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answered Functional equation: Show $0\le f(n+1)-f(n)\le 1$ and find all $n$ such that $f(n)=1025$.
Aug
20
answered Tzaloa 2015 game problem (piles with $1,2,4 \dots 2^{19}$ coins each)
Aug
20
comment What is maximum a number of to form right-triangles from in n straight lines
@Tad You definitely need to justify the assumption of "maximized when the groups have the same size". For example, in the odd case, i believe that the maximum would occur when the lone group only has 1 line in it, in which we are approximating the even case which is much superior than your odd case equal distribution bound.
Aug
20
answered Ordered triples of n-powerful integers
Aug
17
comment 2014 iberoamerican olympiad Problem 3
@edwinisaac What do you think is wrong with that answer in the forum? It looks reasonable to me.
Aug
17
comment Can anybody solve this geometry?
Re the third image: The condition still holds. F lies on BC extended, and CF = 1/2 (CA + CB) > CB.
Aug
17
comment Calculation of $\displaystyle \left[\frac{n!}{1!+2!+3!+\cdots+(n-1)!}\right]$
@LeastSquaresWonderer Do you know what the Floor Function is?
Aug
17
comment 2014 iberoamerican olympiad Problem 3
@MarkBennet Here is a problem I just created, which has a similar setup, but screws with your symmetry argument intentionally. Have fun with it!
Aug
17
comment What is maximum a number of to form right-triangles from in n straight lines
I agree that the maximum seems to happen when $i=2$. I don't know how to prove it yet.
Aug
17
comment What is maximum a number of to form right-triangles from in n straight lines
That claim, if true, will be quite interesting / surprising to me. Then again, I haven't thought about what the general case should be (too busy working on the other problem for now).
Aug
17
revised 2014 iberoamerican olympiad Problem 3
added 50 characters in body
Aug
17
revised 2014 iberoamerican olympiad Problem 3
added 50 characters in body
Aug
17
revised 2014 iberoamerican olympiad Problem 3
added 50 characters in body
Aug
17
comment 2014 iberoamerican olympiad Problem 3
I disagree. The "there is no way to improve this bound" kind of arguments is often just a hand-waving approach with no real basis. I might believe it if you add in some kind of smoothing argument (but also doesn't assume that the n/2014 case is maximal).
Aug
17
comment What is maximum a number of to form right-triangles from in n straight lines
So, once you have two lines at right angles to each other, any other line would either 1. form a right angle to these two lines, or 2. be in a right triangle with these two lines. Hence, your set is an empty set. (Or am i just confused by your phrasing?)
Aug
17
answered 2014 iberoamerican olympiad Problem 3
Aug
17
comment What is maximum a number of to form right-triangles from in n straight lines
That doesn't seem right to me either. Take the first image, BC doesn't make a right angle with any other line, and we don't want to rotate that till it is perpendicular. However, I'm not certain what your "if there is a right-angled triangle ...." phrase is doing in the middle of the sentence.
Aug
17
comment 2014 iberoamerican olympiad Problem 3
It looks good up to the 2nd last paragraph, which is the crux of your argument. Why must the maximal assignment have the convex hull sum to 1? It could be that by reducing that value/sum, we could increase a bunch of stuff elsewhere. As such, I believe this is currently incorrect.
Aug
17
answered Can anybody solve this geometry?
Aug
3
awarded  Nice Answer