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

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4
votes
1answer
54 views

Breaking chocolate bars game

About two weeks ago, a friend of mine taught me the following game without his knowing the answer. It may be famous, but I haven't known it. There are $N\ (\in\mathbb N)$ chocolate bars composed of ...
1
vote
1answer
41 views

total number of combinations?

Patient Age ---> Avg Visits / Year <1 year ---> 7.5 1-4 years ---> 3.0 5-14 years ---> 1.8 15-24 years ---> 1.7 25-44 years ...
5
votes
2answers
92 views

$\pi$, $e$, $\phi$, and sunflowers

While reading some internet materials on design, I came across this picture and comment: I found it a little bit surprising. I knew that the real sunflower follows golden ratio in some way (but I ...
0
votes
0answers
29 views

What is the meaning behind this mathematical rebus? [on hold]

I believe I saw this 'inequality' in someone's profile description here on Math Stack Exchange. I think it expresses a message or has a meaning. What is it?
7
votes
2answers
65 views

Evenly space holes in circle

A picture is worth a thousand words: This gear is part of an interactive SVG Spirograph I'm creating. I'm dynamically generating the gear based on a number of parameters (gear radius, number of ...
1
vote
2answers
86 views

What is the probability of going bankrupt in roulette?

Imagine that the bank has the money $M_1$ and the player has the money $M_2$. The rules are the following: You win with a chance of $\frac{17}{36}$ and lose with $\frac{19}{36}$ each round. Now you ...
2
votes
0answers
76 views
+100

$Z_n \backslash \{0\}$ splits into octets

Let $n=8m+1, m\in\mathbb{N}$. Does the set of nonzero elements of $\mathbb{Z}_n$ split into disjoint octets of the form $8_k=\{\pm a_k,\pm b_k,\pm a_k\pm b_k\}$? The computer tells me it is possible ...
0
votes
1answer
30 views
3
votes
2answers
54 views

Winning a card game

Scenario: Each player has a deck of N cards. The first player controls an object called Grindclock, which means that at each turn, he can either : Add a "charge" counter on Grindclock, or Remove the ...
2
votes
3answers
83 views

What are the properties of the set of the Real Numbers without the Integers?

This question came up in a lunchtime discussion with coworkers. None of us are professional mathematicians or teachers of math. I apologize for any incorrect math or sloppy terminology. We were ...
2
votes
2answers
315 views

Pirates And Coins No.1

I actually like this one: There are five pirates in a ship and they have found 100 coins. The biggest pirate offers a way to divide the coins. If at least half of them agree on the division, it will ...
0
votes
0answers
27 views

An algorithm for linear equation system problem

Is there an algorithm for the following: I have 30 linear Diophantine equations of the following form: $$a_{1,1}x_1+\cdots +a_{1,16}x_{16}=b_1$$ $$a_{2,1}x_1+\cdots +a_{2,16}x_{16}=b_2$$ ...
0
votes
0answers
25 views

How to calculate the number of combinations of getting a pair in a deck of 52 cards?

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 games, ...
0
votes
2answers
82 views

Fun Tan Question [duplicate]

Using only trig identities, how would you approach the following question? Determine the value of $$ \prod_{i=1}^{89} \tan i^° = \tan 1^° \cdot \tan 2^° \cdots \tan 89^° $$
0
votes
1answer
47 views

time and distance

Dexter and Prexter are competing with each other in a friendly community competition in a pool of 50m length and the race is for 1000m. Dexter crosses 50m in 2 min and Prexter in 3 min 15 sec. Each ...
2
votes
3answers
55 views

What is the sum of the numbers in the shaded circles?

Each of the 6 circles contains a different counting number. The sum of all 6 numbers is 21.The sum of the 3 numbers along each side of the triangle is shown in the diagram. so What is the sum of the ...
0
votes
0answers
39 views

Card Shuffling and Convergence in Probability

There are $4n$ cards, and we denote the set of cards with number $4k,k \in \{1,2,\ldots,n\}$ as $S$. The we shuffle the whole cards randomly, which means that each permutation will happen with the ...
0
votes
1answer
57 views

How many times can you round a number?

