Three men decide to share a cheap hotel room which they are told will cost thirty dollars?

..they put in ten dollars each, but later the desk realises that they are meant to pay only 25.00 for that room, so the desk sends back 5.00 via the bellhop. Finding it impossible to actually divide the 5.00 evenly (and since he didn't receive a tip from them) he pockets the 2.00 and hands each guy a dollar. In effect the three men have each spent 9.00. Combined with the 2.00 'tip' their outgoings amount to 29.00. So where is the remaining dollar? And how would you define and assign variables in this case. And what class of problem is this? Is it as deep as say Fermat's Last Theorem which took three hundred years to 'solve' ?Three men decide to share a cheap hotel room which they are told will cost thirty dollars?
My friend told me this puzzle, and I actually figured it out. Because the bellhop took 2 dollars, the men spent $28 total. Because each man got one dollar back, subtract: 28-3 = 25, the amount that the hotel got. The number 27 gets us confused; we think to add 2 to 27 than subtract 2 from 30; this is instinct. This problem is easy to figure out if taken step by step. No way, though, does this match Fermat's Last Theorem.





~Zara SahanaThree men decide to share a cheap hotel room which they are told will cost thirty dollars?
This problem simply demonstrates how misdirection can confuse the analysis of a problem. It is nowhere as deep as Fermat's Theorem, which is INCREDIBLY deep.





We can unravel this confusion by recognizing that there is no reason to add $2 to $27. It should be subtracted.





The $3 amount that has been returned to the guests is a reduction in the amount that the guests paid, so it should be subtracted from the total. The bellhop returned $3 ($1 each), making their total payment $27 (mathematically, $30 - $3). Note that the $3 is subtracted from the total. If the bellhop then changed his mind and returned the additional $2 to the guests, it would also be subtracted from the total. The mistake is made in trying to add this $2 instead of subtracting it. Simple math demonstrates what readers intuitively sense, that there is no missing money. The sum of their payments is $25 in the till, $2 in the bellhop's pocket (totaling $27), plus the $3 in change that the guests now have, which brings the total up to $30.





The incorrect solution is: ($10 - $1) x 3 + $2 = $29. This equation is not meaningful: the number 29 is not significant to the problem, i.e. there is no ';missing $1';.





The correct solution is: ($10 - $1) x 3 - $2 = $25. In this case the solution is the bill amount, which is also the amount of money left in the till.





In other words, $27 is the amount that the guests have paid. Of that $27, $25 went into the till and $2 went to the bellhop. The other $3 is returned to the guests.
http://en.wikipedia.org/wiki/Missing_dol鈥?/a>
Account for net amount paid by 3 guys:


= 3 * ($10.00 - $1.00)


= 3 * $9.00


= $27.00





Where did the money go?


= to desk clerk + bellhop


= ($30.00 - $5.00) + ($5.00 - $3.00)


= $25.00 + $2.00


= $27.00





Another way is to account for the total amount that 3 guys paid at first:


= 3 * $10.00


= $30.00





Where did the $30.00 go?:


= desk clerk + bellhop + 3 guys


= ($30.00 - $5.00) + ($5.00 - $3.00) + ($1.00 * 3)


= $25.00 + $2.00 + $3.00


= $30.00





See? There's no mystery that happened at all.