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 ...

learn more… | top users | synonyms (1)

5
votes
2answers
87 views

If $\sum_{i=1}^n a_n=0$ then you can find a “good” ordering of $a_i$.

I'm trying to prove (or disprove, but I think it's true and I'll be surprised if someone would manage to disprove it) a small theorem. Given an array of real numbers $A=[a_1,a_2,...,a_n]$ such that ...
8
votes
0answers
191 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 ...
1
vote
5answers
246 views

Apple puzzle math

A salesman had 25kg apple. For convenience, he put some apples in 3 types of boxes, boxes of 1kg, 3kg and 5kg. He has a total of 10 cases of various kinds. Can he put 25kg apple to fit into 10 ...
16
votes
2answers
484 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 ...
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. ...
4
votes
3answers
6k views

Probabalistic proof of green-eyed dragons logic puzzle

I came across the "green-eyed dragons" puzzle (alternatively known as the "blue eyed villagers" puzzle). The typical proof uses a straightforward inductive strategy. I came up with a probabalistic ...
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
vote
2answers
172 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... ...
0
votes
1answer
102 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 ...
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 ...
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 ...
2
votes
3answers
645 views

A truth teller and liar puzzle of Ramanujan mathematical olympiad 2013

On an island each person always tells the truth or each person always tells a lie. Three people say $A$ , $B$ and $C$ have a conversation. $A$ says that $B$ is lying , $B$ says that $C$ is lying and ...
2
votes
2answers
97 views

Explaining a Pattern in a Matrix Generated by Minimum Excluded Number in Rows & Columns

I have been given the following math puzzle: You are given a matrix that is filled by the following rule: Every cell i,j is evaluated by taking the lowest non-negative number that is not ...
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 ...
2
votes
3answers
2k views

Maths brain teaser. Fifty minutes ago it was four times as many minutes past three o'clock

Fifty minutes ago it was four times as many minutes past three o'clock. How many minutes is it to six o'clock..? I have got the solution online but have doubts in it : ...
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
139 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 ...
7
votes
2answers
221 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 ...
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 ...
2
votes
1answer
407 views

roulette wheel sequence

Is the sequence of numbers around a European roulette wheel (the integers from 0 to 36 inclusive) random or is there a pattern to it? It is said to have been devised by Pascal, which might be thought ...
1
vote
0answers
144 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 ...
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) ...
-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 ...
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 ...
0
votes
0answers
30 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 ...
5
votes
2answers
237 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
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 ...
3
votes
2answers
179 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: ...
4
votes
4answers
6k views

What is the name of the logical puzzle, where one always lies and another always tells the truth?

So i was solving exercises in propositional logic lately and stumbled upon a puzzle, that goes like this: Each inhabitant of a remote village always tells the truth or always lies. A villager will ...
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
1answer
57 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
1answer
25k views

I don't see the pattern.. does anyone understand this..? [duplicate]

Note.. the numbers are actually in a 7 x 6 grid.. graphics did not show here.. ...
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 ...
2
votes
3answers
361 views

Smallest $k$ s.t. $7x+1=9y+2=11z+3=k$, all positive integers

Find the smallest positive integer, which on dividing with 7 gives remainder 1, on dividing with 9 gives (remainder) 2 and that after division by 11 yields 3 as remainder. i.e., find smallest $k \in ...
5
votes
1answer
97 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 ...
11
votes
5answers
2k views

sangaku - a geometrical puzzle

Find the radius of the circles if the size of the larger square is 1x1. Enjoy! (read about the origin of sangaku)
3
votes
3answers
97 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 ...
6
votes
2answers
2k views

topology puzzle - without cut the rope, separate two rings

hello I wonder whether this puzzle is possible to solve. if possible, what kind of thing should I learn to solve this? the problem is make left one to right one without cut the rope only stretch and ...
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 ...
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 ...
3
votes
2answers
4k views

Jigsaw Puzzle Help

I have a puzzle I'm trying to solve and I have all the border pieces set out but I'm pretty sure some are missing. How do I figure out how many pieces are in the border? It's a 1000 piece puzzle and ...
1
vote
2answers
441 views

Could one be a friend of all?

The social network "ILM" has a lot of members. It is well known: If you choose any 4 members of the network, then one of these 4 members is a friend of the other 3. Proof: Is then among any 4 ...
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
349 views

Striking off a digit from each of the numbers written in seven rows, while preserving arithmetical operations

Problem Strike off any digit from each number in seven rows (need not be at same place) and combine the same operations with 3 digit numbers to get the same addition. After this strike off another ...
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, ...