# Where is the Dollar?

This was a riddle my dad liked to share. I first heard it in the fifties, which explains the dollar amounts.

Three traveling salesmen went to a hotel to get a room. The desk clerk only has one room left, but it was large enough to accommodate all of them. It would be \$30.00. The men agreed that this was okay, and pay ten dollars each.

After the men go to their room, the desk clerk realizes he overcharged them—the room should have been \$25.00. He gave the bellboy five dollars to return to the men.

The bell boy didn’t just fall off the turnip truck—he knew there was no way to split up the five dollars evenly among the three men. He pockets two dollars and returns three dollars to the men. They could easily share that refund. The men were happy to have saved a dollar each and the bell boy is two dollars richer.

To review: the men originally paid \$30.00, or ten dollars each. Then, they each received a one-dollar refund. Simple math therefore confirms they paid \$27.00 (10 – 1 = 9; 9 x 3 = 27). The bell boy kept two dollars for himself. \$27 (the amount they collectively paid) plus the \$2 the bellboy kept for himself equal \$29.00. Any nine-year-old can confirm that.

Where is the other dollar?

## 5 thoughts on “Where is the Dollar?”

1. Scot

Actually Tonya is exactly correct in that the extra \$2 that the Bellboy kept it subtracted from the 27 not added back to it. The \$2 is already in the original amount of \$27 and each sales person got back \$1 adding up to \$30.

1. Wow… intense, I’m sure he’ll respond to this! I knew you would get some fun out of it anyway! ♥

2. Ron

30-1-1-1=27
Bellboy kept 2, therefore: 27+2=29
Look at it from the perspective of the salesmen (and I’m sure their wives approved of this trip):
They each paid 10, got 1 back, so they each paid 9
There were 3 of them (yes, they were all licensed and had the necessary local permits)
3 x 9 =27
Bell kept 2 (sneaky little bugger)
27 + 2 =29

2. Ron

Tonya’s got a point. But, here’s the problem—okay, her method gets us back to \$25, but 9 x 3 (the amount the men really paid—that’s the amount that goes on their expense report) still totals 27. That, plus the bellboy’s 2 still come to 29. It’s complicated math (perhaps even requiring some sort of high level security clearance) with borrowing and carrying and even a couple of Fibonacci numbers thrown in. Let the bookkeepers figure it out after dark some might say. Kind of reminds me of something Groucho Marx said, “Well, Art is Art, isn’t it? Still, on the other hand, water is water. And east is east and west is west and if you take cranberries and stew them like applesauce they taste much more like prunes than rhubarb does. Now you tell me what you know.”

3. I got this comment from our daughter in law, Tonya, and so we will answer it here so everyone can see!

Ok not sure if I will explain this correct…but you aren’t trying to get back to \$30…. They should have only paid \$25…..so if they paid \$30 and got back \$3….then the \$2 that the bellboy kept takes it down to \$25…