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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1
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1answer
30 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
vote
1answer
41 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 , ...
-3
votes
3answers
75 views

How can you use the digits 2 0 1 5 to equal 28 [on hold]

you can use the numbers only once and have to use them all.
1
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1answer
39 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 $k$? ...
-6
votes
1answer
74 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
42 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\\ ...
1
vote
2answers
50 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
34 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
88 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 ...
3
votes
1answer
49 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
48 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
46 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 $w_i$ ...
10
votes
3answers
831 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 ...
2
votes
0answers
49 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 ...
15
votes
4answers
2k views

Solving 9 sons puzzle

The following math puzzle : ...
0
votes
0answers
56 views

How to dissect the 11x11 square with 7x7 hole to get a square

Following shape needs to be cut into minimum amount of pieces to form a square Well, I can't find a solution better than to 8 pieces
2
votes
3answers
114 views

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

Find the last non-zero digit of $30^{2345}$ Source: Athena Healthcare Interview Questions
8
votes
3answers
80 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 ...
3
votes
0answers
96 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 ...
11
votes
8answers
437 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.
-3
votes
0answers
40 views

How can we compute the 6 missing numbers? [migrated]

There are 3 datatables. We forgot the numbers around the third square. How can we compute the 6 missing numbers?(there are question marks instead of them)
1
vote
0answers
39 views

Knights and Knaves island [duplicate]

You appear on the Island of Knights and Knaves. Knights always tell truth, knaves always lie. You meat three inhabitants, Carl, Peggy and Zippy, and hear the following conversation: Carl says, "I ...
1
vote
0answers
100 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 ...
0
votes
0answers
30 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
93 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
37 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, ...
0
votes
0answers
75 views

Logic puzzle of two numbers

The puzzle goes like this.. ...
11
votes
11answers
204 views

Get the numbers from (0-30) by using the number $2$ four times

How can I get the numbers from (0-30) by using the number $2$ four times.Use any common mathematical function and the (+,-,*,/,^) I tried to solve this puzzle, but I couldn't solve it completely. Some ...
5
votes
2answers
136 views

Prisoners Problem

We have an infinite number of prisoners enumerated $\{1, 2, \dots\}$, and on each prisoner there is a hat of either blue or red color. The $n$th prisoner sees the hats of prisoners $\{n+1, n+2, ...
1
vote
1answer
44 views

Probability puzzle : Expected no. of coins in the smaller pot

There are two pots of coins having size m & n. A new coin is thrown and goes to 1st pot with probability m/(m+n) and to 2nd pot with probability n/(m+n). We start with both pots of size 1 & 1 ...
0
votes
2answers
67 views

Lights Out with custom rules set

I'm trying to understand how to use linear algebra to solve a custom Lights Out puzzle with the following rules: There are 8 lights, all the lights are off at the starting point, I need to turn on ...
1
vote
1answer
33 views

Probability : Maximize the expected payoff

Given $2$ random variables $X, Y$ that take integer values with uniform distribution from $0$ to $100$. You play a game in which a random value of $x$ comes first & you have to decide if the ...
0
votes
1answer
42 views

How to count jigsaw puzzle height and width in pieces.

How can I calculate jigsaw puzzle dimensions (height & width) in puzzle pieces? I have a puzzle which consist of $3,000$ pieces (the paper inside the box says that because of technical reasons ...
5
votes
4answers
679 views

A maths number puzzle

We have these digits : $1,2,3,4,5,6,7,8,9$. Using these digits, we have to make two numbers such that their product must be as large as possible. We have to use all digits only once. I did ...
3
votes
1answer
35 views

Four Isosceles Trapezoids

Suppose we have four isosceles triangles with the same area, which must some whole number less than $29$. Denote the the lower base and upper base of the $i$-th triangle with $y_i$ and $x_i$, ...
3
votes
1answer
49 views

Find a seven digit number which describes itself

Find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, ...
2
votes
2answers
49 views

What is the probability for a wood stick of real number length breaking in three piece that can forming precisely a triangle?

What is the probability for a wood stick of any real number length breaking in three piece that can forming precisely a triangle without any extra segment extend from the side of the triangle? My ...
20
votes
4answers
378 views

How many $\mathbb R$s must a Mathematician walk down?

A mathematician is lost on the complex plane. He knows neither his position nor the direction he is facing. He wants to return to the main road, a strip of width $1$ around the real axis (that is, ...
0
votes
1answer
65 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 ...
4
votes
3answers
111 views

Using up letters on a refrigerator is NP-complete

You spend some time with your preschool-age daughter trying to use up all of the magnet letters on the refrigerator to spell words that she knows. Formally, you have a set of letters and you are ...
18
votes
5answers
1k views

Puzzle of gold coins in the bag

At the end of Probability class, our professor gave us the following puzzle: There are 100 bags each with 100 coins, but only one of these bags has gold coins in it. The gold coin has weight of ...
2
votes
1answer
119 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 ...
2
votes
0answers
34 views

determine the number thought of

Ten people are seated around a circular table. Each of the ten people thinks of a number and whispers it to his/her two neighbours. Then these ten people announce the average of the two numbers they ...
0
votes
2answers
46 views

how many days at work?

There are scheduled buses traveling between Somewhere and Nowhere. There is only one road between the two villages, so the buses take this road. From both villages the buses leave for the other ...
2
votes
1answer
38 views

counting hands shake

Mr. and Mrs. Brown gave a party for their friends they have not seen for a long time. Three couples came. During the party, some of the people were so happy to see each other again, that they even ...
0
votes
1answer
15 views

Show that an integer in an odd base system is odd in the base 10 system…

Show that an integer in an odd base system is odd in the base 10 system if and only if it has an odd number of odd digits. I have an idea of how the proof should go in my head, but how do I express ...
4
votes
4answers
74 views

Find a positive integer with prime factors of at most 2, 3, 5, 7 and ends in the digits 11

Does there exist a positive integer whose prime factors include at most 2, 3, 5, and 7, and ends in the digits 11? If so find the smallest positive integer. If not, show why none exists. My professor ...
3
votes
2answers
123 views

how to solve triangles count puzzle

Below is a puzzle of counting triangles.How to solve such puzzle ? source: http://gpuzzles.com/mind-teasers/how-many-triangles-challenge/?source=stackmath
1
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2answers
65 views

Counting problem about pirates and gold coins [duplicate]

Five pirates find a cache of 500 gold coins. They decide that the shortest pirate will serve as the bursar and determine a distribution of the coins however he sees fit, and then they all will vote. ...
0
votes
3answers
61 views

Recovering the original values from given information.

We have some N numbers[1..N] and N students. Originally we assign each number to single student. Call this assignment as the initial state of the assignments. Instance of assignment is described as ...