# Maximum Sum Value

Given 10 non-negative reals such that $$a_i \leq i$$ and $$(1-a_1)(2-a_2)\ldots(9-a_9)(10-a_{10}) \geq 1$$, what is the maximum value of $$a_1 + a_2 + \cdots + a_9 + a_{10}$$?

×