Misleading Maths - The Motel Room Rate Puzzle (Plus Three Gay Hunters and a Cheating Prom Queen)
I remember being intrigued by this puzzle while I was still at school. It appears that the maths gives the wrong answer. See if you can solve the brain teaser.
Three men on a hunting trip check into a cheap motel and share a room together. No they are not gay. They just share a room to save money. They pay $30 in cash for the room to the owner’s beautiful daughter when they check in ($10 each).
You want to know more about Jessica? This has no relevance to the puzzle. OK she has long blond hair, a face like an angel and a figure to die for.
When the owner returns he checks the register and tells his daughter she has over-charged the guests. He has recently dropped his room rates to $25 because of the Credit Crunch and the Recession (this is a topical puzzle) and the new rate is displayed on the sign outside.
So why didn’t they complain to Jessica about being overcharged?
Perhaps they didn’t see the sign and they were tired having driven 700 miles from Chicago.
Perhaps Jessica’s uncommonly good looks and brief shorts distracted them. Remember they aren’t gay.
Anyway, the owner, Frank, gives Jessica a $5 bill to return to the guests.
As she wanders from the motel office to room 17, Jessica tries to work out how to divide the rebate three ways but although she was Prom Queen, maths was never her forte.
Jessica and Pedro
Suddenly she is distracted by Pedro, the new hired hand, who cleans the pool and does odd jobs for her Dad.
Jessica kind of fancies Pedro and his jet black curly hair and dark smoldering eyes. Pedro looks approvingly at her long legs and super tight shorts.
Jessica sidles over and flirts shamelessly with Pedro until she becomes aware her Dad is watching them.
Frank looks really mad so she rushes over to room 17 and knocks on the door.
She still hasn’t worked out how to split the cash so she offers Mike (one of the Chicago hunters) $3 telling him the room has been reduced to $27.
Mike is delighted and Jessica pockets the $2. So now everyone is happy.
The Big Question
Now for the big Question. The hunters have paid $27 for the room. Jessica has pocketed $2. Making $29 in total. So where has the other $1 gone? Has Pedro got it?
This is is one of those puzzles where the question itself is misleading. It is sometimes described as a sematic or logical fallacy. To solve the problem, lets follow the cash.
At the beginning the hunters have $30 that is handed to the Motel for the room. The motel ends up with $25, the new rate for the room. The $5 balance is taken by Jessica. She keeps $2 and hands $3 to the hunters. So there is no missing dollar.
The trick is in the statement that hunters have paid $27 for the room. The hunters only think they have paid $27 for the room. They have actually paid $25 for the room and $2 to Jessica. There is no missing dollar!
Incidentally, this was the start of a downward slide for the lovely Jessica. One day she helped herself to the Motel till contents and ran away with Pedro to Mexico.
Fortunately for her, her Dad and some of his drinking buddies crossed the border and rescued her from the drugs cartel and after rehab she become the mainstay of the local church and married her pastor.
What about the gay hunters I hear you ask? I’ve told you before. Just because 3 guys share a room it doesn’t make them gay. Pedro? He’s doing a long stretch in St Quentin but Jessica keeps in touch and sends him books and study material.
He's studying for an MBA and dreams of winning jessica back and running his own pool installation company. Jessica recently went back to college and majored in Religious Studies and Maths. She also heads up the Sunday School.
This is getting more like a soap opera than a puzzle or a brain teaser so lets finish while we’re still ahead.
Incidentally I know some of you are anxious to known where in California you can get a motel for $25 a night. I tried to get the details from Frank so I could post a link here for you. Unfortunately the Mexican Cartel are very keen to locate Frank so he prefers to remain incognito!