For a typical rounding algorithm, I'm wondering how long the rounding chain goes for when you round up a number. For example, if you have a decimal like 0.4445, you round the last 5 up, which would ...
1
vote
1answer
13 views

Creating switches for piece wise defined function?

How can I create "switches" [the term may be new, but I'll explain it] for piecewise defined functions ? Suppose a function: $$ f(x)=\begin{cases}\alpha\;,x\in D_1\\\beta\;,x\in ...
-1
votes
1answer
92 views

What proportion of the circle is covered by the square?

Or what is the combined area of the circle segments (chords)? Picture a circle which is covered by a square, where the bottom vertices of the square are inscribed within the circle (so that the ...
6
votes
1answer
52 views

Sparsest matrix with full inverse

What is the sparsest matrix in $\mathbb R^{n,n}$ such that the inverse is full? I.e. I am looking for a matrix $A\in \mathbb R^{n,n}$ with as few non-zero entries as possible, such that $A^{-1}$ has ...
0
votes
0answers
26 views

Finding out the wrong number in the series [duplicate]

I need to find the wrong number in the following series.Device a logic to find the wrong number. 2,2,6,52.5,157.5,630 And 2,12,28,72.2,152,312,632 Regards
0
votes
2answers
43 views

Wine problem - ratio and mixture

Question $8$ litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the ...
0
votes
0answers
12 views

Is this a good formalization of self-counting functions?

I have looked on the internet, and I do not see any formal definition of a self-counting function. So I offer my own. The question I put to you is whether this is a good formalization . We have a ...
12
votes
2answers
470 views

Is 39 moves the longest a chess game can go moving only pawns?

I've thought of a few different ways a chess game could go on moving only pawns, but I've only counted moves in one scenario: Both White and Black take 16 moves to line their pawns at the middle of ...
0
votes
2answers
67 views

Questions about area

In math class (I'm in Geometry) I was messing around and decided to try and find the area of a circle using the area of a square if the radii are the same length. The square is inscribed in the ...
3
votes
1answer
60 views

How many orientations are there for pawns (for a single player) on a chess board?

How many orientations are there for pawns on a chess board? Pawns can only move forward or diagonally forward. No two pawns may exist on the same square. Pawns start on the second row, and ...
0
votes
2answers
39 views

Is my solution of this time and distance problem correct or wrong?

P and Q start running in opposite directions (towards each other) on a circular track starting at diametrically opposite points. They first meet after P has run for 75m and then they next meet after Q ...
0
votes
3answers
54 views

what will be the answer either 30 or 31 for this time based question?

A red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals. If both lights start flashing at the same time, how many times do they flash together in ...
2
votes
1answer
39 views

How to use the Lambert W function in an equation like this?

I was thinking of $\frac{4}{3}$ and found that $(\frac{4}{3})^4$ roughly equals $3$ (very roughly), and I though I would try to find the pairs of numbers where the equality suffices. So given the ...
1
vote
1answer
56 views

minimize distance

consider a two dimensional system. two points are given whose co-ordinates are $(h1,h2)$ and $(k1,k2)$. I want to minimize the distance between these two points with the condition that person has to ...
9
votes
0answers
1k views

This should be a piece of cake… right?

You probably know the following problem: We have two circular cakes of the same height but unknown and potentially different radii, and we want to cut them into two equal shares. Each cut can only ...
3
votes
0answers
64 views

A game on a smaller graph

In this question Alice and Bob play a game on $K_{2014}$, Alice directing one edge, Bob directing $1$ to $1000$ edges with Alice trying to make a cycle. The proof that Alice can win depended on the ...
16
votes
2answers
274 views

The expected outcome of a random game of chess?

