Three people check into a hotel.
They pay $30 to the manager and go to their room.
The manager finds out that the room rate is $25 and gives the bellboy $5 to return to the guests.
On the way to the room the bellboy reasons that $5 would be difficult to split among three people
so he pockets $2 and gives $1 to each person.
Now each person paid $10 and got back $1. So they paid $9 each, totaling $27.
The bellboy has another $2, adding up to $29.
Where is the remaining dollar?
Where is the remaining dollar?
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Another variation is as follows
Puzzle: “The Missing Dollar”
Three friends, Alex, Ben, and Chris, decide to stay at a hotel together. The room rate is $30, so each friend contributes $10 to cover the cost. The hotel manager realizes there’s a special promotion going on and gives them a discount, reducing the room rate to $25. Happy with the discount, the manager gives $5 back to the bellboy and asks him to return it to the guests.
The bellboy thinks it’s tricky to divide $5 among three people, so he keeps $2 for himself and returns $1 to each of the three friends. Now, each friend has paid $9 (totaling $27), and the bellboy kept $2, which makes a total of $29. But the friends originally paid $30, so where is the missing dollar?
Take a moment to think about it, and once you’re ready, I’ll give you the answer!
The missing dollar is actually just a trick of misdirection in the wording of the puzzle. Let’s break it down step by step:
Initially, the three friends paid a total of $30 (3 friends * $10 each) to cover the room rate.
The hotel gave them a $5 discount, so the new room rate was $25. The bellboy kept $2 for himself, and the remaining $3 were returned to the friends ($1 each).
Now, let’s account for all the money:
The three friends paid a total of $30.
The bellboy kept $2.
The friends got $3 back.
The total amount accounted for is $30 + $2 + $3 = $35.
The discrepancy arises because the puzzle is misleadingly adding the $2 kept by the bellboy to the $27 paid by the friends, but that’s not the right way to do the calculation. The $2 should be subtracted from the $27 they paid, not added to it.
So, there is no missing dollar. The total amount of money spent ($30) is correct, and the puzzle creates confusion by suggesting there is an extra dollar when it’s just a result of adding unrelated amounts together. It’s a fun puzzle that plays with our expectations and assumptions!