Gareth> On 14/01/2014 14:02, Bill Gosper wrote:

Not bad. But these four terms simplify to Julian's (very unhomely) two term solution privately reported at 23:24 PST.

I'm a little surprised FullSimplify fails this.

It's obvious how to lose one term (move the constant 1 inside one of the floors); how do you get it down to 2? -- g Sum[Floor[y + k/n], {k, 0, n - 1}] == Floor[n*y] (Mma (FunctionExpand) developers: N.B.) --rwg