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

learn more… | top users | synonyms (2)

2
votes
1answer
68 views

Graph Puzzle with labels

There is a Graph G(V,E). All nodes and edges are numbered. Two edges can have same number but all nodes have a unique number. A path $ v_1, v_2,v_3,...,v_k $ exists if and only if the edge ...
0
votes
1answer
18 views

What functions $f_n(k)$ have the property $\sum_{k=r}^n k(k - 1)\ldots(k - r + 1)f_n(k) = n!$

What functions $f_n(k)$ have the property $$\sum_{k=r}^n k(k - 1)\ldots(k - r + 1)f_n(k) = n!\tag 1$$ I found this problem here (p. 140), so I know that one of the functions is $$f_n(k) = P_n(k) ...
0
votes
1answer
40 views

Matchstick game problem

I'm going through past exam papers and this question is proving to be tricky. I can't seem to solve it and have no clue how to, I tried checking numerous ways like odds,evens,primes etc but i'm sure ...
3
votes
2answers
61 views

Find $n$ if $n!$ ends in exactly $100$ zeroes and $n$ is divisible by $8$.

This question was in school maths challenge. I dont know how to approach this one.. any help would be appreciated.
2
votes
1answer
49 views

Construction of the pre-addition

We know that the multiplicative operator is construct by iterating the additive one, and the power operator is construct by iterating the multiplicative one. Which makes us wonder if we can ...
3
votes
1answer
86 views

Covering eleven dots in the plane with eleven coins - counterexample?

The questions here and here relate to the question as to whether, given ten equally sized coins and a configuration of ten dots in the plane, there is a way of placing the coins so that they cover all ...
1
vote
0answers
33 views

prove that using 10 coins is enough to cover any 10 points in a plane [duplicate]

I recently got this puzzle, cant seem to prove it, i have manage to prove that for large enough N there is no solution, but not for 10. the puzzle asks to prove that using 10 coins is enough to cover ...
3
votes
1answer
32 views

Is it known whether a constant $A$ exists, such that there is always a Carmichael-number between $x$ and $Ax$ for $x\ge 561$?

For prime numbers, such a constant is well known. For $n\ge 2$, there is always a prime between $n$ and $2n$, so $A=2$ does the job. Carmichael-numbers are much rarer, so I wonder, whether a constant ...
0
votes
0answers
24 views

Construction of Carmichael numbers with many factors

Is there an efficient method to construct random Carmichael-numbers with $50-100$ prime factors ? The method with vectors $p_1,...,p_k$ , where $\frac{1}{p_1}+...\frac{1}{p_k}=1$ which gives a ...
2
votes
1answer
32 views

word problem concerning speed

A man rows across a river 1/2 mi. wide and lands at a point 1/4 mi. farther down the river. If the banks of the river are parallel straight lines and he takes 1/2 h. to cross, what is his ...
1
vote
0answers
32 views

A closed expression for $\sum_{k=1}^n\cos(kA)$ [duplicate]

How do I find a closed expression for $$\sum_{k=1}^n\cos(kA)$$ any idea about how to go about doing this? Thanks in advance
5
votes
1answer
60 views

How can I improve my problem solving abilities so that I stop missing the obvious?

I'm a generally good math problem solver. I get decent scores on contests, top of my class in math courses, and have a pretty wide array of knowledge from which to relate concepts in order to solve ...
8
votes
7answers
3k views

The number of bottles of beer one can buy with $10, after exchanging bottles and caps [closed]

My answer to this question is 15, but my dad insists I am wrong. Who is right? $2 can buy 1 bottle of beer. 4 bottle caps can be exchanged for 1 bottle beer. 2 empty bottles can be exchanged ...
2
votes
1answer
68 views

equation where the numbers don't matter(SOLVED) [closed]

me and my friends are making an escape room and we had the idea of using a pack of Bean Boozled jelly beans (for those not known with them, it is a small box of jellybeans with 10 pairs of flavours, ...
3
votes
2answers
58 views

What is the Mathematics behind the folding an A4 sheet in 3 equal parts?? [duplicate]

This is an extension question of this question. They have given a plenty nice way to fold a A4 sheet in 3 equal parts. What is the Mathematics behind the foldings? Can we use the same way for ...
1
vote
1answer
20 views

Determining outstanding balance on a loan

A loan of $17,000$ dollars is to be repaid in annual installments of $2,100$ dollars, the first due in one year, followed by a final smaller payment. If the effective rate of interest is $8.8$ ...
24
votes
5answers
505 views

How many passwords can be formed?

