README.md

Grandfather and grandson

Solve the following puzzle:

If you multiply my grand-son age by four, you know how old I am. Now, if you exchange the two digits of our ages then you have to multiply by three my age to get the age of my grand-son!

Task 1

Write a function:

exchange : int -> int

that takes an integer x between 10 and 99 and returns an integer which is x whose digits have been exchanged. For instance, exchange 73 = 37.

Task 2

Write a function:

is_valid_answer : int * int -> bool

such that is_valid_answer (grand_father_age, grand_son_age) returns true if and only if grand_father_age and grand_son_age verify the constraints of the puzzle.

Task 3

Write a function:

find : (int * int) -> (int * int)

that takes a pair (max_grand_father_age, min_grand_son_age) and returns a solution (grand_father_age, grand_son_age) to the problem, where min_grand_son_age <= grand_son_age < grand_father_age <= max_grand_father_age or (-1, -1) if there was no valid answer in the given range.

Hint: use recursion to explore the entire space of solutions.