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 ...
4
votes
2answers
120 views
Elementary Set theory question … it was asked in Exam
There are $21$ people.
$9$ eat dish $A$
$10$ eat dish $B$
$7$ eat dish $C$
$5$ eat dish $A , B$ and $C$
How many people eat at least two dishes?
Answer:
$10$ (given in solutions)
$15$ ...
0
votes
2answers
34 views
Problem related to a given diagram
I came across the above problem but do not know how to tackle it. Can someone point me in the right direction? Thanks in advance for your time.
1
vote
1answer
138 views
Sodoku Puzzles and Propositional Logic
I am currently reading about how to solve Sudoku puzzles using propositional logic. More specific, they use the compound statement $\bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p(i,j,n)$, ...
2
votes
1answer
144 views
What is the probablity that a Rubik's cube is solvable if you randomly switch two squares?
I am trying to learn how to solve a Rubik's cube and the 4x4 rubic cube at school is missing 4 squares, that got me thinking: if you randomly switched two squares, would it still be solvable?
I ...
2
votes
1answer
99 views
Distribution of points on a rectangle
Let $R$ be a rectangular region with sides $3$ and $4$. It is easy to show that for any $7$ points on $R$, there exists at least $2$ of them, namely $\{A,B\}$, with $d(A,B)\leq \sqrt{5}$. Just divide ...
-1
votes
2answers
107 views
Two liars puzzle alternate [closed]
you walk up to two people, one of them always tells lies and the other always tells the truth. they know that the other tells lies or the truth.
asking one question to one person figure out who the ...
7
votes
1answer
205 views
polynomial with rational coefficient have$ -\sqrt{2}$ as it minimal value?
Please help to solve this question:
polynomial with rational coefficients have $-\sqrt{2}$ as it minimal value ?
Thanks allot!
0
votes
0answers
66 views
puzzle creating questions
I am creating a game that player randomly draws 25 elements from 0-9 and 4 basic operations
+-x/ from the sandbox .e.g. {0,1,4,4,5,5,5,+,-,*,/ ....... } , what require to do is based on that 25 ...
4
votes
1answer
42 views
Limitations on orientations of a character on the surfaces of a cube
When looking at a cube you see either two surfaces across an edge or three
surfaces around an apex. Is it possible to arrange a non-symmetrical character (e.g."R") at 0,90,180 or 270 degrees rotation ...
1
vote
1answer
174 views
Spivak Chapter 2, problems 27 (and 28)
To be honest, I have no idea how to even start this problem. I'm sorry I don't have any work to show, but I'm just at a blank. Help?
Chapter 2: Problem 27:
"University B, once boasted 17 tenured ...
0
votes
1answer
145 views
Chess Knights Puzzle
The goal is to move the pieces so as to gather them all in the same square - in the minimal number of moves. Chess pieces can move as normal. Additionally, whenever the king and one or more knights ...
8
votes
4answers
511 views
Minimum number of steps needed to solve a rubik cube
Long time ago I've seen a book on group theory and there was an appendix about rubik cube. I remember there were only three steps that enabled me to solve my cube (three strings with letters encoding ...
1
vote
1answer
131 views
Puzzle of $N$ men around a table
This was asked to me by a friend. $N$ men sit around a circular table. Man 1 has a sword with him and he kills the Man 2, Man 3 picks up this sword and kills the next person i.e. Man 4. Thus the man ...
22
votes
1answer
430 views
Six Frogs - Puzzle
I had come across a puzzle:
The six educated frogs in the illustration are trained to reverse their order, so that their numbers shall read 6, 5, 4, 3, 2, 1, with the blank square in its ...
2
votes
0answers
88 views
Can 24 lines on a cubic surface be realized as 24 identical spiral rods?
It's possible to put 24 lines on a cubic surface. 27 lines is possible, but I don't have a great picture for that surface. It turns out that the 24 lines can be built with Zome. I'm thinking that ...
5
votes
1answer
117 views
A small geometry puzzle out of curiosity
Out of curiosity I've been thinking about the following "puzzle" for a while now and maybe someone here can help.
Situation
We take a rectangle and start off at one of the corners. In that corner, ...
-4
votes
5answers
5k views
Puzzle of number grouping
Combine the three numbers in each group to get the same result in each of the three groups. You can use addition, subtraction, multiplication, division, and exponentiation. Here's an example of a ...
4
votes
3answers
135 views
What is the value of D here?
