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?

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?

Yes that is the puzzle.

To solve this puzzle, let's first assign variables to represent the number of horses each of us has. Let's say you have "x" horses, and I have "y" horses.

According to the information given:
1. If I give you a horse, you will have half as many as me. This can be represented by the equation: y + 1 = (x - 1) / 2.

2. If you give me a horse, I will have twice as many as you. This can be represented by the equation: y - 1 = 2(x + 1).

Now, let's solve the equations simultaneously to find the value of "y" (the number of horses you have).

1. From equation 1: y + 1 = (x - 1) / 2
Multiply both sides of the equation by 2: 2y + 2 = x - 1
Rearrange the equation: x = 2y + 3

2. Substitute the value of x from equation 1 into equation 2:
y - 1 = 2((2y + 3) + 1)
Simplify the equation: y - 1 = 2(2y + 4)
Distribute the 2: y - 1 = 4y + 8
Subtract 4y from both sides: -3y - 1 = 8
Add 1 to both sides: -3y = 9
Divide both sides by -3: y = -3

Therefore, according to this puzzle, you have -3 horses, which doesn't make sense in a real-world scenario. There may be an error or inconsistency in the problem statement.