Waste less time on Facebook — follow Brilliant.

Missing Dollar?!

Hey Brilliant users,

I have recalled a problem I have heard about when I was in 6th grade. The problem goes like this:

3 men rent a room for a hotel. The hotel worker charges them $30.00, and the 3 men split the price equally- each man pays $10.00. Of course, the hotel worker was inexperienced, and the price was actually $25.00. So, the hotel manager tell the worker to give them back the 5 dollars he owed. The worker obviously was mad that he couldn’t get 5 extra dollars. So, he decided to keep 2 dollars, and give the 3 men 3 dollars back. So now, each man has paid $9.00 for the hotel. 9*3=27 dollars, and the worker has 2 dollars. So where did the one dollar go?!

What happened?

Note by Jonathan Hsu
2 years, 4 months ago

No vote yet
1 vote


Sort by:

Top Newest

It is a nice play with words.The sum wont be equal to 30 after redistribution as \[ 10+10+10= 25+3+2\] Now, the hotel kept 25 ,3 were given back and waiter kept 2.

\[ 10-1+ 10-1+10-1=25+2\] Now note that effectively the men have paid $27. Which is consistent with $25 to hotel & $2 to the waiter. I hope its convincing enough

Siddharth Bhatnagar - 2 years, 4 months ago

Log in to reply

Sorry Jonathan, but how come only Lexingtonians solve your problems? I am kinda skeptical...

Jack H. - 2 years, 4 months ago

Log in to reply

I am sorry Jack, my friends on brilliant are always being mean and cheating on my problems. They don't even know how to solved them, I am sorry about that. All of my level 4 and above problems are like this.

Jonathan Hsu - 2 years, 4 months ago

Log in to reply

Each man has PAID $9. But at the end, they only have $3.

$3 + $25 + $2 = $30.

Ashwin Padaki - 2 years, 4 months ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...