When is the sum $1+2+\cdots + n = (n+1) + (n+2) + \cdots +(n+k)$?
The easiest solution $(n,k)$ is $(2,1)$. For example, $1+2 = 3$. Do any others exist?
Roots of $(n+k)^2 + (n+k) = 2n^2 +2n$ give solutions (Is this solvable via a Pell equation?)
If a complete graph has red($n$) and blue($k$) nodes, and I pick an edge at random; the probability of picking one that connects two red vertices is $1/2$, find the number of blue and red nodes.
This may be trivial but I really have no clue so I ask the pros.
A (sort of) variation on the first problem of "Fifty Challenging problems in probability with solutions" Frederick Mosteller.