We are all familiar with the $9$-dotted maze lock screen password that we get in all mobiles today.Now if minimum of $3$ consecutive dots can be joined to form a password total how many passwords can ...
0
votes
1answer
47 views

Basic probability question, choosing between two options for every stage

Suppose that two players are playing a game, players select between two choices: Scenario 1: player $1$ chooses option $1$ with probability $60\%$, option $2$ with $40\%$ player $2$ chooses option ...
1
vote
0answers
53 views

Formulation for solving puzzle game mathematically

I'm developing a solver for a simple constraint-based puzzle game. Here is an example of the puzzle: $$\begin{align} - \;6\; -\\ - - -\\ - \;3\; - \end{align} $$ The given 3$\times$3 grid of "clues" ...
2
votes
0answers
32 views

Alternative Arithmetics

In Anderson et. al 2010, "Cognitive and metacognitive activity in mathematical problem solving: prefrontal and parietal patterns", the experimenters taught people how to solve a novel system of ...
0
votes
7answers
183 views

Why is $\ln 1 = 0 $? [closed]

Yes I know, and believe, and have used it for all the time I have done mathematics as fun as well as a subject. But why is it that $$\ln 1 = 0$$
2
votes
1answer
115 views

Alien Mathematics [closed]

I'd like to pose the community here a challenge. It's often supposed that if we encounter intelligent alien life, mathematics will probably be how we start communicating. We have seen ...
0
votes
2answers
74 views

Probability of Exactly X Successes with Variable Success Dice

I am interested in finding the probability that on any single roll of dice you can have an exact number of successes. However, depending on the particular dice success is a different probability and I ...
2
votes
1answer
71 views

Make all the sixes. Fun [closed]

Given the following it is possible to complete each case so that they are all true? (i.e. so that the equation .... = 6 is true) You can add any mathematical operations and parentheses but you cannot ...
10
votes
3answers
836 views

sum of one hundred numbers

I saw this problem recently. It asks to prove that it is always possible to choose 100 numbers from 200 positive numbers such that their sum will be divisible by 100. Attempt to solve: my first step ...
25
votes
1answer
900 views

What is the optimal strategy in the “Factor Game”?

Edit (Nov 1, 2015): Bounty awarded, but the full question (i.e., what is the optimal strategy) remains open at the time of this update. Consider the Factor Game played as follows: Given a list of ...
0
votes
1answer
48 views

Formula to calculate fastest minute of a horse race

I though of a problem (which is more of a fun to do than anything else), that it's the following: Is it possible to find a formula (or something similar) that calculates the fastest minute of a horse ...
2
votes
1answer
42 views

Optimization and Postage Stamp Problem

(1) Given the set U = {1, 2, 3, ..., 98, 99, 100} of Natural numbers, find the smallest subset S contained in U that: For every element v belonging to U, there are a, b elements of S, not ...
0
votes
0answers
20 views

How to connect a minimum variance portfolio to the Two Fund Theorem using Lagrange?

I've received this question for my Mathematics course at school, and I'm completely stumped as to how we should approach it. I'm unsure how to use the information about a minimum variance portfolio, ...
0
votes
1answer
17 views

Annuities-calculating interest

Janet receives a $ 10,000 life insurance benefit. If she uses the proceeds to buy an n-year annuity immediate, the annual payout will be 1613.36. If a 2n-year annuity due is purchased, the annual ...
2
votes
0answers
49 views

Rifleman game with $n$ players in $D$ dimensions: what is the survivor fraction when $n,D\to\infty$?

This is a follow up to this question where the following problem is explored (for $D=2$): $n$ riflemen are distributed at random points in $[0,1]^D$. At a signal, each one shoots at and kills his ...
6
votes
6answers
437 views

How can you disprove the statement $4=5$?

I know this sounds insane. But bear with me, my friend said this to me with a straight face: Can you disprove the statement: $4=5$? And I was like is that even a question, thats obvious, $5$ is ...
0
votes
0answers
34 views

Finding the co-efficient of $x^{10}$ in $\frac{1}{(1-x^{10})(1-x^5)(1-x^2)(1-x)}$

While trying to solve a problem with from STEP questions, I encountered this. I am not sure whether this approach is right for that question but this doesn't look like the right way to approach. Any ...
0
votes
0answers
26 views

Difficult Proof by Construction Question

A teacher introduced this question to me, and am interested in finding the answer, but cannot figure it out. Given the squares of the numbers 1 through 81, can you separate them into three groups with ...
-1
votes
1answer
22 views

Possible NCAA Bracket Seedings

This is my first post on math.stackexchange. I am wondering how many possible seedings there could be in a seeded NCAA March Madness tournament. As a user suggests here, the number of outcomes of an ...
0
votes
3answers
51 views

Two out of five in a group have the same number of friends…

I recently came across a problem- Prove that in a group of five people,there are two who must have the same number of friends in the group. I assume it must be solved by Pigeon Hole Principle ...
2
votes
2answers
107 views

Very fascinating probability game about maximising greed?

