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

learn more… | top users | synonyms (2)

2
votes
0answers
19 views

How to find the point in a closed geometrical figure which maximizes the “direct-line-of-sight function”

To expand upon the title, and put it in clear terms, I phrase the problem thusly: Consider the interior of any continuous, closed, non-self-intersecting curve in the plane. (I'm not sure if I'm ...
0
votes
2answers
69 views

Is $f(x)f(y)=f(x+y)$ enough to determin $f$? [duplicate]

I had a discussion with a friend and there it came up the question whether $f(x)f(y)=f(x+y)$, $f(0)=1$ and the existence of $f'(x)$ implies that $f(x)=\exp(a x)$. This seems very reasonable but I ...
1
vote
2answers
90 views

Weather station brain teaser

I am living in a world where tomorrow will either rain or not rain. There are two independent weather stations (A,B) that can predict the chance of raining tomorrow with equal probability 3/5. They ...
-3
votes
0answers
66 views

Math glitch or did I do something wrong? [closed]

Suppose: $$a + b = c.$$ This can also be written as: $$4a - 3a + 4b - 3b = 4c - 3c.$$ After reorganising: $$4a + 4b - 4c = 3a + 3b - 3c.$$ Take the constants out of the brackets: $$4 \cdot (a+b-c) = 3 ...
30
votes
14answers
501 views

How to entertain a crowd with mathematics? [closed]

I am a high school student who follows a university level curriculum, and recently my teacher asked me to hold a short lecture to a crowd of about 100 people (mostly parents of my classmates and such, ...
1
vote
2answers
43 views

How can be done by the method of mathematical induction?

We are given that $P(x+1)-P(x)=2x+1$ We also know that $P(0)=1$ We want to prove that $P(2004)=(2004)^2 +1$ Can someone explain how can be solved with mathematical induction? Thank you in advance!
23
votes
2answers
453 views

Predicting Real Numbers

Here is an astounding riddle that at first seems impossible to solve. I'm certain the axiom of choice is required in any solution, and I have an outline of one possible solution, but would like to ...
5
votes
0answers
43 views

Evaluation of a slow continued fraction

Puzzle question... I know how to solve it, and will post my solution if needed; but those who wish may participate in the spirit of coming up with elegant solutions rather than trying to teach me how ...
2
votes
1answer
55 views

A game involving points in the integer plane - who wins?

I am running a workshop on puzzles and problem solving over the weekend and thought that it might be a good idea to get people engaged by phrasing some interesting mathematical results in terms of ...
3
votes
2answers
47 views

Why does the strategy-stealing argument for tic-tac-toe work?

On the Wikipedia page for strategy-stealing arguments, there is an example of such an argument applied to tic-tac-toe: A strategy-stealing argument for tic-tac-toe goes like this: suppose that the ...
5
votes
1answer
116 views

Does there exist a positive integer $n$ such that it will be twice of $n$ when its digits are reversed?

Does there exist a positive integer $n$ such that it will be twice of $n$ when its digits are reversed? We define $f(n)=m$ where the digits of $m$ and $n$ are reverse. Such as ...
1
vote
2answers
59 views

Gold Coins and a Balance

Suppose we know that exactly $1$ of $n$ gold coins is counterfeit, and weighs slightly less than the rest. The maximum number of weighings on a balance needed to identify the counterfeit coin can be ...
30
votes
1answer
530 views

Proving that $x$ is an integer, if the differences between any two of $x^{1919}$, $x^{1960}$, and $x^{2100}$ are integers

For a specific real number $x$, the difference between any two of $x^{1919}$, $x^{1960}$ , and $x^{2100}$ is always an integer. How would one prove that $x$ is an integer?
0
votes
1answer
65 views

Combine the three numbers in each group to get the same result

Combine the three numbers in each group to get the same result in each of the three groups. You can use addition, subtraction, multiplication, division, and exponentiation. Group 1: $3, ...
5
votes
3answers
75 views

palindromic squares of palindromes

This question is inspired by Google's recent programming competition (modified slightly for ease of exposition). For a given $n$, one of the problems was to find all positive "fair" integers $k$ less ...

1 2 3 4 5 34
15 30 50 per page