Logic and Truth

Posted by on August 21, 2013

A Monday Morning Memo from The Wizard of Ads

Three men enter a hotel and ask the price of a room. The desk clerk tells them they may share a room for only thirty dollars – ten dollars each. Delighted to find accommodations at so cheap a price, each of the three men quickly hands over the required ten dollars and proceeds up the stairs to their room.

Moments later, the desk clerk remembers that triple occupancy is priced at only twenty-five dollars. Being an honest desk clerk, he summons the bellhop, hands him five one-dollar bills, and instructs him to take the money to the men who just went up the stairs. The bellhop, being dishonest, says to himself, “I can’t divide five dollars evenly among three men and besides, I saw how delighted they were to get a room for just ten dollars each. They will be even happier when they learn the room will cost them only nine dollars apiece. I’ll give each man back a dollar and keep the other two for myself.” And this he did.

Upon receiving the refund of a dollar apiece, each of the three men has exactly nine dollars invested in the room, just as surely as if they had originally handed the desk clerk nine dollars, right?

Here’s our dilemma: Each man has paid nine dollars to occupy the room (3 x 9 = 27) and the bellhop has only two remaining in his pocket. This gives us twenty-nine.

So where is the missing dollar?

Mathematics is the only branch of science to whose rules there are no exceptions. That each man has invested nine dollars in the room is an utterly immutable and incontrovertible fact. That the bellhop has only two dollars remaining is also fact. You can re-add the numbers as often as you like, but you’ll not find more than twenty-nine dollars. I share this story to illustrate the point that the truth isn’t always logical, and that the logical isn’t always true.

Most bad advertising decisions are made as the result of just such logic. People are wasting enormous advertising budgets as a result of trusting “facts” that are perfectly logical, but which are also tragically untrue. Specifically, I refer to the three sacred cows of advertising: Gross Rating Points, Media Mix, and Decision-Maker Targeting. While each of these is perfectly logical, they lead us to make decisions that are rarely the highest and best use of our ad dollars. *

Back to the story of the three men: Although it’s a fact that each of the men has nine dollars invested in the room, it is also an utterly irrelevant fact. The question, “Where is the missing dollar?” can only be answered by tracking the location of each of the dollars in question. We know the desk clerk has twenty-five of the original dollars. We know that each of the three men has one of the original dollars back in his pocket. We know the bellhop has the remaining two. (25 + 3 + 2 = 30) The location of the money was never a secret. We just got distracted when we began examining a “fact” that was utterly irrelevant.

You haven’t been doing this in your advertising, have you?

Roy H. Williams


* The flaws in each of the sacred cows of advertising are probed and revealed in Roy’s newest book, Secret Formulas of The Wizard of Ads, which you’ll find September 6th on the shelves of every bookstore in America.

Chris Maddock, Wizard’s Assistant

Leave a Reply