Number S is obtained by squaring the sum of digits of a two digit number D. If the difference between S and D is 27, then the two digit number D is?
My thoughts:
Let the two digit number $D$ be ...
1
vote
1answer
66 views
Explanation for a peculiar property of a number
I had come across a problem, where 2 people play a game where think of a number n, and turn by turn subtract a number $p$ from $n$ where $p$ is a prime and is $p < n$ and 1 is taken as prime here. ...
7
votes
2answers
412 views
Find missing number from sum of first few natural numbers
A child was asked to add the first few natural numbers $1+2+3+...$ as long as his patience permitted. As he stopped, he gave the sum as $575$. When the teacher declared the result wrong, the child ...
1
vote
1answer
134 views
Dissection of a chess board into 4 congruent pieces
Consider a standard $8\times 8$ chessboard where a pawn is placed on each of the squares $d1,d2,d3,d4$ . Dissect the board into $4$ congruent pieces (reflections are allowed) such that each piece ...
0
votes
1answer
42 views
Find out the length of a recurrence
I have this rules for creating a list of numbers:
$x/2$ if $x$ is even, repeat
$3x+1$ if $x$ is odd, repeat
if $x=1$, stop
so for example, starting from 15, the list will be: 15, 46, 23, 70, 45, ...
1
vote
3answers
425 views
Escalator puzzle equation
I'm trying to understand the escalator puzzle.
A man visits a shopping mall almost every day and he walks up an
up-going escalator that connects the ground and the first floor. If he
walks up ...
0
votes
4answers
129 views
A logic puzzle from TES: Arena
Its nice when games have riddles hidden in them. While playing TES:Arena, I came across an unusual logical puzzle:
There are 3 cells.
If Cell 3 holds worthless brass, Cell 2 holds the gold key.
If ...
2
votes
2answers
134 views
What area of mathematics is this problem asking about? [closed]
A colleague posted this on a whiteboard (as a brain-teaser I guess):
A $\rightarrow$ B;
B $\rightarrow$ C;
AD $\rightarrow$ E;
BE $\rightarrow$ C;
BF $\rightarrow$ D;
AC $\rightarrow$ F
What is ...
0
votes
4answers
286 views
Can you help me solve these questions related to a Logical theory?
In a group of 200 people, number of people having at least primary education (assuming - Category I): number of people having at least middle school education (Category II): number of people having ...
1
vote
1answer
118 views
In how many ways ( using only whole numbers ) can we divide 49 into 6 parts so that we can obtain any number between 1 to 49?
The series which forms the basis of all the other series is:- 1,2,4,8,16,18.
Some other combinations are:- 1,2,3,7,14,22 ; 1,2,4,7,15,20 ; 1,2,4,8,13,21. However, I obtained the basic combination by ...
4
votes
3answers
148 views
How to formally model the “hesitation” in the hat-guessing puzzle?
Hua Luogeng (in Chinese, 华罗庚) took a hat-guessing puzzle as an illustration in a booklet focusing on mathematical induction. The following description is a literal translation from Chinese.
...
17
votes
1answer
1k views
The $n$ Immortals problem.
I saw this riddle posted on reddit a long time ago, called the "Seven Immortals."
In the beginning, the world is inhabited by seven immortals, ageless and sexless, who begin to multiply and ...
2
votes
2answers
126 views
Divide $40$ to $4$ parts such that every number from $1-40$ can be realized
How can you divide $40$ to $4$ parts such that every number from $1-40$ can be realized just by adding or subtracting those $4$ parts?
6
votes
4answers
229 views
A math teacher thought of a positive integer of two digits.
A math teacher thought of a positive integer of two
digits. She wants her two intelligent students Hanna
and Charlie determine the exact number thought.
For this, Hanna is privately told how many ...
-1
votes
1answer
314 views
If 2 x 6 = 4, 4 x 1 = 7 and 8 x 3 = 1 find the value of 5 x 5.
Please help me find some logical pattern for
If 2 x 6 = 4,
4 x 1 = 7
and 8 x 3 = 1
find the value of 5 x 5.
2
votes
1answer
100 views
Monty Hall Application
Driver A comes to a 3 way path junction but is not sure which one to take.
Just as he decides to take path 1, a cyclist came by and told driver A all he knows is that he is going on path 3 which would ...
1
vote
1answer
70 views
What are good methods for solving Conway's card-stacking puzzle?
