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

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6
votes
1answer
56 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
28 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
45 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
483 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
68 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
47 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
57 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
44 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
59 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
67 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
294 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
64 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
101 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
41 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
31 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
59 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
88 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
53 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
58 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
15 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
56 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
53 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
61 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
134 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, ...
1
vote
0answers
44 views

Fusible numbers — can we prove fuse(4) is finite?

Fusible numbers have been discussed here before. Other links: fusible numbers. OEIS A188545. You have an unlimited number of irregularly burning fuses that will nevertheless burn for exactly 1 minute. ...
5
votes
1answer
50 views

At what point discrepancy, in the NBA, does it make sense to milk the shot clock?

I am admittedly not great with probabilities, so I am soliciting the help of the community. I am watching game 3 of the NBA Finals and I am trying to work out when it makes sense to milk the shot ...
0
votes
1answer
52 views

Winning or Non-losing strategy for A or B

Find a winning or a non-losing strategy for the following game: Consider $25$ sticks arranged in a $5$ x $5$ square. Players alternately take any number of sticks from a single row or column. At ...
1
vote
0answers
20 views

Generalized-knight's tour

Define an $(a,b)$-knight as a chess piece that moves $a$ squares horizontally and $b$ squares vertically, or vice versa, in either order. Thus a normal chess knight is a $(1,2)$-knight. For which ...
0
votes
2answers
56 views

Solving an equation with multiple radicals [closed]

Can this equation be solved for a with no radicals in the answer?
5
votes
1answer
179 views

Placing numbers around a circle

Is it possible to place the numbers $1,2,\ldots,2014$ around a circle so that any number is divisible by the (positive) difference of its two neighbors? This problem was given to me by my neighbor's ...
1
vote
2answers
45 views

The rate change of the radius of a coil.

Suppose I have a tube of radius $r_0$ that I want to wrap a sheet of length $l$ and thickness $\Delta x$. Assuming the radius changes only when the paper overlaps the where the previous section ...
1
vote
1answer
74 views

Math Puzzle Solving

Using each of the digits 1,2,3,4,5,6,7,8 exactly once fill in the boxes so that no consecutive number is adjacent or cross to ...
1
vote
3answers
55 views

Find a function that is surjective and not injective

Rules: No piecewise functions. The function must be even, odd, or both even and odd. It cannot be neither. If this is impossible, prove why. This is just something I came up with for fun while ...
1
vote
0answers
48 views

How do you evaluate $a^b$ where b is irrational using only basic operators.

How would you evaluate $a^b$ where b is irrational and you can only use +,-, multiplication, division, and rational powers. For example $2^\pi.$ We know $2^2$ = $2\times2$ etc... but when the power ...
1
vote
1answer
33 views

How fast will a shape grow if it can grow exponentially only at the border, and growth is limited by crowding?

Take a hypothetical bacterium which divide once per minute. After $n$ minutes there will be $2^n$ bacteria, assuming no constraints. But what if its growth is constrained by resources and space? I am ...
0
votes
2answers
61 views

Another cool logical brain teaser I used to work when on when I was small

A person has 3 cups with him , he has a 8L cup filled with coke , and an empty 5L and 3L cups, using these three can anyone make 2 cups each with 4L to be served to two people. This person has no ...
15
votes
3answers
828 views

A problem I can't solve from my childhood to now.

When I was a child I was given this problem to send a wire from electricity, water, and internet to each of the houses, all three houses must have all three wires connected without being crossed ...
0
votes
1answer
11 views

Common numbers in sequences

Lets say we have a set $S$ of $N$ ($N\geq 3$) finite nonempty sequences of numbers, each of different length. Is the relation of "having some number or numbers in common" transitive on $S$? I have no ...
1
vote
1answer
73 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: http://imagizer.imageshack.us/a/img835/7738/c7gb.png The bases are on the left. The ...
0
votes
1answer
47 views

Exhaustive list of recreational mathematical concepts

There are many simple yet elegant, addictive and entertaining mathematical concepts. For example, drinker paradox, pigeon hole principle, Monty Hall problem, Hilbert's paradox of the Grand Hotel, etc. ...
0
votes
2answers
107 views

how to calculate vehicle speed using mathematics and Image processing?

i am doing my project in image processing.using segmentation i have detected the moving part(i.e the car) in the video successfully. But now i want to calculate speed of vehicle. in the above ...
0
votes
0answers
18 views

Compute hamming distance under security.

I am curious of the follow problem. Two parties each holds a binary vector $\{0,1\}^n$. They want to compute the hamming distance between each other. But they don't want to directly reveal the ...
2
votes
1answer
35 views

maximize the sum of numbers such that all of them are coprime

Suppose we have numbers from $2$ to $n$ (inclusive). We want to choose numbers such that all of them are coprime and give the maximum sum. For example, if $n=10$, then we choose $9,8,7,5$ and the ...
2
votes
6answers
98 views

Investigating the linearity between squares and their roots

I recently noticed that $\sqrt{128} = 11.31$ and that $128$ is $\approx 30\%$ between $121 = 11^2$ and $144=12^2$, that is: $$ \frac{128-121}{144-121} = \frac{7}{23} \approx 30\%$$ and $\sqrt{128} = ...
-1
votes
1answer
75 views

Why lots of people don't like (and sometimes hate) mathematics? [closed]

This is a question which I really can't give an answer. Personally i really like Math and I found it interesting since I was a child, but now I really feel like I'm the only one even if I am not (just ...