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
24 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
37 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 ...
2
votes
2answers
87 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
63 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 ...
-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?
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 ...
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 ...
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 &...
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 ...
-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 ...
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
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 ...
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 $5$ ...
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 ...
0
votes
1answer
184 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
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 ...
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 ...
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-,...
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 ...
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....
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 ...
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. ...
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{...
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 ...
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
391 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 ...
4
votes
2answers
133 views

Find $I$ in $\frac{\overline{SIX}}{\overline{NINE}}=\frac23$

In $\frac{\overline{SIX}}{\overline{NINE}}=\frac23$ every letter denotes a UNIQUE digit,find $I$. Expanding the fraction in base $10$ we have: $300S+30I+3X=2020N+200I+2E$ , but this doesn't ...
0
votes
1answer
58 views

A cool number-theoretic puzzle in IMAT: find the last digit

This test is from IMAT 2015 (International Medical Admission Test): When I made a hotel reservation online yesterday I was given an $8$ digit booking reference which contained no zeros. It did, ...
2
votes
1answer
69 views

Circle Puzzle Geometry

Two friends are playing a game. One friend stands in the middle of a circle radius 100m. His objective is to leave the circle. He may take one step at a time, distance 1m, in any direction. However, ...
1
vote
2answers
76 views

Nice explanation for simple puzzle

There is a simple game with coins that goes as follows. You have $x$ coins and two players who take turns. Each player can either remove one or two coins. The winner is the person who removes the ...
0
votes
1answer
23 views

Devising an $n$-place mastermind variation algorithm

A few days ago I came across such a problem at the contest my uni was holding: Given the history of guesses in a mastermind game using digits instead of colors in a form of pairs $(x, y)$ where $...
3
votes
1answer
50 views

How to tame a Rechenschlange

I found the following problem, called Rechenschlange (literal translation: calculation snake) in a German puzzle calendar: Fill the blanks with the numbers 1-9. Each number must only appear once. ...
4
votes
2answers
55 views

55 Coins- / Young-Diagram Rearrangment-Riddle

this has been a riddle to difficult for me to understand the solution some year ago. Even though the riddle seems really easy. You have got 55 coins. Someone builds an arbitrary number m of stacks ...
-1
votes
1answer
34 views

Two guys pick from $n$ stones, the numbers of stones they can pick lie in a given set S. When the guy who pick first will win?

Alice and Bob take turns to pick stones from a pile of $n$ stones. Each number of stones they pick must lie in a given finite set $S\subset \mathbb{N}$. Who cannot pick will lose. If Alice picks first,...
1
vote
1answer
51 views

finding the missing number by pattern

In this riddle you need to find a pattern between every couple of numbers. Given numbers $5$ and $10$ there is a pattern like in the numbers $10$ and $3$. Given numbers $10$ and $15$ there is a ...
1
vote
1answer
38 views

Create a strictly increasing sequence following criterias

Problem Let y be a sequence of real numbers (of length $n$) bounded in the range [0,1]. I am trying to calculate the sequence x ...
0
votes
2answers
45 views

Do these infinite expressions have a meaning?

While playing with expressions, I came up to the following "infinite sums". I haven't seen them anywhere else but maybe I didn't look long enough. Find the values of $s$ and $t$. $$s=\sum\nolimits_{1}^...
-1
votes
2answers
87 views

Math's puzzle school problem

I got this weird homework situation and i can't find out what the answer is. I got to find out how to get $828$ using the numbers $8, 6, 8, 3, 75$ and $9$. Moreover, I can use all the operators $*, -,...
20
votes
6answers
749 views

Non-trivial “I know what number you're thinking of”

Consider the following 'trick' (WARNING: very lame) Think of a number. Multiply this number by two. Add four. Divide the number by two. Subtract the number you were originally thinking of. I guess ...
4
votes
2answers
61 views

Meeting probability of two bankers: uniform distribution puzzle

Two bankers each arrive at the station at some random time between 5PM and 6PM (arrival time for each of them is uniformly distributed). They stay exactly five minutes and then leave. What is the ...