The flaw in the logic lies in counting the $2 kept by the gatekeeper as part of the $27 paid by the adventurers. The correct way to break down the expenses is as follows:
- Each adventurer initially paid $10, totaling $30.
- The gatekeeper took $2 and returned $1 to each adventurer, totaling $3.
- Therefore, each adventurer paid $9 ($10 - $1) and collectively they paid $27 in total.
- The remaining $2 kept by the gatekeeper is not part of the money paid by the adventurers, so it should not be added back to the $27.
In conclusion, the adventurers paid $27, the gatekeeper kept $2, and there is no missing dollar.
Harrison and Lara—two tireless adventurers who face mathematical roadblocks and puzzles wherever they go—have to cross a wide river before they can continue on their current adventure.
A traveler going in the same direction tells the adventurers that the quickest and safest way over the river is a toll bridge. They agree to cross the bridge together, and split the $30 toll three ways. They each give the gatekeeper 10 one-dollar coins, totaling $30. Right away, they notice a tiny sign that says: Discount for Parties of Three or More. The three travelers demand their discount.
The gatekeeper knows that the official discount for a group is $5. He always pockets the discount when groups don't notice the tiny sign, but he also takes a cut when they do. "OK, the discount is $3," he says, dropping two of the dollar coins in his pocket and returning one dollar each to Lara, Harrison and the traveler.
So, each of the three has paid $9 for a total of $27, and the gatekeeper has kept $2. That’s $29 accounted for but where did the other dollar go? The gatekeeper didn't get it!
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