Puzzles, curiosities, brain teasers and other mathematics done "just for fun".

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0
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2answers
30 views

Finding the d value that will keep all coefficients at a minimum in a Cubic

I have a particular scenario. In this scenario, we have the standard cubic equation, ax^3 + bx^2 + cx + d = y as well as 3 points that are graphed, as can be ...
1
vote
2answers
47 views

Playing with propositional truth-tables

The following is the truth-table describing the definitions which allow us to establish truth values to composite formulae or molecules, which is nothing new: I had an idea about playing with the ...
3
votes
0answers
76 views
+100

Examples of calculus on “strange” spaces

I am interested in examples of calculus on "strange" spaces. For example, you can take the derivative of a regular expression[1][2]. Also the concept extends past regular languages, to more general ...
8
votes
1answer
412 views

Minimum and maximum determinant of a sudoku-matrix

Let $A$ be a sudoku-matrix. Assume that its determinant is positive. What is the lowest, what the highest possible value for the determinant of $A$ ? $A$ must have the dominant eigenvalue $45$, but ...
5
votes
2answers
57 views

Riddle : Given an integer power, does any integer to this power start with the power?

I initially found the following riddle somewhere : Is there an integer $n$ such that $n^{2004}$ starts (from the left) by $2004$ ? I was unable to find an answer, but I found the question rather ...
0
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0answers
25 views

Hanging a painting with nails so that removing any subset of nails from a given collection makes painting fall, and subsets are minimal

So I'm aware of the result that for positive integers $k \leq n$ it's possible to hang a painting with $n$ nails, such that if any $k$ nails are removed then the painting falls, but never when $k-1$ ...
0
votes
1answer
37 views

Find the missing number in the series?

In the given series , find the missing number in the given series :13,14,22,49,113,___,454?
-1
votes
1answer
28 views

Is there any practical use of $0^\circ angles$?

An angle is defined as two rays $\overrightarrow{YX}$, $\overrightarrow{YZ}$ sharing a midpoint $Y$; the angle formed is called $\angle XYZ$ or simply $\angle Y$. Then, the measure of $\angle Y$ is ...
40
votes
3answers
2k views

If the decimal expansion of $a/b$ contains “$7143$” then $b>1250$

I recently stumbled upon this really interesting problem: Suppose we have a fraction $\frac{a}{b}$ where $a,b \in \mathbb{N}$ and we know that the decimal fraction of $\frac{a}{b}$ has the ...
1
vote
3answers
28 views

integration by parts of $25\, (1-\sin^{2}x)$

I need help solving this integration of parts problem. I've tried a few different solutions and keep getting the wrong answer. This question is in regards to this problem take the integral by parts ...
1
vote
1answer
46 views

Greatest number of red coloured points

Problem: Let m and n be integers greater than 1. Consider an m×n rectangular grid of points in the plane. Some k of these points are coloured red in such a way that no three red points are the ...
0
votes
1answer
32 views

Show that a point lies on the diagonal of quadrilateral

In a quadrilateral ABCD we choose a point E on the side AD and a point F on the side CD. Then we choose a point G on the line EF. Let H be the second point of the intersection between the circles that ...
0
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4answers
2k views

Hands of a clock forming certain angles

How many times to the hands of a clock form a 60 degree angle between noon and midnight on the same day? Firstly im not sure weather they require the second hand to be included. And secondly (excuse ...
3
votes
2answers
58 views

Can any $n \in \mathbb{N}$ be reached from 1 by doubling and summing digits?

For $n \in \mathbb{N}$, let $f(n) = 2n$ and let $g(n)$ equal the digit sum (in base ten) of $n$. Can any $n \in \mathbb{N}$ be reached from $1$ after a finite series of applications of $f$ and $g$?
1
vote
1answer
43 views

Fun math books for 8 year old with math aptitude [closed]

My 8 year old showed interest and aptitude for math well above the level they teach in her school. I would like to find some math books that would spike her interest in math and make it fun for her.
2
votes
2answers
38 views

Soft Question: Combinatoric reading material

I am curious if anyone can recommend a good introductory text on combinatorics in similar vein as Richard J. Trudeau's Introduction to Graph Theory put out by Dover. For those who have not read it, ...
1
vote
1answer
56 views

Sharing items to a particular number of people [closed]

