### Unsolved Problems in Mathematics

09Feb11

The main reference is: http://wapedia.mobi/en/Unsolved_problems_in_mathematics.

Major open problems in combinatorics include:

**Number of Magic squares**(sequence A006052 in OEIS)- Finding a formula for the
**probability that two elements chosen at random generate the symmetric group** **Frankl’s union-closed sets conjecture**: for any family of sets closed under sums there exists an element (of the underlying space) belonging to half or more of the sets See wikipedia entry**The Lonely runner conjecture**: if runners with pairwise distinct speeds run round a track of unit length, will every runner be “lonely” (that is, be more than a distance from each other runner) at some time?**Singmaster’s conjecture**: is there a finite upper bound on the multiplicities of the entries greater than 1 in Pascal’s triangle?**The 1/3-2/3 conjecture**: does every finite partially ordered set contain two elements x and y such that the probability that x appears before y in a random linear extension is between 1/3 and 2/3?

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