Choose any whole number. You are allowed to use only two operations (multiply by 2 and subtract 5) but you can use them as often as you like. The aim is to reach the number 50.

For example, starting with 15:
15 x 2 = 30
30 - 5 = 25
25 x 2 = 50

What is special about the starting numbers that allow you to reach 50?

Can you prove that all these special starting numbers allow you to reach 50?

Can you prove that no other numbers allow you to reach 50?