Short changed
Three men go to a hotel. They pay for a $30 room to share, each giving $10. Later the manager realizes that the room was only $25 and so gives $5 to the bellboy to return to the men. The bellboy takes the $5 to the men. They give the bellboy $2 as a tip. Just after the bellboy left, one of the men says, "We each spent $9 just now, since we each got back $1, and we gave the bellboy $2, that's $29". Where's the missing $1?
This must have been a long time ago.
This must have been a long time ago.
Labels: mathemagic
posted by Chris at
3:10 PM
17 Comments:
Each person paid $9, totalling $27. The manager has $25 and the bellboy $2.
The bellboy's $2 should be added to the manager's $25 or subtracted from
the tenants' $27, not added to the tenants' $27.
Oh dear, these problems are being gobbled up as fast as I can spew them out.
Anonymous, was that a hat-trick? I'm seeing a sharp mind at work tonight.
Aussie boy here again - I'm on a roll!
There is no missing $1. The men pay $9 each, that's $27. The manager has $25 and the bellboy $2. The confusion seems to be where the $2 tip came from - it adds to the room rent of $25, not to the men's contribution 0f $27.
Boy from Oz here: No, I missed the hat-trick by 7 minutes!
Looking like it could be two sharp minds.
I won't hold it against you. I know you didn't cheat.
Actually, I did get the hat-trick: water jug, xth root and marbles puzzles, but just too slow to claim the room rent one.
Keep sending them - I love this!
I'd forgotten I'd posted that. I'll take a gander.
it`s true the three tenants spent $9 each thus totaling up to $27. this total is inclusive of the amount for the room($25) and the tip for the bellyboy($2)
this problem is so totally nooby.. there's no $1 missing... my relatives already asked me a problem like this and i proved it that there's no missing $1
I do like explanatory answers. Thanks andrew. Not sure what the next post was about though.
This particular problem seems to show up about every 2 to 3 months on here.. lol
I am the anonymous who sent in the first post. I am completely hopeless at maths. I don't know how I got the answer right. Apologies to anonymous from Oz for getting in first.
I cannot really understand why I like these puzzles so much. I very rarely work out the maths ones, although I do love thinking outside the box.
Chris, keep sending in your conundrums. I cant do them, but I admire people who can.
Hi Anonymous, thanks for you remarks. As with too any I've posted, they are too well known.
Some of the logic / seeming paradoxes are quite good.
Trouble is I like the calculus and complex number types best. But I realise that's not fair on the visitor's who are too young to have done that stuff. So I'm trying to aim for different levels.
I can't think up the logic types. It's easier, for me,to think up maths/physics one's (so far!)
if they originally paid $30 and got back $5 they each got $1 back and gave a $2 tip, if you add it up there is no missing dollar.
Hi Anonymous. Your sentence isn't clear about what you're adding up.
It could still be interpreted as 30-3+2 = 29 => missing dollar or it could be interpreted as 30-5+2 = 27 = 3*9 (which of course is the correct way to do it). But notice no-one says $3 is now missing. It's partly psychological. It is a cunning misdirection problem though.
However, I'm sure you know what you meant and that you are doing it right really. Goodnight.
Of course, the men have each paid $(8+1/3) for the room and $(2/3) for the tip => $9 total.
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