Maegan, I won’t make any judgment on whether you’re nuts or not (instinct of self-preservation and all that), but here’s how the whole transfer of money and products in this riddle goes:

1. *At the start, the buyer has the fake $20, the seller has the $10 hat, and the neighbour has $20 dollars:*

B = $20 (fake)

S = $10 (the hat)

N = $20

2. *The buyer gives the fake $20 to the seller:*

B = $0

S = $30 (the hat and the fake $20)

N = $20

3. *The seller gives the fake $20 to the neighbour:*

B = $0

S = $10 (the hat)

N = $40 (including the fake $20)

4. *The neighbour gives $20 back to the seller:*

B = $0

S = $30 (including the hat)

N = $20 (fake)

5. *The seller then gives the hat and $10 to the buyer:*

B = $20 (including the hat)

S = $10

N = $20 (fake)

6. *The seller then has to give $20 to the neighbour:*

B = $20 (including the hat)

S = $-10

N = $40 (including the fake $20)