The first I know has been discussed here. It’s the one where three guys share a hotel room, they each fork over $10, then it turns out the hotel room is $27 so somebody gives them money back, and somehow the amounts don’t seem to add up.
If someone could lay out this problem as presented I would be grateful, as I can’t quite remember how it goes. (And does the amount given in the problem matter?)
The second one I read in a medical publication–not a journal, but one of those things that ends up in doctors’ waiting rooms, with healthy tips and big ads for drug therapies. It was a variation of the old “one tribe always tells the truth, the other tribe always lies” except it had a third iteration and was presented in psychological terms. Something on the order of, “Patients from this wing are autistic and always tell the truth. Patients from this wing are schizophrenic and always tell lies. Members of the staff are likely to tell the truth half the time and lie the other half of the time. You don’t know whether you’re talking to a patient or a staff member…”
The solution was on some other page, which I didn’t get to, because I was trying to solve the problem and then the nurse called me in for my appointment, and the magazine was never there again. I would really, really like to see this problem written out. I guess I’d like the solution, too. It couldn’t be the usual one, could it?
My dad told me the hotel puzzle years ago, it’s simple a trick in the way it’s presented.
Three salesmen are each looking for a room, in a town where all the lodgings are full. They show up at the last place at the same time. The room rents for $25.00, but the desk clerk sees an opportunity to make a few bucks. He tells the three guys they can share the room for $10.00 apiece. They take the deal, but the desk clerk regrets his dishonesty. He gives the bellboy 5 ones and tells him that he accidently overcharged the three guys and instructs the bellhop to refund their money. On his way to the room the bellboy tries to figure out how he can divide 5 dollars three ways, then it strikes his the he can make a couple of bucks by just giving each guy a dollar, problem solved to his benefit.
So that means each guy paid $9.00 for the room, for a total of $27.00, but if you add the two bucks kept by the bellhop that comes to $29.00. What happened to the other buck?
The problem is presented in a deceptive way.
The ‘truth teller, liar’ problem is a legitimate exercise in logic, but I’ve forgotten the explanation, so I’ll let someone else tackle that.
There are lots and lots of truth-teller/liar riddles. Here’s one.
Some patients are autistic and always tell the truth. The other patients are schizophrenic and always tell lies. Members of the staff tell the truth half the time and lie the other half of the time. You don’t know whether you’re talking to a patient or a staff member. Bill said “Bob is autistic.” Ben said “Bill is autistic.” Bob said nothing. One is autistic, one is schizophrenic, one is staff. Which is which?
If Bill were autistic, he must tell the truth and would not lie and say that Bob was autistic. So Bill cannot be autistic.
Same reasoning for Ben. If neither Bill nor Ben are autistic, we know Bob must be autistic.
If Bob is autistic, then Ben is lying and Bill is telling the truth. If Bill is telling the truth, he can’t be schizophrenic, so he must be staff.
Among Raymond Smullyan’s books of logic problems are a couple that are devoted entirely to liar/truth-teller puzzles. The variations are endless. He’s also very keen on those “the statement on the other side of this card is false” riddles.
Basically, the “problem” is set up so you’re comparing two independant sums and then asked why they aren’t equal. The answer is that there’s no reason for them to be equal. It’s like saying 2+3=5 and 2x3=6; where did the missing number go?
Follow the path of the thirty dollars that existed in the puzzle. At the beginning, three men have ten dollars each: 10+10+10=30. Then they each give ten dollars to the hotel for a total of thirty dollars: 30=30. Then the hotel clerk realizes he overcharged them and gives five dollars back to the bellhop: 25+5=30. The bellhop gives each of the men back a dollar and pockets the rest: 25+1+1+1+2=30. There was never any missing dollars.
The notion that somehow the sums should involve a total of $30 based on what they originally paid is contradicted by the statement that each man paid $9. And the $27 includes both the room AND the bellboy’s graft, so counting the $2 he pocketed twice is erroneous.