An Amusing Brainteaser

A relative of mine just sent me the following brainteaser. Since it never hurts to flex one's mental muscles, I thought I'd pass it along:

It is the month of August; a resort town sits next to the shores of a lake. It is raining, and the little town looks totally deserted. It is tough times, everybody is in debt, and everybody lives on credit.

Suddenly, a rich tourist comes to town. He enters the only hotel, lays a 100 dollar bill on the reception counter, and goes to inspect the rooms upstairs in order to pick one.

The hotel proprietor takes the 100 dollar bill and runs to pay his debt to the butcher. The Butcher takes the 100 dollar bill and runs to pay his debt to the pig raiser. The pig raiser takes the 100 dollar bill and runs to pay his debt to the supplier of his feed and fuel. The supplier of feed and fuel takes the 100 dollar bill and runs to pay his debt to the town's prostitute that, in these hard times, gave her “services” on credit. The hooker runs to the hotel, and pays off her debt with the 100 dollar bill to the hotel proprietor to pay for the rooms that she rented when she brought her clients there.

The hotel proprietor then lays the 100 dollar bill back on the counter so that the rich tourist will not suspect anything. At that moment, the rich tourist comes down after inspecting the rooms, and takes his 100 dollar bill, after saying he did not like any of the rooms, and leaves town.

No one earned anything. However, the whole town is now without debt, and looks to the future with a lot of optimism.

Actually, this scenario reminds me of something I once saw in -- of all things -- a Beavis and Butt-head cartoon.

Beavis and Butt-head were supposed to be selling candy bars as part of a school fundraiser. They each had twenty candy bars, each one costing one dollar. Butt-head pulls out a dollar and buys a candy bar from Beavis. Beavis now hands the dollar back to Butt-head, thereby buying a candy bar for himself. They keep passing the dollar bill back and forth and before long they have both “sold” all of their candy bars.

It was very funny.

More like this

This town seems to have reverted to the barter system of economics. It's not much of a brain twister and becomes more obvious if only two people (barterers) are involved: the baker gives the cobbler $100 worth of bread for $100 worth of shoes. They could continue the fiction that each owes the other $100, but on their respective balance sheets, payables and receivables perfectly cancel out.

The greater brain teaser is the following: The US has 10 million unemployed workers. It also has 10 million man-years of unmet labor needs (for infrastructure repair, health care for the uninsured, pot hole filling, etc., etc.). So, why does the US have any unemployed and any unmet labor requirements? WPA anybody?

Your Beavis/Butthead story reminds me of the best explanation I ever heard for the dot-com meltdown we had a few years ago. There were hundreds of dot-com enterprises and they all seemed to be doing very well financially with good and growing income. However, all this income was based on ad revenue and all the ad revenue was coming from the other dot-com companies. That $100 bill just kept circulating around them at cyberspace speed and they all looked like real winners. Unfortunately, not much nutritional value in ads. In less polite circles, this process is referred to as a circle jerk.

By AnswersInGenitals (not verified) on 15 Jun 2009 #permalink

The recent commercial and home real estate bubble that's triggered the current recession had in some areas exactly that kind of a situation. In Fresno and the rest of the Golden Valley in particular, there was a large housing boom, and with it, a demand for more banks, more mortgage brokers, more real estate agents, more insurance brokers, and more construction. As the arrival of people into the area started to fill in that demand, the area realized that to support that, they would need more housing and more offices, so they built them, which required even more of those classes of people to manage, build, and sell.

But the inevitable happened there: nobody else came. nobody came into the area that brought in any real employment other than the housing industry itself. Large office buildings were being built that never got filled.

Macroeconomics 101: if you don't bring in external money into a system, the weight of the local system will collapse it. Farming communities survive because their stock is sold elsewhere. Manufacturing communities survive because they make money selling the products elsewhere. Military communities survive from the income provided by the government. "College Towns" thrive from the money made from the government/school (teacher, admin, and support salaries), and the money brought in by the students from their own respective families.

Communities with more than one external income source thrive, even if they remain small like many in the Shenandoah Valley.

But no community can exist on retail alone. When the primary income center dies (say, Michael Moore's favorite: Flint, Michigan), the remaining retail systems can't fill the jobs needed. Retail is a sink: your money is meant to go elsewhere, just as your money was supposed to come from elsewhere.

In this case, they only money coming in were new residents filling in their own void. the system itself was built on kind of local pyramid scheme that eventually ran out of new people to contribute to it with money from outside the locality.

The one thing unrealistic about the brainteaser was the other side of the external element. Yes, it showed that the community recovers and thrives on external money, but what was missing was the reality that the debt itself is a sink: nobody collected interest. The reality is the middleman collecting interest on EVERYBODY's debts, the middleman who isn't part of their community at all...

By Joe Shelby (not verified) on 15 Jun 2009 #permalink

Funny, I was recently asking somebody if there's an algorithm that is commonly used to avoid loops in debts. He said something of the sort, blabla accounting blabla you'd think so, but I'm none the wiser now. Anybody knows more?

What Joe above said is wrong btw, the reason for a bubble is not a loop but a gain that somebody can profit from by selling on debt, which results in unsustainable pyramid schemes.

Seems like the Broken Window Fallacy to me.

The citizens in the town ARE worse off. Assuming that they all owed each other money since the beginning of tourist season (say 3 months), they are all worse off because of all the things they could have bought or invested in, but weren't able to because of their lack of liquid assets: the butcher wasn't able to buy sharper knifes enabling him to work faster, the hog farmer wasn't able to buy higher quality stud services to produce larger hogs, and the hotelier wasn't able to advertise his hotel more widely, thus driving in more business for all of them.

I got as far as figuring out that the Rich Tourist supplied an interest free loan.

