Tagged Questions
0
votes
4answers
103 views
How to verify method used to solve integral was actually the fastest?
Is there any way to verify if the method I chose to integrate (by hand) was indeed fastest, or if there exists some better technique? Can a computer tell me or show me what the fastest method was, ...
1
vote
1answer
110 views
A follow-up question on an arithmetic function satisfying a certain inequality
In the MSE question here, I asked whether the inequality:
$$\frac{a}{b} + \frac{b}{a} < \frac{f(a)}{f(b)} + \frac{f(b)}{f(a)}$$
would imply $a < b$ (where $f(x) \in \mathbb{N}$ is a function ...
1
vote
1answer
95 views
A quick question on general mathematics
I have the following question that I am currently unable to satisfactorily answer myself.
My question is:
Does the inequality
$$\frac{a}{b} + \frac{b}{a} < \frac{f(a)}{f(b)} + ...
3
votes
3answers
182 views
Cyclic sums — How do you use them?
Can someone give me an example of how cyclic sums are used? I don't really understand how they're used in problem-solving. For example, $$\sum_{a,b,c}a^2$$ Any help would be appreciated, and I'm not ...
14
votes
5answers
642 views
Is high school contest math useful after high school?
I've been prepping for a lot of high school math competitions this year, and I was just wondering if all the math I learn would actually mean something in college. There is a chance that all of it ...
1
vote
2answers
76 views
combinations problem about apples and pears
Carlo has six apples and six pears: how many ways he can set in a row 6 fruits so that there should never be a pear between two apples?
Thanks in advance to everyone who will help me resolving this ...
1
vote
1answer
235 views
Multiplication Table with a frame and picture of equal sum
Is there an $n \times n$ multiplication table such that if you form a border of width $k$ ("the frame") and sum its elements, the total will equal the sum of the remaining elements ("the picture")?
...
2
votes
3answers
355 views
How many unit hexagonal tiles can be placed inside a larger hexagon of sides $a,b,c,a,b,c$?
How many unit hexagonal tiles can be placed inside a larger hexagon of sides $a,b,c,a,b,c$? I originally came across this puzzle on the codeforces website.
My first question: what is the mathematics ...
4
votes
2answers
336 views
Counting ordered triples of non-negative integers not greater than 100
Can we find the number of ordered triples $(x,y,z)$ of non-negative integers satisfying
(i) $x \leq y \leq z$
(ii) $x + y + z \leq 100$?
Source:Regional Mathematics Olympiad India (2003)
Thank you.I ...
