Documenting Problems That Were Difficult To Find The Answer To

Old Math Riddle/Joke Explained

In Season 5 Episode 1 of “Highway to Heaven” an old math riddle was quoted:

Three sailors check into a motel. At the front desk the clerk charges them $10 each for a total of $30.

The clerk later realises the room price was $25 and gives a bellhop $5 to take back to the sailors as a refund.

On the way to the room the bellhop decides to pocket $2 for himself – and hands each of the sailors $1 each.

Now each sailor had effectively paid $9 each ($10 minus the $1 refund). Three times nine is twenty-seven – $27. The bellhop had the other $2. That makes $29.

Where did the other dollar go?

Mentally it seems like a real puzzle – the men spent $27 on the room. And the bellhop had $2. If you add the two numbers it does result in $29.

The problem is the sign. Spending is the opposite of receiving. Which is why you can’t just add the two numbers. If somebody receives $2 (as the bellhop did) then they technically spent negative $2. So the sailors spent $27 and the bellhop spent $-2 making a total spending of $25.

Let’s do it with algebra:

let sailor’s original $10 spend be s s = 10
original spend on room 3s = 30
refund of $5 3s – 5 = 30 – 5
bellhop keeps $2 3s – (3 + b) = 25
bellhop b=2 3(s – 1) – b = 25
rearrange formula 3(s – 1) = 25 + b
substitute constants 3(10 – 1) = 25 + 2
finalise 27 = 27

There’s no imbalance.

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