Regions from ten lines

What is the maximum number of disjoint regions into which 1010 lines can divide the plane (no two parallel, no three meeting at a point)?

Show hints (2)+
  1. The kk-th line crosses the previous k1k-1 lines, so it's split into kk pieces and adds kk regions.
  2. Total =1+k=110k=1+n+(n2)=1+\sum_{k=1}^{10}k = 1+n+\binom{n}{2}.

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Asked at: Jane Street, Citadel

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