Two people play a mathematical game. Each person chooses a number between 1 and 100 inclusive, with both numbers revealed at the same time. The person who has a smaller number will keep their number ...
1
vote
1answer
17 views

Is 42 in the French Premier League the maximal number of points possible to be relegated?

This is Saturday night mathematics, yet, it is not an absurd exercise The French premier league has 20 teams. After 38 matches (all teams meeting each other twice), the last 3 by point total are ...
5
votes
0answers
85 views

$f(x+1)=f(x)+f(\alpha\cdot x)$

I try to find an analytic increasing function $f_\alpha$ ($0\le\alpha\le1$) from $\mathbb R$ (or $\mathbb R^+$) to $\mathbb R$ such that for all $x$ $$f_\alpha(x+1)=f_\alpha(x)+f_\alpha(\alpha\cdot ...
2
votes
0answers
66 views

Is there a contiguous locus of the equality $a = b$ in $\zeta(\rho + \varepsilon)=a + î b$ in the near of a root?

This is just by an accidental couriosity: In the near of a root $\rho$ of the Riemann's zeta - can there be a continuous line starting from $\zeta(\rho)=0$ to $\zeta(\rho + \varepsilon_j)=a_j + î b_j ...
3
votes
1answer
65 views

Infinite prisoners with hats where the prisoners do not know their position.

The infinite prisoners with hats puzzle runs as follows. We have a countably infinite group of prisoners numbered $\{1, 2, \dots\}$, each of whom is wearing either a white hat or a black hat. The ...
0
votes
0answers
21 views

What's the best way to represent $N$ numbers with the smallest number of symbols and shortest string length?

Supposedly Base $e$ would be the best base system, but that's if you want to represent all numbers. What would be the best way to describe only $5$ numbers? Using $5$ unique digits, or roman numerals ...
1
vote
1answer
48 views

A further question to “does-there-exist-a-tool-to-construct-a-perfect-sine-wave”

After viewing the question and answer in Does there exist a tool to construct a perfect sine wave? . I have a question of interest and for fun:- “How to choose the size (in term of radius R) of tube ...
2
votes
1answer
86 views

Does there exist a tool to construct a perfect sine wave?

For example, a perfect circle can be constructed using a compass and a perfect ellipse can be constructed using two pins and a piece of string, because a circle can be defined as the locus of points ...
0
votes
0answers
21 views

calculating opportunity costs of different pay rates.

i've been fiddling with an opportunity cost calculator just for fun and seem to have figured out the math, but it's ugly and cumbersome. i'm pretty sure there is a way to simplify the equation, but ...
5
votes
2answers
172 views

Determine whether a point lies inside the curve or outside a random curve using pencil and scale

Say, I am given a point and a closed curve. I don't know anything about the curve (where it is, what it is, its size etc.;say it is hidden somewhere)."I just can't see the curve but I can see the ...
6
votes
4answers
199 views

Why is the following NOT a proof of The Chain Rule?

In Leibniz notation of the chain rule, $$\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$$ Where $y\left ( u\left ( x \right ) \right )$ is a composite function of x. I understand that the du's ...
1
vote
0answers
32 views

Probability of termination of random teleportation

In Minecraft, with mods, there's a liquid called Resonant Ender, which if you touch it, teleports you randomly up to 8 blocks on both the north-south and east-west axes. Consider an infinite sea of ...
6
votes
1answer
127 views

Deriving the surface area of a sphere from the volume

I am a high school student, so I know how to derive the volume $V=\dfrac{4}{3}\pi r^3$ using calculus, but I am unable to derive its surface area. However, I notice that we can approximate the ...
25
votes
4answers
347 views

How many ways are there to pile $n$ “$1\times 2$ rectangles” under some conditions?

A friend of mine taught me the following question. He said he created the question by himself and conjectured the answer, but couldn't prove it. Though I've tried to solve the question, I've been ...