The Missing Dollar (math/logic puzzles!)

Previous posts about Chief Theresa Spence -- the icon of the Idle No More "movement" -- have mentioned the damning auditor's report into mismanagement of the millions of dollars doled out by the Canadian government (read Canadian taxpayers) to her band council. Under the supervision of her boyfriend -- a bankrupt -- taxpayers' money just vanished, paid to persons unknown without proper documentation or, indeed, sometimes without any documentation.

The story reminded Walt of an article that appeared in the University of Toronto Magazine about six years ago. Marcel Danesi wrote about "contrary-to-expectation" puzzles, designed to show how susceptible human logic is to the power of deceptive language.

The use of numbers and language to confuse the reader was known to the ancient Greeks, and persists to this very day in such things as misleading advertising. Case in point: TV infomercials that promise you a great deal on, say, padded bras, and then tell you they'll send you a second set of the same, absolutely free. Of course you pay extra for the shipping and handling of the bigger package, but hey, it's free, right?

This works because many people have trouble understanding mathematical logic if a set of numbers is presented in a deceptive manner. A classic brainteaser (Danesi writes) was described by R.M. Abraham in Diversions and Pastimes (1933). Here is The Missing Dollar.

Three women check into a motel. The women are charged $10 each for their rooms, or $30 in total. (Hey, this was in 1933, remember!) Later, the manager discovers that he has accidentally overcharged the three vacationers. Their rooms cost only $25 in total, so he gives a bellhop $5 to return to them.

The sneaky bellhop knows that he cannot divide $5 into three equal amounts, so he pockets $2 for himself and returns only $1 to each of the women.

Here's the conundrum. Each woman paid $10 originally and got back $1. So, in fact, each woman paid $9 for her room. Therefore, the three of them together paid $27. If we add this amount to the $2 that the bellhop dishonestly pocketed, we get a total of $29. Yet the women paid out $30 originally. Where is the other dollar?

Figured it out already? Here's another one.

A customer in a bookstore gives a sales clerk a $10 bill for a $3 book. (Still 1933, I guess.) The clerk, having no change, takes the $10 bill across the street to the record store (definitely 1933!) To get it broken into $1 bills. (Canadian readers can substitute loonies for the singletons.) The bookstore clerk returns and gives the customer the $3 book and seven $1 bills in change.

An hour later the record store clerk brings back the $10 bill, claiming that it is counterfeit. To avoid quarrelling, the bookstore clerk gives the record store clerk ten $1 bills and takes back the $10 note. How much has the bookstore clerk lost?

Answers tomorrow.

The chiefs meet the Dear Leader -- right out of Seinfeld

First, for those following the progress (?) of the Idle No More protests, an update from the Great White North. When last we looked into the tipi of Chief Theresa "What Money?" Spence, she was demanding some face time with Canadian Prime Minister Stephen Harper. Apparently she didn't offend him by calling him "Steve", so Harpoon said he'd meet with her. And he didn't even say, "Show me the money!" -- that which vanished down the Attawapiskat rathole. Request granted.

Apparently flummoxed by her success -- not to mention the prospect of having to look into the Dear Leader's icy blue eyes -- Chief Spence and Shawn Atleo, the Biggest Chief of All, upped the ante. The Governor-General has to come to the meeting too, they said, because he represents the Great White Mother Over the Waters.

Reference was made to a number of treaties made with the Indians in the name of the GWM. The original GWM (Queen Victoria) died over a century ago, but the present GWM is her great-granddaughter, so nothing would do but the Chiefs meet with her viceroy. And, said Spence, if the G-G doesn't attend, then I'm not attending!

Surprise surprise, His Excellency David Johnstone said the chiefs -- or some of them, at least -- could come to a big potlach at Rideau Hall (his residence) after the meeting with Harper. Said the chiefs, that's not good enough! The G-G has to come with the PM to the same table at the same time, otherwise we won't meet with them. Or maybe some of us will, but not Chief Spence. Or not. We'll see.

As I write, a meeting of some kind is set to begin. The CBC reports that it's to be held in Harper's office in the Langevin Block, across from Canada's Parliament Buildings. Again, not good enough! The chiefs think the meeting should be in the nearby Château Laurier so that more of them could attend -- larger quarters, you see -- and those that couldn't get in the meeting room could repair to one of the hotel's very agreeable bars. Canadian taxpayers would pick up the tab, of course.

What everyone wants to know is not whether the meeting will come off, but exactly what will be discussed if it does. CBC-TV's famous "At Issue" panel of pundits attempted to make sense of the whole thing last night, and fell short...way short. All they could say was that if the meeting didn't happen, it would look bad for Shawn Atleo, who might even lose his position as Grand Chief.

Would it matter? Oh yes, the panel said, because then the Canadian government would be left with no-one to talk with. Which begs the question: talk about what? What is it that the First Nations people want? Chief Atleo finally held a presser yesterday and answered the question in a word -- more. Whatever it is the FNs are getting, it's not enough. They want more!

Walt would love to be a fly on the wall in Harper's office right now. My guess is that the meeting will be just like the famous Seinfeld episode in which Jerry and George are asked what their proposed TV show is going to be about. Even the At Issue panel should remember their response.

Footnote from Ed.: We were going to headline this post "Walt is puzzled", because it is so. The idea was to segue into a little math puzzle to amuse you while we wait to see what happens today, but Walt has already gone on too long... much too long. So the puzzle -- "The Missing Dollar" -- will appear, errr, later.