From: greg@manifold.berkeley.edu (Greg Kuperberg)
Newsgroups: rec.puzzles,sci.math
Subject: Math problems with $6700 in prizes!!!!
Date: 17 Jun 92 00:39:31 GMT
Great rewards are available to problem solvers worldwide! Here is a
list of math problems with $6700 in prizes!
If you are the first person to answer one of these questions, you get
the prize! Warning: The poser of each question is the sole and final
arbiter of what constitutes a completely correct solution, who is the
first to solve it, how much money a putative solution deserves, and all
other terms of the offer. The wording of the problems given here
is due to me, and the wording preferred by the problem posers may differ.
If you have ideas for one or more of these problems, you can send me
mail at greg@math.berkeley.edu. If the ideas are interesting and
especially if you crack one of the problems, I will try to get you
in touch with the relevant problem poser or posers.
In addition, if you have your own math problem (or problems) with a
prize attached, please contact me. New contributions are always
welcome. I can't promise that I will include your problem in my list,
but I will give it serious attention.
The problems are listed by the size of the award, with the person
offering the prize and the amount wagered for a completely correct
solution. In the future there may be problems with a non-monetary
prize like a bottle of wine, a live goose, or tickets to the opera, as
well as problems for which the prize depends on the answer to the
question, for example $1000 for a yes and three lemons for a no. All
problems so far offer the same prize independent of the answer to the
question.
And now, what you've all been waiting for: The problems!
----------------------------------------------------------------------------
Paul Erdos: $3000
If the sums of the reciprocals of a set of positive integers is
infinite, does the set contain arbitrarily long finite arithmetic
progressions?
John Conway: $1000
A thrackle is a graph drawn in the plane with straight or curvy edges
in such a way that any two edges either cross each other exactly once
or share one endpoint, but not both. No other kinds of incidence
between edges or vertices or self-intersections of an edge are
allowed. Is there a thrackle with more edges than vertices?
Ron Graham: $1000
If you 2-color the integers from 1 to 2^2^...^2 (k times), is there a
monochromatic arithmetic progression of length k?
David Gale: $500
Are there infinitely many positive integers n such that 2^n
does not contain a 7 in its decimal expansion?
Ron Graham: $500
What is the shortest curve (not necessarily closed) that does not
fit in an equilateral triangle?
Ron Graham: $500
Are there infinitely many positive integers n such that 2n choose n
is not divisible by 3,5, or 7?
David Gale: $200
In the game of chomp, players alternate stating triples of non-negative
integers, and once a triple (a,b,c) is named, then for ever after
neither player can name a triple (d,e,f) with d>=a, e>=b, and f>=c. A
player who names (0,0,0) loses. Does the first or second player have a
winning strategy?