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Hello,

I have enabled ads on this blog as a fund for my future education. Please cooperate with this and if they annoy you, click the down arrow button next to the ad to hide it.

Thank you!

- Get link
- Other Apps

Problem : We have $2^m$ sheets of paper, with the number $1$ 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 $a$ and $b$, then we erase these numbers and write the number $a + b$ on both sheets. Prove that after $m2^{m -1}$ steps, the sum of the numbers on all the sheets is at least $4^m$ .

oh ok

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