If the room is total cost $25, then the 3 saliors were supposed to only pay 25/3 = $8.33 ea. But they effectively paid $9 each, and therefore overpaid $0.666 ea x 3 = $1.99 = $2.

The answer is there is no extra dollar, because by unknowingly overpaying, they effectively "tipped" the bellhop $2 - which is the same $2 the bellhop thought he stole!

Which ironically is what the sailors were trying to avoid!

The bottom line is that the sailors paid a total of $27, $25 of which went to the hotel and $2 to the bellhop, making $27, so it all matches up. The error in the above equation is where it says 27+2 instead of 27-2.

Stumped

Gordian knot approach. On the floor where it fell through a hole in the Bellhop's pocket!

It must be similar to what I've heard Scottish whiskey makers say about the bit in each cask that evaporates over time - "It's the angels' share!" Best wishes for your continued success!

Ok, answer:

25 ÷ 3 = 8.3333 (30 - 5 return to sailors)
28 ÷ 3 = 9.3333 (30 - 2 tip)

9.3333 - 8.3333 = 1 dollar

30 - 25 = 5 then -2 (tip) = 3 what each sailor got back
Each paid 10 - 1 = 9 x 3 = 27

So its: 27 + 2 + 1 = $30

Leon - I could be wrong but it's in the forced tip to the bellhop .67 cents to each sailor for a total cost to sailors of $28 dollars. When it come to math riddles MS Excel is your friend. As my 7th grade math teacher drilled into our little heads... show your work! So here it is.

Thank you for sharing Leon! You got me really thinking about this, but I can't figure it out.

What if the other sailor wasn't in the room when the bellhop was giving back the ones?

I like this puzzle, I could not figure it out.