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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8
votes
0answers
199 views

Here is a riddle that I have no idea how to solve.

Okay, so I was trying to solve this riddle found here. It is a diagram of a star with 16 points. Each point corresponds uniquely to a number between 1 and 16. The letters on each point represent a ...
81
votes
18answers
8k views

Fastest way to meet, without communication, on a sphere?

I was puzzled by a question my colleague asked me, and now seeking your help. Suppose you and your friend* end up on a big sphere. There are no visual cues on where on the sphere you both are, and ...
0
votes
1answer
27 views

Deriving a function based on a relation/characteristic

Say I give you an integer set [1, N], which is the initial step, and define a notion of a step by this example: given N=16 ...
0
votes
1answer
59 views

Pick a random integer $x\in[1,N]$ and guess the value of $N$

$N$ people arrive at a concert, with tickets numbered $1$ to $N$. At the entrance, they all throw their tickets to a nearby trash can. You pull out a ticket with some number $x$ written on it. ...
2
votes
2answers
95 views

show that at least 3 balls have same weight

You are given 49 balls of colour red, black and white. It is known that, for any 5 balls of the same colour, there exist at least two among them possessing the same weight. The 49 balls are ...
-1
votes
1answer
103 views

kind of mathematical puzzle

i was recently doing this problem--- problem statement You have r red, g green and b blue balloons. To decorate a single table for the banquet you need exactly three balloons. Three balloons ...
3
votes
4answers
543 views

Math Puzzle: Largest number which cannot be written as the sum of distinct fourth powers

I've come across this question which I can't seem to solve. Write the largest number that cannot be written as the sum of distinct fourth powers. First I'm stuck with the interpretation: I was ...
2
votes
2answers
112 views

Enumeration of Solved Sudoku puzzles

I tried asking this on StackOverflow and it was quickly closed for being too broad, so I come here to get the mathematical part nailed down, and then I can do the rest with no help, most likely. From ...
1
vote
2answers
173 views

The Probability Riddle

While working on a mathematical model we have come across a problem that seems easy yet has a bunch of intelligent, mathematically trained people start doubting themselves :). Riddle us this... ...
4
votes
2answers
57 views

Rearranging a Staircase Grid into a Square

Is there any way to rearrange the above "staircase" grid into three pieces that can be rearranged into the 6x6 square grid below it? I have tried this problem for over six hours and have not arrived ...
16
votes
2answers
485 views

The Weaver Android app $\rightarrow$ cute combinatorics problem

There's an Android puzzle app called "The Weaver". My question is why every level seems to be solvable in far fewer moves than one might naively think. Here's a link for people who want to play along ...
2
votes
1answer
44 views

Strategy for 2-player game, drawing uniform variables and optionally redrawing

Player 1 and Player 2 secretly and separately draw uniform random variables in [0,1]. They may (secretly) elect to redraw once and replace their value. Highest value wins. What is the optimal ...
1
vote
1answer
74 views

Quiz: people and hats

I've created this quiz, but I'm not sure if the answer that I've found is correct or not. Three people meet at a pub, each of them has a blue or a red hat on his\her head. Nobody knows the colour of ...
1
vote
1answer
142 views

Two Buckets Water Puzzle

When reading up on graph theory, I came across this puzzle and on further investigation, learned that a general solution for this is similar to this problem. However, I haven't been able to ...
1
vote
1answer
87 views

Buffons needle crossing both lines?

Buffon's Needle Problem : Given a needle of length $l$ dropped on a plane ruled with parallel lines $t$ units apart, what is the probability that the needle will cross a line? I am working out ...
1
vote
1answer
62 views

Combinatorics question about alternately-coloured diagonal halves of sides of a cube

Diagonal halves of each side of a cube are painted in alternate colours. Let the vertex at which such a half forms a right angle be its base vertex. What is the minimum number and the maximum number ...
1
vote
0answers
147 views

How to solve a “logic grid/table puzzle” as well as a “logic game” from the LSAT

Dear fellow members of the prestigious brotherhood of philosophical and mathematical logicians, I am familiar with symbolic logic on a level such as is covered in Patrick Hurley's textbook A Concise ...
-2
votes
1answer
76 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,C round 2: player c moves one distance closer to the midpoint of B,D ...
3
votes
0answers
105 views

Worst case in decanting puzzles (pouring water from one jug to others).

