Math problem Teacher Liu bought 64 bottles of soda, and every four empty bottles were changed into 1 bottle of soda. How many bottles can he drink at most?

A recursive problem:

There are 64 bottles of water at the beginning, and after drinking it, you can change it to 64÷4= 16 bottles.

So now 16 bottles can be replaced by 16÷4=4 bottles.

So now there are 4 bottles, which can be changed into 16÷4= 1 bottle after drinking.

So now 1 bottle, you can only throw away the empty bottle after drinking it, and you can't change it.

So a * * * can drink 64+ 16+4+ 1=85 bottles.

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Or you can think of it this way:

At first, there were 64 bottles of water, and every four empty bottles were replaced with one bottle of water.

Change three empty bottles and one bottle of water at a time.

64÷3=2 1... 1

So you can change 2 1 time (more 1 empty bottle), which means you can drink 2 1 bottle of water.

So a * * * can drink 64+2 1=85 bottles.

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You have to do it in one step, because you have to do mental arithmetic:

So the formula is 64+[64÷3]=85 bottles (rounded by division).

Note: [] is an integer operator.