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?

×