Suppose there is a table with three marked spots, $A, B, $ and $C$, on which playing cards can be put, face up. Initially, an ace (1), a deuce (2), and a trey (3) are placed on one or more of these ...
0
votes
0answers
113 views
Room switching logic puzzle
How can one solve this logic puzzle?
I think the key ideas may have something to do with 11.,12. and common knowledge
An Arab man and an Israeli woman are abducted by extraterrestrials. The E.T.s ...
0
votes
4answers
107 views
Is there a theorem that disproves this or is this just some made up meaningless thing?
I find this slightly funny. I saw this on a meme:$$\begin{align}a=x\\ a+a=a+x\\ 2a=a+x\\ 2a-2x=a+x-2x\\ 2(a-x)=a+x-2x\\ 2(a-x)=a-x\\ 2=1\end{align}$$ How can these strange algebraic manipulations not ...
1
vote
3answers
101 views
Monty Hall problem vs. roulette systems - how are they different?
So I got interested in the Monty Hall problem - I understand what it's about, but somehow I can't wrap my head around the idea of the final choice not being 50/50. More precisely: we all know (or ...
2
votes
2answers
169 views
Use three 11's and various math symbols to make an equation equal to 6
The puzzle is to use the following symbols $$+,\;-,\;*,\;/,\;(\;,\;),\;!, \;\sqrt(\cdot)$$ in order to make a valid equation out of $$11~~~~~~11~~~~~~~11 = 6.$$
(There are three elevens with space in ...
2
votes
2answers
60 views
Tower of dice - Abstracting a practical problem to a mathematical method
This question arose when playing yahtzee with some friends. Not entirely sure if I'm in the right area, but hope you can help.
How many dice do you need to create a tower whose walls have the same ...
1
vote
1answer
174 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 ...
16
votes
7answers
1k views
“How long 'til we get there?” Road trip puzzle
Road trips can be fun, but they often appear to go slower the closer you get to your destination. I thought up this puzzle while on a recent trip. Thought it would be good food for thought. Curious ...
5
votes
5answers
381 views
Puzzle: Dropping balls along the way
A man has some balls in his pocket. Let the number of balls in his pocket be $n$.(Consider $n$ as an integer. If any decimal value occurs, consider its floor value. For example, if $n$ = 2.6 then take ...
3
votes
0answers
57 views
Card passing game, maximum length
Quoting from this question:
There are 25 people sitting around a table and each person has two cards. One of the numbers 1,2,..., 25 is written on each card, and each number occurs on exactly two ...
1
vote
2answers
194 views
Numerical puzzle
I'm stuck here with some numerical rebus -
Given: $A^2=BC, A^3=CA$
Find: $A+B+C$
$13$
$12$
$11$
$10$
(only one correct solution)
Note that letters represent digits.
I can't think of any idea ...
1
vote
2answers
148 views
Numerical rebus
Given:
${AA}\times{BC}=BDDB$
Find $BDDB$:
$1221$
$3663$
$4884$
$2112$
The way I solved it:
First step - expansion & dividing by constant ($11$):
$AA\times{BC}$=$11A\times{BC}$
$1221$ => ...
4
votes
2answers
156 views
Cut the rope puzzle
This question was asked to me in an interview, I still cannot think of its solution. Can anyone help? Following is the question:
Given an infinite number of ropes of length $R$, you have to ...
-1
votes
1answer
288 views
knight and knave problem
For this question, suppose you are on the island of knights and knaves. Remember that knights always speak truth while knaves always tell a lie.
(a) Suppose you come across two of the natives. You ask ...
10
votes
1answer
241 views
Given a set of digits, what is the biggest number we can make using exponentiation - numberphile noodle quiz
The question is motivated by a question on a can of number noodles.
Each item is a digit between $0$ and $9$. Clearly, if you form a string and consider it to represent a base $10$ integer, then ...
2
votes
2answers
131 views
Prove or disprove a chessboard with diagonal corners removed, cannot be tiled with L shape pieces or size 2
I think this is impossible, but I don't know how to prove an integer solution doesn't exist for a given equation. Here's my approach:
First, observations:
The removed tile will be of the same color. ...
3
votes
2answers
149 views
A less challenging trivia problem
There are 25 people sitting around a table and each person has two cards. One of the numbers 1,2,..., 25 is written on each card, and each number occurs on exactly two cards. At a signal, each person ...
