Anecdotes
by math_explorer, May 1, 2011, 2:17 PM
Lots of V/LA for a while around now.
Scene: some random IMO a few years ago. Day 2, Problem 6, geometry. Somebody from Taiwan with 3 hours left decides to use a coordinate bash. At its moment of highest glory the expressions involved reach an amazing 288 terms.
7/7 => gold
o_O
Some random cute old shortlist problems and the like (I've solved all of these too):
points in the plane are given. The distance of any two is at most 
. Prove that there are at most 
point pairs with distance 
; discuss when equality holds. (with sufficient geometric and combinatorial intuition, solution length is two syllables. two syllables I still haven't mastered pronouncing)
The edges of
are labeled with positive integers 
such that in any triangle, two of its sides have equal labels and this label is larger than the third. Also, every positive integer in range appears as a label. (a) Find the maximum of 
; (b) count how many labelings for which this is attained. (100 syllables ought to suffice)
there used to be an incredibly cute inequality here but it just might be from the 2010 shortlist so I shouldn't post it derp. I had no idea I was capable of solving this kind of problem by myself. anyway
My algebra and geometry have been confirmed to be approximately equally weak. hmm
Scene: some random IMO a few years ago. Day 2, Problem 6, geometry. Somebody from Taiwan with 3 hours left decides to use a coordinate bash. At its moment of highest glory the expressions involved reach an amazing 288 terms.
7/7 => gold
o_O
Some random cute old shortlist problems and the like (I've solved all of these too):
points in the plane are given. The distance of any two is at most 
. Prove that there are at most 
point pairs with distance 
; discuss when equality holds. (with sufficient geometric and combinatorial intuition, solution length is two syllables. two syllables I still haven't mastered pronouncing)The edges of
are labeled with positive integers 
such that in any triangle, two of its sides have equal labels and this label is larger than the third. Also, every positive integer in range appears as a label. (a) Find the maximum of 
; (b) count how many labelings for which this is attained. (100 syllables ought to suffice)there used to be an incredibly cute inequality here but it just might be from the 2010 shortlist so I shouldn't post it derp. I had no idea I was capable of solving this kind of problem by myself. anyway
My algebra and geometry have been confirmed to be approximately equally weak. hmm
This post has been edited 4 times. Last edited by math_explorer, May 1, 2011, 10:46 PM
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