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 ...
0
votes
1answer
71 views
Puzzle identification and solving algorithm
I am trying to solve 8x8 puzzle (total 64 buttons). Similar to LightsOut, but in this rules are different. Goal is turn ON every button.
Example:
...
1
vote
1answer
89 views
Raise a number to the “y” power without using exponents.
This is kind of a spinoff on my question Divide by a number without dividing.
Can anyone think of some clever ways to raise any given number to any given power without using an exponent anywhere in ...
0
votes
4answers
141 views
Divide by a number without dividing.
Can anyone come up with a way to divide any given x by any given y without actually dividing?
For example to add any given x to any given y without adding you would just do:
$x-(-y)$
And to ...
6
votes
4answers
191 views
number of solutions to an equation?
Given $x$ and $y$ are multiples of $2$ satisfying
$$x^2 - y^2 = 27234702932$$
Find the number of solutions to $x$ and $y$.
1
vote
1answer
70 views
Question about a puzzle in to mock a mockingbird
In to mock a mockingbird, we have the following puzzle: There are four people:
A is an accurate truth teller
B is an inaccurate truth teller
C is an accurate liar
D is an inaccurate liar
Smullyan ...
3
votes
2answers
57 views
Probability in Minesweeper
Suppose I click a random tile during a Minesweeper game. It is a 1. During each time I click an adjacent square, what are the chances of hitting a mine? How would this change if it were a 2 or another ...
1
vote
1answer
26 views
average no of vertices per triangle in a graph of infinite triangles
An infinite two-dimensional pattern is indicated above.
The smallest closed figure made by the lines is called a unit triangle. Within every unit triangle, there is a mouse. At every vertex there is ...
4
votes
0answers
66 views
Colored balls puzzle
Imagine you have $n$ balls in a bag that are colored from $1$ to $n$. At each turn you take two balls at random out that have different colors and color one the color of the other. You then put them ...
1
vote
0answers
51 views
You are Johnny Depp 3!
An extension of this question.
As @Jared stated in his answer the solution is:
we assume that the head pirate chooses between multiple possible proposals that maximize his profit by rewarding ...
0
votes
0answers
35 views
Is there a two name Wikipedia pangram? [closed]
Benjamin Franklin Goodrich and François-Xavier Wurth-Paquet are people in Wikipedia with the letters A-O and N-X.
Is there a pair of names in Wikipedia that has all the letters A-Z? I use ...
2
votes
1answer
145 views
Another hat problem
A finite number of prisoners, after being given their hats (black or white), are able to see one another but themselves, and then they are ordered to jot down their guess on the color of their own ...
6
votes
2answers
255 views
You are Johnny Depp 2!
An extension of this question repeated below.
A band of 9 pirates have just finished their latest conquest -
looting, killing and sinking a ship. The loot amounts to 1000 gold
coins.
...
3
votes
1answer
33 views
Combination of natural numbers (1-10) in a triangle
I have the numbers 1..10 and want to arrange them in a billiard triangle such that they add up to the value on the right hand side thus. I can only use each number once.
Is there a formula for ...
2
votes
1answer
71 views
Riddle - cover a $62 \times 66$ board using only $341$ straight rows of $12$ squares each
Is it possible to cover a $62 \times 66$ board using only $341$ straight rows of $12$ squares each?
0
votes
2answers
47 views
A Nim variant: Number of stones
Alice and Bob play the following game. There is one pile of $N$ stones. They take turns to pick stones from the pile, Alice will play first. In each turn, a player can only pick $k$ $(a \le k \le b)$ ...
1
vote
1answer
63 views
Dividing a rectangle in 3 equal parts half at time?
Here's an interesting puzzle that has got me thinking:
You need to divide a rectangle into 3 equal parts along it's length. However you can only divide things into half. You don't have any other ...
9
votes
2answers
370 views
9 pirates have to divide 1000 coins…
A band of 9 pirates have just finished their latest conquest - looting, killing and sinking a ship. The loot amounts to 1000 gold coins.
Arriving on a deserted island, they now have to split up the ...
