# Help, I'm Trapped in a Math Factory!

Algebra Level 5

A certain factory produces numbers to be used in math problems. A worker there named Alex is given a batch of $$N$$ numbers. First, he removes one number for inspection, then packages half of the remaining numbers. From the remaining numbers, he removes one and packages half the numbers after that. He repeats this process $$2014$$ more times (remove one, package half the remaining), and at the end, he is left with one number that he keeps for himself. Find the units digit of $$N$$.

Notes:

After the first sorting, Alex is left with $$\frac{1}{2}(N-1)$$ numbers. After the second sorting, he is left with $$\frac { 1 }{ 2 } \left(\frac { 1 }2(N-1)-1\right)$$ numbers, and so on.

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