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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2
votes
2answers
26 views

Find the Wrong Student

There are 15 student in the class and each of them has a different number 1 to 15. Student #1: wrote the natural number on the board. Student #2 said : This number is divisible by my number(number ...
-4
votes
0answers
38 views

Length of left stick [on hold]

Break the stick into 3 pieces and what would be the expected length of left stick? I need answer for this to verify my answer. Can somebody give me the answer? My thoughts: My answer is 1/4. First ...
23
votes
3answers
2k views

Find a thousand natural numbers such that their sum equals their product

The question is to find a thousand natural numbers such that their sum equals their product. Here's my approach : I worked on this question for lesser cases : \begin{align} &2 \times 2 = 2 + 2\\ ...
2
votes
2answers
88 views

A 3-valued mathematical logic?

Classical propositional logic is consistent and in conformity with human language. A formal statement is true or not true and it is possible to develope rules with which it is possible decide which ...
1
vote
1answer
35 views

Shortest possible distance to locate an unknown road

You are stranded in the middle of a large desert and the only way home is a through a straight road, which unfortunately you do not know the location of. If the perpendicular distance from you to ...
-4
votes
1answer
37 views

A simple discrete math riddle [on hold]

Let P be a set of integers. Let N be the number of the elements in P. Prove that there must be a subset of P that it's sum is divided by N. Any idea?
0
votes
1answer
64 views

Distances over a rectangular parallelepiped

It is given a rectangular parallelepiped $3\times4\times5$. Which are the farthest points from a given vertex, provided one can only walk on the surface of the parallelepiped? [Edit, for ...
0
votes
1answer
27 views

Maximizing the chances of picking up a red marble. [closed]

You have 2 jars, 50 red marbles and 50 blue marbles. You have to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it'll be ...
0
votes
0answers
28 views

Cake slicing problem for irrational angles

I came across the following question "A person plays the following game with a cake. He cuts a piece forming a circular sector of x degrees and flips the piece upside down, with the icing on the ...
4
votes
1answer
1k views

Prove that there is only one way to make a square using all six tangram pieces

I am pretty sure there is only one way to make a square from the six tangram pieces: How can I prove this is the only way respecting all symmetries?
-1
votes
1answer
66 views

Next term in the given series

What will be next term of given series: $$​50, 30, 40, 75, 170, ?$$ I am not able to find the pattern in the series. Could someone help me with this?
-3
votes
1answer
68 views

Who becomes king? [closed]

5 earls argue which becomes king and which becomes treasurer. A will be happy only if D or E is treasurer. B will be happy only if C is treasurer. C will be happy only if D is either king or ...
4
votes
4answers
7k 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
0answers
49 views

Venn diagram puzzle problem

All batangos are crentons , some franters are volns, and some kijuxes are not batangos. If no kijuxes are franters, which of the following CANNOT be true, given each group was observed to only 2 ...
2
votes
3answers
1k views

Basic probability : the frog riddle - what are the chances?

A few days ago I was watching this video The frog riddle and I have been thinking a lot about this riddle. In this riddle you are poisoned and need to lick a female frog to survive. There are 2 frogs ...
0
votes
1answer
24 views

Three players were presented with 3 red balls and 2 yellow balls, 3 balls were chosen at random

and each was concealed in a different box. The challenge was for each player in turn to look inside two of the boxes to see if they could determine the color of the ball in the other box. The first ...
3
votes
6answers
3k views

How many faces does the resulting polyhedron have?

Take a regular tetrahedron of edge one. Also take a square-based pyramid, whose edges are all one (therefore the side faces are equilateral triangles of same size as the faces of the tetrahedron). ...
3
votes
2answers
102 views

Is there a winning strategy for this tic-tac-toe?

The figure shows a variation of a tic-tac-toe board, with the usual rules: three small balls each player and three in a row wins. Is it possible to transform the layout isomorphically so the same ...
4
votes
1answer
75 views

How many lines are needed on the plane to get all angles from $1$ to $359$ degrees?

