Missing dollar riddle facts for kids

The missing dollar riddle is a famous brain teaser that plays a trick on your mind using numbers. It's an old puzzle, but similar ones have been around for a very long time. It makes you think a dollar has disappeared, but it's just a clever way of mixing up numbers!

Here's how the puzzle usually goes: Three friends check into a hotel room. The manager says the room costs $30, so each friend pays $10. That's $30 in total. Later, the manager realizes the room should have only cost $25. To fix this, he gives the bellhop $5 in one-dollar bills to return to the friends. On the way to the room, the bellhop thinks, "I can't split $5 evenly among three people." So, he decides to give each friend $1 back and keep $2 for himself as a tip. Now, each friend got $1 back, so they each really paid $9 ($10 - $1 = $9). If each of the three friends paid $9, that's $27 in total ($9 x 3 = $27). The bellhop kept $2. If you add the $27 the friends paid and the $2 the bellhop kept, you get $29 ($27 + $2 = $29). But the friends originally handed over $30! So, what happened to the missing $1?

It seems like there are two different answers ($29 and $30), which can't be right for the same math problem. On one hand, the $25 in the hotel's cash register, plus the $3 returned to the friends, plus the $2 the bellhop kept, all add up to $30. But on the other hand, the $27 the friends paid plus the $2 the bellhop kept only adds up to $29. This is where the riddle gets tricky!

Solving the Mystery: The Real Math

The riddle tries to trick you by adding numbers that don't belong together. The $27 the friends paid already includes the bellhop's $2 tip. So, if you add the $2 bellhop's tip to the $27, you are counting it twice! There's no reason why the $27 (what the friends effectively paid) plus the $2 (bellhop's tip) should add up to the original $30.

Let's look at the numbers correctly: The friends paid $27 in total. This $27 covers the $25 the hotel got and the $2 the bellhop kept. So, $25 (hotel) + $2 (bellhop) = $27 (what the friends paid). This makes sense!

To find the original $30, you need to count all the money and where it ended up:

• $1 in Guest 1's pocket
• $1 in Guest 2's pocket
• $1 in Guest 3's pocket
• $2 in the bellhop's pocket
• $25 in the hotel's cash register

If you add all these amounts: $1 + $1 + $1 + $2 + $25 = $30. This shows that no money is actually missing! The trick is in how the riddle makes you add the numbers.

Why the Riddle Tricks You

The riddle makes you think this way:

• Friends paid $9 each, so $27 total.
• Bellhop kept $2.
• Then it asks you to add $27 + $2 = $29. This is the wrong step!

The $27 that the friends paid is the total cost they ended up paying for the room, which includes the bellhop's tip. Think of it this way:

• The hotel received $25.
• The bellhop received $2.
• The friends received $3 back ($1 each).
• $25 (hotel) + $2 (bellhop) + $3 (friends got back) = $30. This is the correct way to account for all the money.

The riddle makes you add the $2 bellhop's tip to the $27 that the friends paid. But the $27 already includes that tip! It's like saying you paid $27 for a pizza, and then adding the $2 tip you gave the delivery person to that $27 again. You wouldn't do that, because the $27 already covers the cost of the pizza and the tip.

Another Example of the Trick

Let's change the riddle a lot to make the trick clearer: Three friends check into a hotel room. The manager says the bill is $30, so each friend pays $10. Later, the manager realizes the bill should only be $10. He gives the bellhop $20 to return to the friends. The bellhop decides to give each friend $6 back and keeps $2 for himself. Each friend got $6 back, so they each paid $4 ($10 - $6 = $4). Total paid by friends: $4 x 3 = $12. The bellhop has $2. If you add $12 + $2, you get $14. But the friends originally handed over $30! What happened to the remaining $16?

Now it's even more obvious that adding $12 (what friends paid) and $2 (bellhop's tip) doesn't make sense. The $12 already includes the bellhop's tip and the hotel's share. The hotel got $10. The bellhop got $2. The friends got $18 back ($6 x 3). $10 (hotel) + $2 (bellhop) + $18 (friends got back) = $30. All the money is accounted for!

History of Tricky Puzzles

Puzzles like the missing dollar riddle have been around for a long time. They are designed to make you think carefully about how you add and subtract numbers.

One similar puzzle from 1933 involved a man withdrawing money from a bank: A man puts $50 in the bank. He withdraws $20, leaving $30. Then he withdraws $15, leaving $15. Then he withdraws $9, leaving $6. Finally, he withdraws $6, leaving $0. If you add the amounts left in the bank ($30 + $15 + $6), you get $51. Where did the extra dollar come from? The trick here is similar: you shouldn't add the amounts left in the bank. The correct way to track the money is to see that the total money withdrawn ($20 + $15 + $9 + $6 = $50) matches the original amount.

Another puzzle from 1933 is about a traveler in New York: A traveler has a $10 money order, but his train fare is $7. The ticket clerk won't take the money order. So, the traveler pawns the money order for $7. On his way back, he meets a friend who buys the pawn ticket from him for $7. The traveler then buys his train ticket for $7 and still has $7 when he gets to New York. Who lost money? In this puzzle, no one actually lost money! The traveler started with a $10 money order, which he turned into $7 cash (by pawning it and selling the ticket). He spent $7 on the ticket, so he should have $0 left. The riddle says he has $7 left, which is the confusing part. The friend paid $7 for the pawn ticket, which is what it was worth. The pawn shop gave $7 for the money order. Everyone got what they paid for or what they were owed.

These riddles are fun ways to learn about how important it is to keep track of money and numbers carefully!