If I have a game where everyone contributes money, but only $n$ ($11$ in this case) people can win. How do I share the winnings such that the prize amounts do not diverge significantly as the amount ...
0
votes
1answer
154 views

Gradually rising or falling numbers

I'm looking for a number series I can use for gradually rising or falling numbers. The number series should not be linear and should converge to a number at some point. $\sqrt[N]{N}$ where $N > ...
8
votes
1answer
248 views

The case of Captain America's shield: a variation of Alhazen's Billard problem

I'm sure a lot of you are acquainted with Alhazen's Billiard problem, which involves finding the point on the edge of a circular billiard table at which a cue ball at a given point must be aimed in ...
5
votes
2answers
142 views

find a group of lowest N numbers so that no 2 pairs have the same bitwise or

I am trying to find the lowest group of N numbers (i.e. N=1000) so that no 2 pairs from the group have the same bit-wise or. more specific need to find a group $A = \{a_1,a_2,a_3,..,a_N\} $ such ...
1
vote
2answers
366 views

Number of Ways to Draw a Pair in a Poker Deck

I am confused over calculating the number of ways in which I can select a pair out of a deck of 52 cards. This is how I go about solving the problem: Following the definition of a pair in card ...
2
votes
1answer
77 views

Does an Eulerian semi-graceful polyhedral graph exist?

In a graceful graph, the vertices have number values that range from 0 to $n$ and $n$ edges with all values from 1 to $n$ that are differences between the vertex values. Here's a graceful but boring ...
1
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0answers
47 views

Can 1 be expressed with only irrationals in a non-trivial way?

There is an equation which I found interesting: $1=\phi+\frac{e^{i\pi}}{\phi}$ where $\phi$ is the golden ratio (either its positive or negative value). Are there other ways to express 1 with only ...
3
votes
0answers
132 views

The mathematics of a drinking game called Spoon

This question is about the drinking game Spoon. It was asked on reddit.com/r/math : http://www.reddit.com/r/math/comments/3i9790/drinking_game_turned_mathematical/ The question is whether the person ...
11
votes
1answer
183 views

Fibonacci numbers and the nontrivial zeros of the Riemann zeta function

Is this a mathematical coincidence? For $n=1,\dots,7$: $$ \left\lfloor \prod_{k=1}^n \arg\left(\rho_k\right)\right\rfloor = F_{n+1}, $$ where $\arg$ is the complex argument, $\rho_n$ is the $n$th ...
2
votes
1answer
2k views

Sum of cubes of the digits of a number equal to to the number

I have a number, I don't know how large or small, but if I cube the digits of the number and sum them, the sum is equal to the number itself. In other words, $$\sum_{k=1}^n{a_k^3}=\sum_{k=1}^{n}{a_k ...
0
votes
0answers
26 views

Conjecture on different type of triangle in a complete graph?

How many different triangles are there in $K_5$? The Answer is 35.(The Moscow Mathematics Puzzle) Then I asked what about $K_6$, $K_7$ and so on ...? With my intuition I arrived at this ...
3
votes
2answers
1k views

Flipping Cards Probability

You have a deck of cards, 26 red, 26 black. These are turned over, and at any point you may stop and exclaim "The next card is red.". If the next card is red you win £10. What's the ...
1
vote
3answers
661 views

$5n+1$, $3n-1$ problem, smallest repeating cycle and Collatz conjecture

Among the Collatz conjecture we have other "similar" problems that are solved and have repeating cycles. $5n+1$ has the repeating cycle $13, 66, 33, 166, 83, 416, 208, 104, 52, 26$, with a length of ...
3
votes
0answers
67 views

Trajectories on a circular billiards table

This question is related to The case of Captain America's shield: a variation of Alhazen's Billard problem, but more focused. Let the unit disc in the plane be our billiards table, and let $C$ ...
1
vote
1answer
43 views

Lunchroom Question: primes adding up to counting numbers?

Our lunchtime group got into another math related discussion. I apologize in advance if this isn't a rigorous question, as none of us are professional mathematicians. This is the question: Is it ...
1
vote
2answers
20 views

Fixed points of iterates of a certain map $\Bbb N \to \Bbb N$

I have stumbled onto chains of numbers that are interesting in that, when they are split up into their digits, summed, squared, and repeating some number of times, yield the original number. This ...
3
votes
1answer
88 views

Is it possible to solve sudoku without backtracking?

