Missing dollar riddle
[1] Although the wording and specifics can vary, the puzzle runs along these lines: Three guests check into a hotel room.
So if the guests originally handed over $30, what happened to the remaining $1?There seems to be a discrepancy, as there cannot be two answers ($29 and $30) to the math problem.
The misdirection in this riddle is in the second half of the description, where unrelated amounts are added together and the person to whom the riddle is posed assumes those amounts should add up to 30, and is then surprised when they do not — there is, in fact, no reason why the (10 − 1) × 3 + 2 = 29 sum should add up to 30.
The exact sum mentioned in the riddle is computed as: SUM = $9 (payment by Guest 1) + $9 (payment by Guest 2) + $9 (payment by Guest 3) + $2 (money in bellhop's pocket) The trick here is to realize that this is not a sum of the money that the three people paid originally, as that would need to include the money the clerk has ($25).
When added to the $27 revised cost of the room (including tip to the bellhop), the total is $30.
To obtain a sum that totals to the original $30, every dollar must be accounted for, regardless of its location.
One cannot simply add a couple of payments together and expect them to total an original amount of circulated cash.
That abstract formula holds regardless of the relative perspectives of the actors in this exchange.
6) 27 = 27How the riddle is deceptive comes in line 7: 7) 9 + 9 + 9 = 25 + 2 8) 9 + 9 + 9 + 2 ≠ 25 (pushing +2 to the other side without inverting the sign) 9) 27 + 2 ≠ 25
Each guest ends up with a balance of b − p (a negative amount), the manager with np − r and the bellhop r − nb.
Professor David Singmaster's Chronology of Recreational Mathematics[3] suggests these type of mathematical misdirection puzzles descended from a problem in an 18th-century arithmetic book, Francis Walkingame's Tutor's Assistant[4] which was published, and republished, from 1751 to 1860 where it appeared on page 185, prob.
His puzzle produces an extra dollar: A man puts $50 in the bank.
"A traveller returning to New York found that he had only a ten-dollar postal money order, and that his train fare was seven dollars.
On his way back to the station he met a friend, who, to save the traveller the trouble of returning to redeem the money order, bought the pawn ticket from him for seven dollars.
Even more similar is the English, The Black-Out Book by Evelyn August in 1939; What happened to the shilling?, pp.
The riddle is used by psychotherapist (Chris Langham) with his mathematician client (Paul Whitehouse) in episode 5 of the 2005 BBC comedy series Help.
[6] A variation, also involving shillings and three men in a restaurant who are overcharged, appears in the third volume of Jennifer Worth's Call the Midwife books, Farewell to the East End (2009).
