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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0
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0answers
5 views

Need tools for this jigsaw-like problem

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 ...
1
vote
1answer
44 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 ...
0
votes
1answer
19 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
0answers
43 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. The host of the game, then calls out random numbers (between 1-25, ...
20
votes
3answers
642 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 ...
1
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0answers
55 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 ...
1
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0answers
35 views

Position games: how to fill a matrix with dominos?

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 ...
-2
votes
0answers
43 views

Number of Holes in a Number [on hold]

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
70 views

Random Room changing in the Hilbert hotel. [on hold]

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
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0answers
52 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 ...
-5
votes
0answers
39 views

math riddles with connections to pigeon hole principle and binary representation [closed]

1) Let an infinite sequence of numbers be : $a_1=1,a_2=1,a_n=a_{n-1}+a_{n-2} \ (mod \ 10)$ so the sequence goes like this : $1, 1, 2, 3, 5, 8, 3, 1,...$ and so on. Does this sequence periodic? (i.e. ...
6
votes
2answers
65 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 ...
0
votes
1answer
24 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 ...
0
votes
0answers
42 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
17 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 ...
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 ...
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
50 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 ...
20
votes
0answers
140 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
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 ...
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, ...
6
votes
0answers
140 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. ...
1
vote
6answers
260 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
26 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
1answer
111 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
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 ...
-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 ...
1
vote
1answer
63 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
49 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
52 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
333 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
30 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
47 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
191 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
vote
2answers
59 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.
-1
votes
5answers
99 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
58 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
88 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
115 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
90 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
72 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
73 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 ...
3
votes
1answer
76 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
61 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
112 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
41 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
95 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 ...