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

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3
votes
1answer
103 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
43 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
48 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
49 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
19 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
174 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
43 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
60 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
52 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
32 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
59 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 ...
14
votes
3answers
818 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
10 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
40 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
90 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
17 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
34 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
73 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 ...
0
votes
0answers
36 views

writing a number as a sum of odd integers

How many ways are there of writing $n$ as a sum of odd integers, where the order doesn't matter? For example, there are $2$ ways of writing $3$: $(1,1,1)$ and $(3)$.
0
votes
1answer
64 views

How can I transition my dogfood can opening procedure from the morning to the evening?

My 2 dogs are each fed twice a day. They are each given 1/4 can of dog food with every feeding; 1/2 a can a day per dog,;1 can consumed total, daily. I intended to open a can of dog food every night, ...
8
votes
2answers
330 views

An alternating decimal sequence: Does its average have a limit?

Define a sequence of decimals $x_n$ by alternating the digits $1,2,\ldots,n$ left and right, as follows: $$x_1 = .1$$ $$x_2 = .21$$ $$x_3 = .213$$ $$x_4 = .4213$$ $$x_5 = .42135$$ $$x_6 = .642135$$ ...
21
votes
2answers
323 views

The Plank Problem 2 Dimensions

We were trying to solve this wonderful problem, but have not succeeded to solve. It goes like this: Let $R=[0,1]^2$, and $D\subseteq R$ be a convex set which intersects each side of $R$. Define a ...
2
votes
2answers
130 views

How can I get a good estimation of the following function

The function is $$ f(n) = \sum_{i=1}^{n} \frac{1}{2i-1}$$ How can I compute for example $f(20)$ or $f(50)$ without using a calculator. I want to have an approximation
3
votes
1answer
61 views

Interesting sequence question

I saw a puzzle the other day and it was as follows: Find the next number in the sequence: 1 11 21 1211 111221 312211 ... If anyone wants to have a go at the ...
1
vote
0answers
66 views

Finding the 'best' way in a card-arrangement-game

Let $n\ge 2\in\mathbb N$. Suppose that we have a card on which $1$ is written, a card on which $2$ is written, $\cdots$ , and a card on which $n$ is written. Now these $n$ cards are arranged from left ...
0
votes
1answer
144 views

Two Genius Mathematicians

This is actually a question I find really hard to answer.any hints are appreciated. By the way feel free to edit the tags as i really do not know which category is this question is in. Two genius ...
4
votes
2answers
94 views

expected value of a game with a n sided die

Suppose we have a n-sided die. When we roll it, we can be paid the outcome or we can choose to re-roll by paying $1/n$. What is the best strategy and what is the expected value of this game? As an ...
5
votes
1answer
127 views

Rooks in 3D chess board

How many rooks are needed for a 3D chess board of size NxNxN so that every empty cube on the board can be reached by a rook in a single move?
1
vote
2answers
73 views

hitting a dart board probability

You have a dart board which is split in half. If you hit the left half, you get $2$ points, if you hit the right half, you get $3$ points. You have an 80% chance of hitting the dart board on any ...
0
votes
1answer
54 views

A Bug Crawls Along a Square

A wire of length $4$ is bent into a square. At time $t = 0$, a bug starts crawling from the corner of the square to an adjacent corner, and continues traveling along the rest of the square until it ...
1
vote
1answer
45 views

find the sales tax from a tax included price that does NOT apply tax to the portion of the total that IS tax

I, a vendor, need to find the sales tax from a tax included price that does NOT apply tax to the portion of the total that IS tax. Most answers result in overpayment of taxes. Please do not tell me ...
2
votes
0answers
136 views

Homework Question for a 15 year old

My younger brother(age: 14 years 7 months) and his classmates were given a set of eight questions by his class-teacher, which included the following two questions: (i) Find, if you can, the fallacy ...
0
votes
1answer
19 views

How to Find the Remaining Length of a Cone With Only a Part of It

I took three measurements for a certain plastic cup in my kitchen. One was of the circle on the bottom of the cup, and the other was the top(the larger opening) and the height in between the two. ...
12
votes
4answers
588 views

expected value of a sum of a 10 sided die

Suppose you have a fair die with 10 sides with numbers from 1 to 10. You roll the die and take the sum until the sum is greater than 100. What is the expected value of this sum?
1
vote
0answers
41 views

Prove that eventually Hannah and the other swimmer will settle into a pattern where they pass each other (Please refer to the context in my question)

From the 2014 Mathcamp quiz: Hannah is about to get into a swimming pool in which every lane already has one swimmer in it. Hannah wants to choose a lane in which she would have to encounter the other ...
1
vote
1answer
40 views

Graph-like problem

Each shop in a town has an odd number of customers and each pair of shops shares an even number of customers. Prove that there are at least as many customers as there are shops. Any hints are ...
1
vote
0answers
39 views

Non-symmetric polynomials, game

This is a game I thought was easy but appears to be too hard for me... I'm trying to find a polynomial in x,y,z (they commute) such that permutations of the variables only give rise to 2 different ...
1
vote
2answers
28 views

Efficient random guessing

Let $(x,y)$ be a random point on the plane with some unknown continuous distribution. Your opponent randomly chooses one of the coordinates and tells you. You shall guess whether this coordinate is ...
1
vote
1answer
37 views

counting of numbers

In a garden there are three kind of roses-red, yellow and white. No matter which 9 roses are selected at least 2 of them are white; and no matter which 10 roses are selected at least 2 of them are ...
1
vote
1answer
35 views

Characterization of nowhere differentiable functions

Let $N:=\{f\in C([0,1])\vert \text{ f is nowhere differentiable } \}$ and $A_n = \{f\in C([0,1]) \vert \exists x\in [0,1]s.t. \forall y\in[0,1]: |f(x)-f(y)|\leq n |x-y|\}$. Now I have already ...
3
votes
3answers
40 views

Unbounded sequence with convergent subsequence

I'm just wondering if anyone knows any nice sequences that are unbounded themselves, but have one or more convergent sub-sequences?
0
votes
1answer
45 views

How often does $p^k$ divide the Fibonacci numbers?

I would like to know about the Fibonacci numbers $F_n = 1,1,2,3,5,8, \dots$ in $\mathbb{Z}/p^k\mathbb{Z}$. $$ \mathbb{P}[p^k \text{ divides } F_n ] = \frac{\#\{1 \leq n\leq N: F_n \equiv 0 \mod ...
5
votes
0answers
83 views

Geometrical question just for fun

Was puzzling with the following (home made) puzzle: Given the square $ABCD$ with $A = (1,1)$, $B = (1,-1)$, $C = (-1,-1)$ and $D = (-1,1)$ And given point $E = (0,2)$ What is the smallest (by ...
1
vote
2answers
39 views

Arrangement of Numbers to Get a Common Sum

I'm having trouble with a math problem. I need to arrange 6 numbers on a certain diagram: At every intersection of two circles, I have to put one of these six numbers: 4, 5, 5, 6, 6, or 7. The sum ...
6
votes
6answers
316 views

Do the differences of perfect squares apply to perfect cubes and more?

I'm curious about a special property of squares. The difference between perfect squares starting from 0 are 1,3,5,7,9..., where each difference goes up by 2. I want to know if there are any patterns ...