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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2answers
58 views

Minimum number of moves in Chocolate Puzzle

I've seen this problem on an algorithms competition and although there is an explanation on the website, I couldn't understand it. The abridged problem statement is as follows: Suppose you have two ...
1
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1answer
33 views

Figuring out the amount of 'straight edge' pieces in a puzzle?

I was wondering if there was any set way to determine the number of 'straight edge' pieces in a puzzle, assuming the pieces are all in neat rows and columns? Does the ratio of edge pieces to middle ...
62
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13answers
19k 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 ...
22
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8answers
3k views

There is a subset of positive integers which no computer program can print

It's said that a computer program "prints" a set A ($A \subset \mathbb N$, positive integers.) if it prints every element in A in ascending order (Even if A is infinite.). For example, the program can ...
5
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1answer
123 views

Number of valid NxN Takuzu Boards a.k.a 0h h1 (details inside)?

Takuzu a logic puzzle which has a NxN grid filled with zero's and one's following these rules: 1) Every row/column has equal number of 0's and 1's 2) No two rows/columns are same 3) No three ...
2
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1answer
131 views

3 dimensional $6\times 6\times 6$ lit cube problem involving looking for a specific lit pattern and quantity of them.

Suppose we have a $6\times 6\times 6$ cube such that it has $216$ subcubes, each with a visible, discernible light in it. A random number generator is connected to the cube and it will choose ...
0
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2answers
75 views

Points on a sphere puzzler [closed]

For a perfect sphere that has $n$ random points on it's surface: is it possible to connect all the points on the surface with geodetic segments around the surface of the sphere such that each point ...
2
votes
1answer
188 views

Game between 2014 card players where everyone with at least 2 cards passes a card to each of his neighbors

2014 card players sit around a big table. One of the players begins with 2014 cards on his hand, and the other have none. The rules for the game are: Every minute shall every player, who ...
78
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10answers
9k views

Mathematician vs. Computer: A Game

A mathematician and a computer are playing a game: First, the mathematician chooses an integer from the range $2,...,1000$. Then, the computer chooses an integer uniformly at random from the same ...
0
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0answers
83 views

Algorithm to calculate powers

Is it possible to write an algorithm that uses only multiplication and addition to calculate $a^b$ where both a and b are real numbers?
2
votes
2answers
66 views

Cracking license plate checksum

Suppose a city has license plates assigned to cars with 7 digits $a_1$ to $a_7$ and a checksum calculated by the following algorithm: ($m_k$ are integers) $$m_1a_1+m_2a_2+\cdots+m_7a_7\mod 28$$ (which ...
0
votes
4answers
3k views

Math Riddle in Combinatorics.

A blind man is on a strange island and he has 2 red pills and 2 white pills, completely identical and has kept in his pockets, he needs to take 1 red pill and 1 white pill order doesn't matter. If he ...
8
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1answer
486 views

Puzzle: Give an algorithm for finding a frog that jumps along the number line

You are playing a game, your goal in this game is to catch a frog that's leaping between natural numbers. At first, the frog is found at the number $a \in \mathbb N$ which is not known to you. Each ...
2
votes
1answer
191 views

Is this a correct solution to determine as to whom I should invite for the party?

I was working my way through some Propositional Logic Questions in Discrete Maths by Rosen, when I came across the following question: When planning a party you want to know whom to invite. Among ...
0
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2answers
68 views
9
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7answers
3k views

Rainbow Hats Puzzle

Seven prisoners are given the chance to be set free tomorrow. An executioner will put a hat on each prisoner's head. Each hat can be one of the seven colors of the rainbow and the hat colors ...
1
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2answers
135 views

Algebraic solution to the Broken Weight Problem

Here is a problem I was sent, which it turns out was first posed by Claude Gaspard Bachet de Méziriac in a book of arithmetic problems. The problem is as follows: A few years ago, a King's ...
1
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1answer
33 views

Finding the count of paths with K turns from corner to corner in a square box

I'm having trouble understanding the solution given for the problem here: http://www.codechef.com/DEC11/problems/MOVES/ Given a square table sized $N \times N$ ($3 ≤ N ≤ 5000$; rows and columns ...
1
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1answer
253 views

Is this a correct solution to determining which of two people is the liar using one question?

