[ Arithmetic. Mental calculation, etc. ]  $[$ Word problems (miscellaneous). ]

Authors: Yashchenko I.V., Botin D.A.

Gulliver found himself in the land of Lilliput with 7,000,000 rubles. He immediately spent all his money on bottles of kefir, which cost 7 rubles per bottle (an empty bottle cost 1 ruble at the time). After drinking all the kefir, he returned the bottles and used all the money he received to buy more kefir. He noticed that both the cost of the kefir and the cost of an empty bottle had doubled. Then he drank all the kefir again, returned the bottles, and used all the money he received to buy more kefir, and so on. Each time he visited the store, both the cost of the kefir and the cost of an empty bottle doubled. How many bottles of kefir did Gulliver drink?
Conduct calculations in "hard" currency - empty bottles. Then there will be no inflation!

## Solution

Note that if all transactions are conducted in hard currency - empty bottles, - there will be no inflation. That is, a bottle of kefir will always cost 7 empty bottles, and the kefir in it - 6 empty bottles. Gulliver, initially having enough "money" for 1166666 bottles of kefir (without the container) and 4 more empty bottles, will be able to conduct his commercial operations until he is left with only four empty bottles, which, when returned, will no longer allow him to buy kefir again.

## Answer

1166666 bottles.