The original puzzle
Three men take a hotel room priced at $30.00. they each give $10.00 to the desk clerk. When the owner returns, he changes
the price to $25.00, the season being over. He gives five $1.00 bills to the clerk and tells him to reimburse the clients.
The clerk gives 3 bills to the clients and keeps 2 for himself. Each client takes one of the bills. The clients have now paid
$9.00 each, a total of $27.00. The clerk has $2.00 in his pocket. That makes $29.00 in all. There was $30.00 at the beginning.
What happened to the missing dollar ?
The clients have now paid $9.00 each, a total of $27.00.
No problem here.
The clerk has $2.00 in his pocket. That makes $29.00 in all.
Here is the mistake.
The $2.00 in the clerks pocket should not be added to the $27.00 the clients gave,
but subtracted from it, giving the $25.00 at the front desk.
Adding always seems simpler than subtracting,
the way binary is always simpler than ternary,
as we saw in other puzzles.