Question

You have horses. I have horses. If I give you a horse, you will have half as mnay as me. If you give me a horse, I will have twice as many as you. How many horses do i have?

Answer 1

I have x horses, you have y horses

first giveaway, I give one to you
I have x-1 , you have y+1
"you will have half as mnay as me" --->y+1 = (1/2)(x-1
2y + 2 = x - 1
x - 2y = 3

second giveaway, you give one to me
I have x+1, you have y-1
"I will have twice as many as you" ---> x+1 = 2(y-1)
x+1 = 2y - 2
x - 2y = -3

contradiction: these two equations have no solution.

Am I understanding your question correctly?

Answer 2

Yes that is the puzzle.