# Tagged Questions

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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### 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 ...
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### 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 ...
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### 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\\ ...
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### 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 ...
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### 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 ...
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?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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). ...
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 ...
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### 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 ...
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### 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 &...
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### 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 ...
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 ...
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 ...
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! ...
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 ...
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### 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 ...
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### 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 ...
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### 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-,...
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### 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 $5$ ...
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### 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 ...
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### 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. ...
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 ...
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 ...
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### 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 $B$ ...
I have found the sum it's $180$ but using right triangle and sine theorem.