] is a toy with twenty-four wedges that are right isosceles triangular prisms. The wedges are connected by spring bolts, so that ...
5
votes
1answer
100 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
102 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 ...
4
votes
4answers
2k views

Some digit summation problems

What is the sum of the digits of all numbers from 1 to 1000000? In general, what is the sum of all digits between 1 and N? f(n) is a function counting all the ones that show up in 1, 2, 3, ...
2
votes
6answers
202 views

Algebra problem stumping me

I have recently run into an algebra problem that goes as follows. Using the digits $1$ to $9$, $$ \left\{ \begin{align} A + B + C + D &= EF \\ E + F + G + H &= CJ \\ B + G + J ...