Caesar Mathematics : I

Algebra Level 3

"Ape alone... weak. Apes together... strong." -Caesar


The Apes are gathering resources for the upcoming winter. This time, Caesar and others went gathering wood. To store the gatherings, Maurice - a wise ape, and Caesar's best friend - has devised a plan on how the resources should be distributed:

All the logs are to be divided into \(n\) piles. After this, \(\frac{1}{n}\)-th of the logs from the first pile are to be shifted into the second pile. Then, \(\frac{1}{n}\)th of the logs in the second pile, after the first transfer, are to be shifted into the third pile. Next, \(\frac{1}{n}\)th of the logs in the third pile, after the transfer from the second pile, are to be shifted to the fourth, etc...

Finally, from the \(n\)-th pile, \(\frac{1}{n}\)th of the logs in the \(n\)-th pile, after the previous transfer, are to be shifted to the first pile. After that, each pile will have \(A\)-amount of logs.

Caesar and Maurice agreed to divide the resources into \(101\) piles.

If, before shifting, the amount of logs in piles 1, 2, and 3 combined is \(150\), how many logs were gathered?

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