Imagine a game of chess where both players generate a list of legal moves and pick one uniformly at random. Q: What is the expected outcome for white? 1 point for black checkmated, 0.5 for a ...
1
vote
1answer
63 views

Magic square of numbers

What is the logic behind filling up a magic square? I have understood the algorithm of filling up a magic square of 3*3 or 5*5. I really do not know how to derive this
1
vote
1answer
81 views

logic\math question [closed]

Hi, This is allegedly a very simple question....most of the people answered that the answer is 9=90. i claim that theoretically, you can't be 100% sure about the right answer because you don't know ...
1
vote
2answers
32 views

How is this card/paper plate magic trick done?

There are 3 paper plates, in which A is written on one, B on the 2nd, and C on the third. Now the person performing the trick knows the initial order of the paper plates. He then asks an audience ...
0
votes
1answer
27 views

A simple Question. How much “faster” is A than B as a percentage figure?

A simple question If two people complete the same task, and Person A completes the task in 10 minutes, Person B in 8 minutes, what figures can/should be quoted in terms of how much quicker A is than ...
2
votes
1answer
57 views

Polynomial equal to the ceiling of x

For a few days, I've been looking for a polynomial who's value is equal to the ceiling function of the only variable it contains. I thought about it for while and I haven't got a clue.
3
votes
0answers
82 views

Interesting Number Game

Let's say you are given some random positive integer. Next, assume you are given the following sequence of integers: $$[1, 2, 3, 4, 5, 6, 7, 8, 9].$$ Now, assume you are allowed to use the following ...
0
votes
2answers
33 views

IS the sequence right?

What i think is that, the sequence isn't correctly formulated. I have tried like this 7x5-9=35 2x3-1=5 8x6-4=44 4x5-9=?=11
1
vote
2answers
49 views

Concept of Probability in math first level

I am trying to teach myself the concepts of probability and I was wondering if this is correct. I am only 13 years old and did not learn this yet. I am just reading parts of a probability book to get ...
-1
votes
1answer
53 views

Mean and Standard Deviation self thought problem

I am 13 years old trying to teach myself about standard deviation and was wondering how this problem would look like. I know I am young to be learning this but I was reading about this and got ...
0
votes
0answers
17 views

3 team competition, 4 rounds, 12 teams- each teams plays other team once/Seeding

So I'm trying to make a schedule for a competition I run. In this game, 3 teams play at a time and there 12 teams total, ranked by performance. The teams play 4 rounds of competitions, and I don't ...
0
votes
0answers
13 views

Eigenvalues and fft of sound trying to find similarities

I'm looking at sound resonance patterns using matlab/octave to see if there may be patterns between FFT and Eigenvalues. I can get the frequencies and each of the frequencies amplitude to recreate ...
1
vote
1answer
42 views

Largest factor of sum of all 3-digit numbers…

What is the largest number (so, yes, I am looking for a discrete integer not an algebraic expression) by which the sum of all 3-digit numbers formed with the non-zero, distinct digits a, b, and c MUST ...
2
votes
1answer
50 views

Reverse Hex board game winning strategy

I just wanted to know the winning strategy to this question: In a reverse Hex board game I know it means where the player who first forms a path between his/her edges loses. Find a winning ...
3
votes
2answers
45 views

Rotating position in a square grid

I was asked a question about the following problem (maybe puzzle would be a better word), which originally came from programming. The person, who asked me this, was programming something involving ...
3
votes
1answer
100 views

When to be sure that we have counted all the squares in such problems [duplicate]

My first question is: How would one solve such problems (in general,squares+rectangles). What should be the general technique?How can this problem be reduced to a mathematical problem? My second ...
0
votes
1answer
30 views

Finding average speed

Your must reach from point A to point B in 20 minutes. Distance between the two points in 9.95 miles. 3 miles from point A, there is a tunnel the length of the tunnel is 1.2 miles. Inside the tunnel, ...