I am a newbie to Stack-Exchange and if there is any problem in my question -- I apologize beforehand . I was working my way through some Propositional Logic Questions in Discrete Maths by Rosen , ...
1
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1answer
47 views

Pebble Problem Maximum$=\big\lceil \log_3(n)\big\rceil$?

In the pebbles problem, you are given $n$ number of pebbles that has one of the $n$ weigh less. If you are given a balence that you can you $k$ times, what is the minimum amount of $k$? ...
-7
votes
1answer
210 views

Why is it possible to find the birth year by subtracting one's age from 114?

I noticed that any person can find their birth year just by subtracting their age from the number $114$. For example, if I am $25$ years old then from $114-25=89$ I know the birth year is $1989 $. ...
4
votes
1answer
65 views

Puzzling Sequence

Today I was given a question that first I thought might be easy to solve but then no matter how hard I tried I couldn't solve it.(It's not really related to maths just some puzzle) if: $$ 9999=4\\ ...
59
votes
24answers
11k views

Blue eyes: a logic puzzle

Today I read the Blue Eyes puzzle here. I also read the solution which I find quite interesting. But there are three follow up questions which I don't know the answer to: What is the quantified ...
7
votes
4answers
946 views

Can the product $AB$ be computed using only $+, -,$ and reciprocal operators?

Can the product of $A, B$ be computed using only $+, -,$ and reciprocal operators using a calculator? You can use calculator's memory function (multiply and divide are broken though). Additional: I ...
1
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2answers
63 views

Scores of six soccer matches

In the first round of the city soccer tournament, the teams in group A finished as follows: ...
0
votes
1answer
77 views

How to find a recursive formula for some sequence

I know how to find a non-recursive formula for a recursively defined sequence. However, now I have this puzzle which gives me a sequence (but not the recursive definition) and challenges me to find ...
4
votes
1answer
105 views

The Island in the Miracle Sea. (Christmas edition)

To all of you who love math like me, I have this puzzling riddle that I hope you find interesting : On Christmas Eve just after midnight, Santa was riding his sleigh over the Miracle Sea when ...
6
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2answers
824 views

Lights Out Variant: Flipping the whole row and column.

So I found this puzzle similar to Lights Out, if any of you have ever played that. Basically the puzzle works in a grid of lights like so: 1 0 0 00 0 0 00 1 0 0 0 0 1 0 When you selected a ...
3
votes
1answer
141 views

Knuth's algorithm for Mastermind question

I'm reading about Knuth's algorithm to solve the mastermind game, so I've looked in wikipedia and read the pseudo-code (http://en.wikipedia.org/wiki/Mastermind_(board_game)#Five-guess_algorithm). I ...
3
votes
2answers
55 views

Objects into two bags puzzle

I found a maths puzzle somewhere and a part of it as below: Kelly wants to place n objects $a_1,a_2,⋅⋅⋅,a_n$ into two bags. For each $i=1,2,⋅⋅⋅,n$, the weight of $a_i$ is $w_i$ kilograms. The ...
2
votes
1answer
50 views

Weights - Objects into bags puzzle

I found a maths puzzle somewhere and a part of it as below: Kelly wants to place n objects $a_1 , a_2 , ··· , a_n$ into $k > 1$ bags. For each $i = 1 , 2 , ··· , n $, the weight of $a_i$ is $w_i$ ...
2
votes
4answers
573 views

balance scale problem for 13 (not 12) items

The 12-item balance scale puzzle is very familiar. The object is to find the lone non-standard item (if one exists) out of a group of 12 seemingly identical items, using a balance scale and a maximum ...
10
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3answers
893 views

riddle that involves elementary geometry

$3$ frogs are positioned at the vertices of an equilateral triangle whos sides are of length $1$. We have $1$ frog on each vertex. The frogs are able to "leap" one over another. When they do, they ...
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4answers
2k views
2
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0answers
76 views

How can this paradox be resolved?

