# 32 nails

So if you are putting horse shoes on a horse it takes 32 nails. Imagine telling the horse owner you will do the first nail for a penny and the second nail for 2 pennys. Each nail will be double the prior nail.Once the final nail is installed ant the total is tallied up, will he be able to pay you? You might be surprised at your bank account if he actually writes you a check for the correct amount. That would be a lot spending cash at your disposal.

phinds
Gold Member
2019 Award
So if you are putting horse shoes on a horse it takes 32 nails. Imagine telling the horse owner you will do the first nail for a penny and the second nail for 2 pennys. Each nail will be double the prior nail.Once the final nail is installed ant the total is tallied up, will he be able to pay you? You might be surprised at your bank account if he actually writes you a check for the correct amount. That would be a lot spending cash at your disposal.
This has been known since ancient times. The original was 1 grain of wheat one the first square of a chessboard, 2 on the 2nd, etc.

jbunniii
$$\sum_{n=0}^{N-1} 2^n = \frac{2^{N} - 1}{2 - 1} = 2^{N} - 1 = 2^{32} - 1$$
$$\sum_{n=0}^{N-1} 2^n = \frac{2^{N} - 1}{2 - 1} = 2^{N} - 1 = 2^{32} - 1$$