A classic puzzle is to start with $3$ jugs of nonzero integer capacity ($A \ge B \ge C$) and have some water (integer) in each jug (the initial position). The goal is to get to some final (integer) ...
1
vote
1answer
47 views

A very simple math puzzle: An object O weights 1 N and the half of the weight of object O. What is the weight of object O?

So, today I came across a very simple (or so I though) math puzzle. If this is the wrong StackExchange please point me to the right place to ask. The puzzle goes as such: An object O weights 1 N ...
1
vote
1answer
37 views

How to approach more Puzzle-like problems (octagon, intersection points)

In physics I understand the situation and can derive formulas to describe it. But when it comes to more puzzle-like math problems like this: "All 20 diagonals are drawn in a regular octagon. At how ...
7
votes
2answers
223 views

reversing digits and squaring

If we reverse the digits of $12$ we will get $21$. $12^{2}=144$. If we reverse its digits we will get $441$ which is $21^{2}$. Here is the puzzle. How many such two digit numbers are there? Digits ...
5
votes
2answers
239 views

Find the next term in the sequence. $\frac{7}{3},\frac{35}{6},\frac{121}{12},\frac{335}{36},\ldots $

$\dfrac{7}{3},\dfrac{35}{6},\dfrac{121}{12},\dfrac{335}{36},\ldots $ $\bf\text{Answer}$ given is $\dfrac{865}{48}$ I found that $4^{th}$ differencess of the numbers $7,35,121,335\cdots$ are not ...
3
votes
2answers
180 views

An alien comes to Earth and says $7\times7=41$. How many fingers does he have?

I understand this sounds ridiculous at first but I got asked this question by a supply teacher $3$ days ago and I haven't been able to answer it so it's driving me insane. I got given two hints: ...
3
votes
1answer
76 views

The fly and its owner

This is a related problem to Fly and Two Trains Riddle, but must not be confused for a duplicate. A man is taking a leisurely walk with his pet fly at a pace of $v_m$. While the fly is buzzing at ...
0
votes
3answers
81 views

Number theory puzzle

If $(ABCD)÷(DCBA)=9$ where $A,B,C$ and $D$ are distinct and all them belong to ${0,1,2,3,4,5,6,7,8,9}$ but $A$ and $D $are not equal to zero then find $A,B ,C$ and $D$. I tried with the decimal ...
0
votes
5answers
87 views

Given $n$, what function returns $0$ for $n < 1$, but $1$ for all else?

I'm looking for a simple operation that returns $0$ if $n$ is less than $1$, but $1$ for anything greater than or equal to $1$. What does the trick?
1
vote
2answers
69 views

Question involving area and perimeter of two parallelograms sharing a diagonal.

Given two parallelograms $P1$ and $P2$ sharing a diagonal, such that area of $P1$ is greater than area of $P2$, can we say that the perimeter of $P1$ is greater than the perimeter of $P2$ ? Actually ...
1
vote
1answer
58 views

The merchant and the fake coin [duplicate]

Next is a riddle that I found interesting and I decide to share it with you. Try solve it by yourself before reading the answer. A merchant has 13 fair gold coins with one fake among them. The fake ...
0
votes
0answers
67 views

Marbles that are distinguishable and indistinguishable at the same time

Thinking about a question and my answer to it and another question I asked earlier. I've come up with the following problem: Consider two otherwise very similar marbles, a red one and a blue one. Let ...
5
votes
1answer
98 views

Intersection of 8 spheres: find the volume

From a long time ago, I remember a puzzle asking for the common area available to four cows: each cow is attached to a different corner of a square with a rope that has the same length as the sides of ...
3
votes
3answers
98 views

Propose an algorithm to find a “celebrity”

A celebrity is a person that everyone knows, but he doesn't know anyone. If we think of a group of people as a graph, where if there is an arrow from $A$ to $B$ that means "$A$ knows $B$", then a ...
2
votes
1answer
35 views

how to calculate nth term of mth row of this table?

there is a table which grows as 1,1 1,1,2 1,1,3,3 1,1,4,4,6 1,1,5,5,10,10 1,1,6,6,15,15,20 .....and so on If i want to find an specific element of the table ...
1
vote
2answers
147 views

Area of portion of circle inside a square.