I am trying to solve following problem: How many lines are needed on the plane to get all angles from $1$ to $359$ degrees? We can move lines in parallel. I am thinking that since moving in parallel ...
3
votes
1answer
24 views

Sorting rows then sorting columns preserves the sorting of rows

From Peter Winkler's book: Given a matrix, prove that after first sorting each row, then sorting each column, each row remains sorted. For example: starting with $$\begin{bmatrix} 1 & -3 &...
2
votes
3answers
176 views

Coin problem: 11 coins, 7 fake ones [closed]

There are 11 coins, 4 real, 7 counterfeit, the weights of the counterfeit ones are different for each counterfeit coin and different from the weight of the real coin. What is the minimal number of ...
2
votes
2answers
43 views

Number of Spaghetti loops

From Peter Winkler's book: the 100 ends of 50 strands of spaghetti are paired at random and tied togethed. How many pasta loops should you expect from this process on average? I took ages because ...
1
vote
2answers
2k views

The 100 Coins Puzzle

There are 10 sets of 10 coins. You know how much the coins should weigh. You know all the coins in one set of ten are exactly a hundredth of an ounce off, making the entire set of ten coins a tenth of ...
4
votes
5answers
3k views

How to calculate the number of pieces in the border of a puzzle?

Is there any way to calculate how many border-pieces a puzzle has, without knowing its width-height ratio? I guess it's not even possible, but I am trying to be sure about it. Thanks for your help! ...
0
votes
1answer
187 views

Puzzle question finding Calvin

How to solve this problem. I have reckoned that I need to take as optimization problem finding minimum value for waiting time. Any suggestions? Calvin has to cross several signals when he walks from ...
1
vote
0answers
20 views

How to find the best way with the least amount of steps to find the matching hole (2 balls and 100 holes given)? [duplicate]

To extend the heading a little bit further. There are 100 holes ordered from min to max (min-hole with minimal radius, max-hole with maximum radius). There are two balls given which are to be used to ...
5
votes
0answers
52 views

Towers of coins puzzle [duplicate]

Let $n$ be a natural number. You are given $\frac{n(n+1)}{2}$ coins which are arranged in towers. Every turn you pick up the top coin of each tower and gather all these into a new tower. Prove that ...
6
votes
2answers
134 views

A weight problem

I am having a hard time solving the following puzzle. Could you please me to figure it out? A chemist has a set of five weights. She knows that it includes one 1-gram weight, and also one each 2-, 3-,...
0
votes
1answer
60 views

die game where we roll until we get a 5 or a 6

We roll a die until we get a $5$ and a $6$ for the first time, not necessarily consecutively and not necessarily in that order. We need to pay $x$ dollars before each die throw, and once both a $5$ ...
4
votes
4answers
10k views

Missing dollar problem

This sounds silly but I saw this and I couldn't figure it out so I thought you could help. The below is what I saw. You see a top you want to buy for $\$97$, but you don't have any money so you ...
0
votes
1answer
53 views

Puzzle : calculate value of $\pi$ given area of circle

I have seen in many interview experiences, interviewer asks find the value of [Pi] given area of the circle. What the interviewer is looking for and what is the answer for this?
3
votes
2answers
117 views

Binary encryption puzzle

There are 8 rooms, one containing a pot of gold. You know which room the gold is in, but your partner does not. The task is to inform your partner which room the gold is in under the following ...
1
vote
1answer
27 views

Bidding problem

From Peter Winkler's 'Mathematical puzzles' You can make a bid on a widget whose value to the owner, as far as you know, is uniformly randomly distributed between 0 and 100 dollars. However its ...
7
votes
8answers
2k views

3 trams are coming every 10, 15 and 15 minutes. On average, how long do I have to wait for any tram to come?

