Riddle on finding numbers of nails that Jon gives and Ron uses.

Question

Suppose there's Jon & Ron. Jon gives Ron a certain number of nails to hammer in on each corner of a blackboard.

Ron uses a certain number of those given nails and finishes one corner with some nails left. Now Jon again gives some nails to Ron that is equal to that Ron has left. Ron then finishes the second-corner, and again Jon gives Ron the number of nails Ron has left. This continues on the third corner. But on the forth corner. Ron finishes off all the nails that is in his hand.

Note that Ron uses the same number of nails on each corner of the blackboard.

So, how many nails did Jon give Ron at-first and how many did Ron use at each-corner?

Answer 1

Let $N$ be the number of nails Jon gave Ron at first and $n$ the number of nails Ron hammered at each corner.

Below are what Ron had:

1st corner - before $N$ and after $N-n$;

2nd corner - before $2(N-n)$ and after $2N-3n$;

3rd corner - before $2(2N-3n)$ and after $4N-7n$;

4th corner - before $2(4N-7n)$ and after $8N-15n$.

Set,

$$8N-15n = 0$$

which yields

$$N=15,\>\>\>\>n=8$$

Thus, Jon gave Ron 15 nails at-first and Ron nailed 8 at each corner.