Consider a square grazing field with each side of length 8 metres. There is a pillar at the centre of the field (i.e. at the intersection of the two diagonals). A cow is tied to the pillar using a ...
2
votes
0answers
59 views

Finding a murderer from statements from suspects [closed]

Officer X was entrusted with the duty of investigating a murder. The dead body was found in the living room. Preliminary investigation suggested that four of the six suspects were liars (at least one ...
0
votes
1answer
66 views

Probability puzzle involving crickets on a chess board

I was given the following problem in a technical interview: Suppose you have a normal 8x8 chessboard, and crickets are placed on every single square. The crickets begin to hop from square to ...
2
votes
1answer
62 views

What's the geometry of a puzzle key called?

Is there a name for the geometry of a classic puzzle key? It's not an ellipse, neither a circle, ...
0
votes
1answer
22 views

Count Shared Customers

GIVEN: A company has multiple "retail" locations (10 as an example). They collect data on customers, so they are able to identify customers that shop only 1 location versus customers that shop at ...
0
votes
3answers
74 views

Swimming pool problem: Time required to empty the swimming pool

In a swimming pool, 6 swimmers have to swim such that 3 swimmers start from end A at intervals of 1 minute and the remaining 3 start from end B at intervals of 2 minutes where A and B are opposite ...
2
votes
0answers
46 views

The $8$-Puzzle and $2$-Cycles

I have been studying the $8$-puzzle and have thus far managed to wrap my head around the following information: The following illustrates the solved position of the $8$-puzzle, where $9$ is the empty ...
1
vote
0answers
65 views

Looking for an alternative solution for the mutilated chessboard problem

Given a mutilated chessboard where two diagonally opposite squares are missing (the unmutilated version of it has $64$ squares), and given $31$ domino pieces, is it possible to cover the entire ...
2
votes
5answers
100 views

A peasant and his cows

A peasant owns $2n+1$ cows. When he separates a cow from the rest of the herd, he can split the $2n$ remaining ones into two groups of $n$ cows such that the sum of weights of each group are equal. ...
4
votes
2answers
88 views

A tale of two palindromes (sum of squares of two palindromes is a perfect square).

I am just curious on wether there are infinitely many palindromes say $p_1$ and $p_2$ satisfying: $p_1^2+p_2^2$ is a perfect square with $\gcd(p_1,p_2)=1$. I believe that there are some but, are ...
0
votes
1answer
189 views

How many different ways can I add three numbers to get a certain sum?

I'm working on a little program and I stumbled across a small math problem I can't quite solve. This is what the program does. A sum is generated. Now, the user can subtract either 3, 4, or 5 from ...
1
vote
1answer
63 views

Find appropriate number fill in the blanks [closed]

Find appropriate number fill in the blanks
3
votes
1answer
74 views

What gambling/board game or real life thing can (surprisingly) be modelled as a linear programming problem?

So I've taken Linear Programming 101. I've read my textbook, took the test and all that, and - besides all the theory, the nice algebraic interpretations, etc - I've encountered a lot of textbook ...
2
votes
0answers
238 views

How to solve instant insanity puzzle with graphs.

So I have a 10 cube insanity puzzle, I constructed the graph (I'll post pc later) based on the colors the problem is that there is just way to many lines and nodes to see the solution. Is there any ...
7
votes
1answer
3k views

Maths question from an IQ test [duplicate]

It is possible that 25 is the correct answer since I guessed (educated guess) that and got a predication of 170 IQ (obviously not accurate) I saw that 63 + 25 = 88 and 16 + 9 = 25 but then ...
3
votes
1answer
50 views

Numbers interpreted as sets and functions

In set theory numbers are defined as sets $$\emptyset,\{\emptyset\},\{\emptyset,\{\emptyset\}\},\{\emptyset,\{\emptyset\},\{\emptyset,\{\emptyset\}\}\},\dots$$ where $n+1=n\cup\{n\}$ and ...
2
votes
2answers
112 views

Prove a length of 6 in a triangle diagram.

A puzzle: Three equilateral triangles of size 3, 4, and 7 touch at a corner. The other corners of the size 4 triangle are 3 away from a 3 corner, and 7 away from a 7 corner. How far apart are the ...