1
vote
1answer
48 views
On the arrangement of digits on a dice
In a cubic dice, the sum of the numbers on 2 opposite faces is 7, why are numbers arranged in such a way? Would the result of throwing a dice (1 or more times) still yield a random number if the ...
7
votes
3answers
170 views
Blending Colors
Three one-gallon buckets of red, blue, and yellow paint are each two-thirds full. Without the ability to measure, is it possible to equally mix all of the paint through a finite sequence of pours ...
5
votes
1answer
84 views
Tiling an $n\times n$ Grid
Given an $n\times n$ grid, and $2\times 2$ checkered tiles (white in the upper left and bottom right corners, and black in the upper right and bottom left corners), what is the smallest number of ...
4
votes
2answers
74 views
Math Puzzle: Area of Concentric Rings
The problem below appeared on the latest round of Google Code Jam:
Maria has been hired by the Ghastly Chemicals Junkies (GCJ) company to help them manufacture bullseyes. A bullseye consists of a ...
3
votes
2answers
64 views
sliding a shape with area= 5 on a grid so it covers at least 6 of it's points - riddle
place a shape on an integer coordinates grid, which is continuous without holes, and that its area is 5. Explain why you can slide it (without twisting or warping it), so that it will cover at least ...
3
votes
0answers
42 views
How to find an expression whose value is 190
Given a set of numbers (in this case):
3, 7, 7, 100, 50
Either:
prove it is impossible to form the number k = 190 using ( ) + - * / operators between sub set of the these numbers ex: 1000 = ((3 + ...
1
vote
2answers
146 views
Weather station brain teaser
I am living in a world where tomorrow will either rain or not rain. There are two independent weather stations (A,B) that can predict the chance of raining tomorrow with equal probability 3/5. They ...
2
votes
1answer
67 views
Geometry brain teaser (Candle in the room with mirrored walls)
King wants 2D room with smooth walls and columns (second derivative exists) that reflects light. King asks you to build it in such way that there exists a spot, where you can place a candle and there ...
5
votes
2answers
67 views
100-sided die probability
The question is as follows: You are given a 100-sided die. After you roll once, you can choose to either get paid the dollar amount of that roll OR pay one dollar for one more roll. What is the ...
3
votes
2answers
47 views
What to bid for this treasure chest? (puzzle)
Suppose you are given the opportunity to bid for a treasure chest, which you know to be priced anywhere between 0-1000 dollars inclusive). Treasure price is uniformly distributed. If you bid equal to ...
1
vote
1answer
59 views
Polygon made up of 12 unit sticks with an area limit
A polygon is made up of 12 unit sticks and its area is 3 units^2. Find as many such polygons as possible. Note that a side of the polygon could be made up of more than 1 stick but a stick could not be ...
1
vote
2answers
44 views
Pigeon hole principle question
Their are a group of finite aliens on a spaceship. Show that their are at least two aliens who know the same number of aliens on the spaceship.
I was given a hint, and that was to use the pigeon ...
28
votes
2answers
545 views
Predicting Real Numbers
Here is an astounding riddle that at first seems impossible to solve. I'm certain the axiom of choice is required in any solution, and I have an outline of one possible solution, but would like to ...
0
votes
1answer
47 views
A word problem concerning probability. Its pretty interesting
I found an interesting word problem. Check out this link:
http://www.math.hmc.edu/~ajb/PCMI/pcmi12.pdf
It is problem $A7$. I have been working on it and have reached the following conclusion: Say ...
3
votes
3answers
101 views
A puzzle about graph coloring.
Let $G$ be a graph with three disjoint triangles(i.e. the graph is not connectd and has three connected components each of which is a triangle). If each vertex of G is assigned a red or a green color, ...
0
votes
1answer
35 views
Faulty machine problem variation
I don't know if this problem is known by any other name. The classic problem is:
We have 10 machines that produce balls, each weighing 10grams. One of the machines, however, produces balls weighing 9 ...
1
vote
2answers
71 views
Gold Coins and a Balance
Suppose we know that exactly $1$ of $n$ gold coins is counterfeit, and weighs slightly less than the rest. The maximum number of weighings on a balance needed to identify the counterfeit coin can be ...