I occasionally solve sudoku puzzles on smartphone in spare time. My approach is based on the belief that at each stage in solving a sudoku puzzle there is at least one cell where there in only one ...
7
votes
3answers
2k views

How many turns can a chess game take at maximum?

The shortest number of moves that a game of chess can have is 2, as far as I know: White moves pawn from f2 to f3, black moves ...
5
votes
5answers
357 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. ...
3
votes
1answer
87 views

Puzzling Sequence [closed]

Today I was given a question that first I thought might be easy to solve but then no matter how hard I tried I couldn't solve it.(It's not really related to maths just some puzzle) if: $$ 9999=4\\ ...
1
vote
2answers
68 views

Ghosts closing and opening doors [duplicate]

There are $1000$ doors $D_1,D_2,D_3,\dots,D_{1000}$ and $1000$ persons $P_1,P_2,\dots,P_{1000}$. Initially all the doors were closed. Person $P_1$ goes and opens all the doors. Then person $P_2$ ...
8
votes
1answer
279 views

Here is a riddle that I have no idea how to solve.

Okay, so I was trying to solve this riddle found here. It is a diagram of a star with 16 points. Each point corresponds uniquely to a number between 1 and 16. The letters on each point represent a ...
1
vote
0answers
36 views

How comes plotting affine curve as shadows of gray modulo integer resembles its real locus?

Let $f(x,y)$ be polynomial with integer coefficients. Pick integer $n>2$. Let $M$ be $n \times n$ matrix. Set $M_{i,j}=f(i,j) \mod n$. Plot $M$ as bitmap in shadows of gray where larger value is ...
0
votes
0answers
12 views

CAT Percentile calculation?

How the percentile score is calculated in CAT? Can anyone exactly score 100 percentile score? How can two or more people score 100 percentile each?
1
vote
1answer
43 views

Maximum number of non-zero entries ,such that no two non-zero entries are on the same row or column.

In an M x N matrix such that all non-zero entries are covered in "a" rows and " b" columns. Then the maximum number of non-zero entries ,such that No two non-zero entries are on the same row or column ...
3
votes
0answers
35 views

Is there a heuristic reason behind this numerical coincidence?

Write $N(m, n; c)$ for the number of $m\times n$ zero-one matrices where each zero is adjacent to precisely $c$ others, where by "adjacent" I mean up/down/left/right but not diagonally. (Notice that ...
2
votes
1answer
105 views

Prove that in any base the number of digits composing the repetitive mantissa of the reciprocal of a prime $p$ never exceeds $p-1$.

I was trying to find bases where the reciprocals of primes have a short repetitive mantissa. Here is what I found: The bases are on the left. The primes are at the top. The numbers represent the ...
1
vote
4answers
1k views

The largest number that cannot be made using a combination of $5$ and $11$?

Using just the numbers $5$ and $11$, what is the largest number that can not be made? An example of a feasible combination: $5 \cdot 20 - 11 \cdot 9 = 1$. An example of an unfeasible number is 13 ...
0
votes
1answer
42 views

Prove that 5 points lie on the same circle

How do I prove that 5 points lie on the same circle? I know about the theorem that opposite angles in a quadrilateral are supplementary, but how does that help me prove that 5 points lie on the same ...
12
votes
2answers
532 views

What is an “interesting integer” and are there uninteresting integers?

On a site, someone asked which number is most interesting and I answered, "Every number is interesting. Give me a number and I shall tell you why it is!". Now not going into philosophical ...
1
vote
1answer
367 views

Arithmetic progressions of perfect powers

Find the largest positive integer $n<100$, such that there exists an arithmetic progression of positive integers $a_1,a_2,...,a_n$ with the following properties. $1)$ All numbers ...
1
vote
1answer
85 views

Number puzzle : “You can't determine my sum.”

Albert said to Bob, "I have two unequal positive integers; the smaller is at least 2; the larger is at most 25. I will only tell you their product." So he did. Later, Albert has forgotten the numbers ...
-4
votes
3answers
47 views
3
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2answers
62 views

Proving the rules of a complicated game are well defined

What strategy could one use to formally model a game and prove that the rules do not lead to any self contradiction? A major example that comes to mind is Magic the Gathering. The card ...