Erasing sheets for points.

Algebra Level 4

We have 2 2018 2^{2018} sheets of paper, with the number 1 1 written on each of them. We perform the following operation. In every step we choose two distinct sheets; if the numbers on the two sheets are a a and b b , then we erase these numbers and write the number a + b a + b on both sheets. Then after how many steps the sum of the numbers on all the sheets is at least 2 4036 2^{4036} .

4018. 2 4017 4018.2^{4017} 2018. 2 2018 2018.2^{2018} 2018. 2 2017 2018.2^{2017} 2017. 2 2018 2017.2^{2018} 2018. 2 4036 2018.2^{4036}

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