3 trams are coming to the stop every 10, 15 and 15 minutes. On average, how long do I have to wait for any tram to come? It's a practical problem, not some kind of a riddle for which I have a ...
1
vote
1answer
30 views

expected value of game involving uniform variable and its square

I am trying to determine the expected value of the following game: Let $u$ be drawn from a uniform distribution on $[0,1]$. We write down $u$ on one side of a piece of paper and $u^2$ on the other ...
5
votes
3answers
10k views

How many times are the hands of a clock at $90$ degrees.

How many times are the hands of a clock at right angle in a day? Initially i worked this out to be $2$ times every hour hence the answer came to $48$. But then in case of $3$ o'clock and $9$ o'...
0
votes
2answers
43 views

infinite square grid of resistors

Given an infinite, 2-d, square grid of 1 Ohm resistors, what is the resistance between two adjacent nodes? (Something like a very large window screen, where the wires have finite resistance, but no ...
4
votes
2answers
67 views

Can someone give me some ideas of algorithm for this card question?

Problem There is a $N$ by $1$ long card consisting of $N$ square cards, each having the number $1, 2, \cdots, N$ regardless of the sequence of cards. Find whether or not the long card could be in ...
1
vote
1answer
27 views

Area of all triangles involved in a big triangle.

I have a big triangle made up of several small triangle as depicted in picture given below. Suppose, there is one generic triangle of this shape which is formed by joining points arranged in n rows....
4
votes
7answers
557 views

Puzzle about technique of fair using of unfair coin

There is an unfair coin. It tends to land on one side more than on the other. It is unknown which side is it. There is Mr. A and Mr. B. They argue about something and they want to use that coin to ...
1
vote
0answers
46 views

Watches on a table

From Peter Winkler's 'Mathematical puzzles', taken from an All USSR Mathematical Competition, 1976: 50 accurate watches lie on a table. Prove that there exists a moment in time when the sum of the ...
2
votes
1answer
445 views

Counting the number of cubes in an isometric view

I had seen questions in a sample aptitude test, where an isometric view of an object made up of cubes was given, with some of the cubes removed. We were supposed to count the number of cubes present ...
3
votes
2answers
49 views

Which functions can be obtained by applying these syntactic rules?

Here's an intentionally weird question for ye all. Start off with the expression $x$. Rule 0. We're allowed get a new expression from an old expression by replacing a subexpression with an $\mathbb{...
18
votes
5answers
4k views

Tiling pentominoes into a 5x5x5 cube

I have this wooden puzzle composed of 25 y-shaped pentominoes, where the objective is to assemble them into a 5x5x5 cube. After spending quite a few hours unsuccessfully trying to solve the puzzle, I ...
1
vote
1answer
25 views

Voting with 3-way ties

From Peter Winkler's 'Mathematical puzzles' Ashford,Baxter and Campbell run for election and end up in a 3-way tie. To break it, they solicit voters' second preference and there is also a 3-way tie. ...
2
votes
2answers
408 views

Number of songs sung.

There were 750 people when the first song was sung. After each song, 50 people are leaving the hall. How many songs are sung to make them zero? The answer is 16, I am unable to understand it. I am ...
3
votes
2answers
137 views

Math Snake Puzzle

A colleague recently showed me the following puzzle game and I'm interested in how this can be solved. I thought it would be a good talking point for you guys as well :) A detailed description of ...
0
votes
1answer
51 views

Work and efficiency puzzle

There are $2$ people $A$ and $B$. $A$ requires $a\;$ days to complete certain amount of work and $B$ requires $b\;$ days to complete the same amount of work. If $A$ begins the work a day before $B$ ...
4
votes
4answers
392 views

Find the sum of angles without trigonometry?

I have found the sum it's $180$ but using right triangle and sine theorem.
0
votes
0answers
34 views

Maximum length sequence with negative and positive subsequences

From ' mathematical puzzles' By Peter Winkler: " At the stockholders' meeting the CEO presents month-by-month profits and losses and declares : ' Since the last meeting we have made a profit in ...