I came up with a (probably unoriginal) paradox today, and was wondering how it might be resolved. Its approach to reasoning seems to resemble basic game theory techniques. Suppose a casino game has ...
1
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0answers
118 views

How to find solutions of coin weighing problems with multiple light coins and prove optimality

So the classical coin weighing problem with $3^n$ coins all equal weight except for one light coin, where we want to find the one light coin, can be solved optimally with $n$ uses of a balancing ...
2
votes
1answer
127 views

Cops and robbers in a square

A problem from Moscow Mathematical Olympiad in 1973. goes like this: At the center of a square stands a cop and at one of the square’s vertices stands a robber. The Rule allows the cop to run ...
8
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3answers
164 views

Dividing an obtuse triangle into acute triangles

Can an obtuse triangle be subdivided into only acute triangles (right triangles are not allowed)? Any number of subdivisions can be made as long as all of the angles in all resulting triangles are ...
5
votes
1answer
457 views

Apparent paradox for the bird traveling between two trains puzzle

Gretings. Trying the "hard solution" for the puzzle below (which has been discussed, with a different angle, elsewhere on this forum) I got to a point where I have three seemingly valid solutions, ...
2
votes
3answers
168 views

Find the last non-zero digit of $30^{2345}$

Find the last non-zero digit of $30^{2345}$ Source: Athena Healthcare Interview Questions
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8answers
471 views

Make the number $100$ out of $1,2,3,$ and $4$ digits, without repeats

How can we make the number $100$, using only the following digits: $1,2,3,4$. You cannot repeat any of them.
4
votes
0answers
112 views

Is it a “paradox”, or a flaw in the question?

(Clearly not a pardox per-se but I would like to hear what you think) The basic riddle (not a very interesting one even) goes as follows: A first client comes into a barber shop, takes a hair cut ...
4
votes
6answers
1k views

The final state of 1000 light bulbs switched on/off by 1000 people passing by

There are 1000 light bulbs and 1000 tutors. All light bulbs are off. Tutor 1 goes flipping light bulb 1,2,3,4... tutor 2 then flips 2,4,6,8... tutor 3 then 3,6,9...etc until all 1000 tutors have ...
2
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1answer
155 views

Knight Knave puzzle with three boxes

Could you please help me with the following puzzle: Consider the following puzzle: Suppose there are two box makers: Knight and Knave. Knight always writes true statements on his box, ...
0
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0answers
31 views

$n$th number of concatenating consecutive integers [duplicate]

How do I find the nth digit of concatenating consecutive integers as in: $123456789101112131415161718\cdots$ where the $10th$ digit = 1$ , $11$th$ = 0$, $12$th $= 1$, $13$th $= 1$ $\cdots$ How do I ...
3
votes
2answers
136 views

empty boxes puzzle

The problem is N large empty boxes (assume they are of type:1) are initially placed on a table. An unknown number of boxes (type:1) are selected and in each of them K smaller boxes (type:2) are ...
0
votes
1answer
78 views

Conditions for magic square.

So I've messing around with magic squares and something occured to me: Assume we have a nxn grid of numbers which respects the sum conditions of a magic square as in it has the appropriate column, ...
2
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2answers
807 views

Puzzle, Permutation and Combination problem?

I have a puzzle here: There are five colored balls: 2 green, 2 blue and 1 yellow Rule 1: All balls of the same color must be adjacent to each other. I wrote a program to find all the ...
0
votes
1answer
76 views

Probability Paradoxes that Puzzle Professors.

There is a class of probability puzzles that includes Monty Hall/Three Prisoners, Three Cards/Pancakes, Two Children/Boy or Girl, their common antecedent Bertrand's Box Paradox, and (a more ...
41
votes
16answers
14k views

Interview riddle

On the Mathematics chat we were recently talking about the following problem @Chris'ssis had to solve during an interview : $$3\times 4=8$$ $$4\times 5=50$$ $$5\times 6=30$$ $$6\times 7=49$$ ...