All Questions
5
questions
6
votes
4
answers
4k
views
Books for maths olympiad
I want to prepare for the maths olympiad and I was wondering if you can recommend me some books about combinatorics, number theory and geometry at a beginner and intermediate level. I would appreciate ...
16
votes
2
answers
473
views
Is $\prod_{1\leq i< j\leq n} \frac{a_i - a_j}{i-j}$, with distinct integers $a_i$, an integer?
It is known that for every $n$ consecutive integers, their product is divisible by $n!$, since $${{m}\choose{n}} = \frac{m!}{n!(m-n)!}$$ is also an integer.
So is it true that for every distinct ...
- 1,705
7
votes
1
answer
833
views
Traversing the infinite square grid
Suppose we start at $(0.5,0.5)$ in an infinite unit square grid, and our goal is to traverse every square on the board.
At move $n$ one must take $a_n$ steps in one of the directions, north,south, ...
- 8,759
1
vote
0
answers
43
views
In how many primitive pythagorean triples can some odd integer $a$ be a non-hypoteneuse edge?
In how many primitive pythagorean triples can some odd, positive integer $a$ be a non-hypoteneuse edge?
In the footnote to this question Daniel Fischer does most of the work:
Let $a$ be the odd ...
- 9,299
0
votes
3
answers
518
views
What is the maximum number of T-shaped polyominos (shown below) that can be put into a 6x6 grid without any overlaps? The blocks can be rotated.
I just drew the figure and manually tried the question but I am wondering is there a way to do this problem via permutations and combinations.
PS: I got answer as 7.
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