There are 4 brothers who are to greedy and they have a dog and a bottle of cookies. The first brother wakes up at night and goes to the kitchen and does the next thing.

Firstly, he gives a cookie to the dog and secondly he eats the 4th part of the cookies that are left. nd he comes back to bed. After this the second brother wakes up and does the same thing, what it means that he gives one cookie to the dog and the eats the 4th part of the cookies that are left.

The third brother does the same thing and the 4th brother too. The next day when they are going to take the breakfast(the 4 brothers), first they give 1 cookie to the dog and after they divide the cookies that are left in equals parts(by 4).

The question is how many cookies there were in the bottle? I have to solve this problem by natural language, and a type of logic that is a mixture of predicate logic and mathematical logic, could somebody help me , please? Thank you