5
votes
2answers
122 views
When is $\frac{2^n+1}{n^2}$ an integer? [duplicate]
Can anyone see how to solve this number puzzle?
Find all integers $n>1$ such that
$$\frac{2^n+1}{n^2}$$ is an integer.
4
votes
3answers
104 views
paper punch puzzle
I was told this lovely puzzle recently which I thought people here might enjoy.
Consider a paper punch that can be centered at any point
of the plane and that, when operated, removes from the
plane ...
1
vote
2answers
29 views
Counting ordered triples of sets, with empty intersection.
I was recently asked this question which I couldn't solve.
Give the number of ordered triples $(A_1, A_2, A_3)$ of sets which have the property that
$A_1 \cup A_2 \cup A_3 = ...
4
votes
1answer
61 views
Classrooms and students puzzle
My school has many classes. Any two students share exactly one class. Any two classes share exactly one student. A class must have at minimum $3$ students, and there is at least one class with $17$ ...
3
votes
1answer
93 views
Safes and keys probability puzzle [duplicate]
I have $100$ keys and $100$ safes. Each key opens only one safe, and each safe is opened only by one key. Every safe contains a random key. 98 of these safes are locked. What's the probability that I ...
0
votes
1answer
48 views
Enigmatic optimization problem
My problem, which I proposed to myself months ago is based on the simple optimization problem
in which you find the best path for a lifeguard to rescue a drowning victim. Obviously the
shortest ...
4
votes
2answers
53 views
Find $x,y$ such that $x=4y$ and $1$-$9$ occur in $x$ or $y$ exactly once.
$x$ is a $5$-digits number, while $y$ is $4$-digits number. $x=4y$, and they used up all numbers from 1 to 9. Find $x,y$.
Can someone give me some ideas please? Thank you.
1
vote
1answer
69 views
puzzle: A spy and the keypad
A spy encounters a keypad that requires a 4 digit PIN. He uses a fine dust to find which keys are used in the combination. He does not know the sequence of keys, nor which ones repeat if any. ...
0
votes
1answer
82 views
MATH PUZZLES involving chess board
This is a very simple question: how many squares are there in a three dimensional chess board?
-5
votes
1answer
72 views
complex maths puzzle problems
What is the value of $X$ ?
\begin{align}
X= \frac{(76^2-67^2)}{(9^2-3^2)} \cdot \frac{(85^2-58^2)}{(9^2-8^2)} \cdot \frac{(93^2-39^2)}{(7^2-6^2)}
\\
\cdot \frac{(98^2-89^2)}{(8^2-5^2)} \cdot ...
1
vote
1answer
65 views
Maximizing fire-breathing power of multi-headed dragons
Dragons are gathered up on a battlefield. Certain dragons are chosen in order to provide maximum fire breathing power. A dragon can have any number of heads. The only rule is that no more than $1000$ ...
6
votes
1answer
170 views
Unfaithful husbands [duplicate]
In a parallel universe when Neil Armstrong landed on the moon, he found it to be inhabited by a tribe of humanoids. He discovered that:
they were all married
the husbands of 10 of the wives were ...
3
votes
3answers
140 views
Find the poisoned pie
You are a pie maker and you are holding a fair to display your pies. You have 1000 pies. You have 10 workers to help you. The fair is in two hours. Unfortunately you discover that a rival pie maker ...
1
vote
2answers
88 views
Recreational Puzzle
$n^{3}$ cubes are glued together to form one solid cube which is then hung in the air. As time proceeds, the most outer layer of this solid cube begins to dissolve and eventually those smaller cubes ...
10
votes
6answers
255 views
When two voters meet, they switch allegiance; might they all ally with the same candidate?
Let's assume that there are three candidates running in an election.
Right before the elections (when there is no more propaganda), it is
forbidden to gather in groups of more than two people ...
10
votes
1answer
95 views
How can one determine the chess configuration that maximizes the number of possible moves?
To clarify, what is the chess-board configuration that would maximize the number of valid moves one player could make on his or her turn? I thought of this question while playing chess, how apropos. I ...