I am not sure if this helps or hurts.

Reminds me, too, of the Lady who drops off her expensive car at a New York Bank as collateral for a $10,000 loan that she will pay off in two weeks. The bankers keep trying to find out the hook, but it looks legit so they take the loan.

Lady comes back from a trip in two weeks, pays her $16.00 interest and says, "Where else can I park my car in New York for $16 in New York and expect to find it in one piece when I return?"

"The citizens in the town ARE worse off. ...the butcher wasn't able to buy sharper knifes enabling him to work faster, the hog farmer wasn't able to buy higher quality stud services to produce larger hogs, and the hotelier wasn't able to advertise his hotel more widely, thus driving in more business for all of them. Posted by: Kevin | June 15, 2009 5:34 PM"

I don't know about that. The butcher has had the same knives for 10 years. He sharpens them every day. A new one will not speed his work; anyway he is idle 50% of the time so saving time does him no good.

The hog farmer has his own boar. He considers it best as it is adapted to local conditions.. and is willing to work for food.. (haha)

The hotelier does not advertise but instead depends on the hooker to bring in business. The hooker is the only one providing any valuable service in the town.

The hotelier needs to set up a friendly poker game.

The butcher should open a barBQ shack next to his store. THe hog farmer should start drying hams and growing pot for pig food.

Now that hooker needs to get on Craiglist and bring in a whole lot of new money and then they will be better off.

but in economic terms they are exactly the same. They owed out a 100 and they were owed a 100. dead even .. if they actually talked to each other they could have passed a quarter between them and called it even.

By Kevin (nyc) (not verified) on 15 Jun 2009 #permalink

How much money there was seems entirely dependent upon the economic model that one uses for analyzing the situation. If the system is based on a standard then there was only $100 anywhere. And when it was taken back the town returned to a zero-sum-gain.
But if the system is floating, and like ours was credit-driven, then each debt (one man's debit is another man's credit) accounted for $100 of value at each stage. (Was that $600?) But the end result was the same -- when the money was taken back it all returned to zero.
Yry the difference was in the economic processes, not simply in the money itself. It is the model that affects daily life.

What they achieved could have occured without the $100.

The hotel clerk could have achieved the same thing by saying 'Butcher, the hooker owes me $100, I owe you $100, why don't I transfer the debt so the hooker pays you instead of me.'
Now the hooker owes the butcher $100 and the hotel clerk is free.

Likewise the hooker can say to the butcher: 'The supplier owes me $100, and I owe you $100, so why don't I just say the supplier owes you $100'. Now the supplier owes the butcher $100 and the hooker is free.

You can repeat this till you get to the Pig raiser saying: 'I owe you $100, but you owe me $100, so lets call it square'.

ie. the net debt is actually $0.

So basically, all the $100 did was facilitate the above situation and therefore you can't say the town is better off, but nor can you say its worse off.

...therefore you can't say the town is better off...

It has a more relaxed hooker, doesn't it?

The town is now better off because people are free to spend another $100 on credit (if we assume that $100 is the maximum credit traders will allow). So each person can now buy and sell another $100-worth of goods or services. (But they won't have any money to replenish stocks from an external source.) In a sense, the money supply has been increased from -$500 to $0.

Even though the net debt was zero, the circular debt situation was not equivalent to one in which there was no debt at all. Traders were exposed to loss if their debtor defaulted. Apart from that, there's the psychological factor that people feel better off and are more inclined to spend when they have more money in their pocket, or less debt, even if their net worth is the same.

Of course, the same thing could have been achieved without the tourist, as Simeon describes. Alternatively, the municipality could have boosted the money supply by printing $500 of its own currency and distributing it to the traders.

By Richard Wein (not verified) on 15 Jun 2009 #permalink

In my opinion, the tourist's (unwilling) intervention only brought into light the fact that there was a circular debt, that it could be wiped off, but only upon agreement. I see it as a similar situation to "I owe you 100 and you owe me 100": both can insist that they want to be repaid; or they can agree that each one's debt cancels the other one's.

I interprete this as showing that the system works better if it can see things from higher than the mere atomised interactions of individual players. That is, it needs to be organised.

By Christophe Thill (not verified) on 15 Jun 2009 #permalink

Additionnal reflexions :

In the case of Beavis and Butthead, it only works because they're dishonest. They're supposed to keep the money they make from selling candy bars, not to spend it.

In the story, things could have worked differently, but in an equivalent way. At the beginning of the chain, the prostitute could have written a note to the hotel manager: "I owe 100 to the bearer of this note, signed X". When the manager buys meat, he has no money to pay it with; but this note is a guarantee for a $100 payment, so he can actually pay with it. The note goes all round the chain. At each step, each player cancelled their debut with it. In the end, when the fuel supplier goes to see miss X, he can give the note back to her.

Actually, in this case, the town residents would have reinvented currency.

By Christophe Thill (not verified) on 15 Jun 2009 #permalink

This hardly seems a brainteaser to me, yeah.

It's just a circular debt situation.

The town is better off now than they were before, because individually one is better off neither owing or being owed than they are owing and being owed the same amount - as you may not be able to guarantee that your debt won't come due before the debt you're owed gets repaid, and you're carrying risk in case something happens to the person who owes you.

The town could indeed, as others have noted, solved their problem by one of the individuals involved writing an IOU, or simply by negotiating trades of debt, or even just realizing that there was circular debt and canceling it all out - the tourist's $100 was simply a facilitator.

This certainly isn't a Broken Window Fallacy situation, since nobody whatsoever lost anything (although the tourist could have, if the debt hadn't been a closed loop!) - they presumably gained by entering into their debts at the time they entered into them, and certainly wouldn't've returned what they got to get rid of the debt, even in the cases where that was possible.

By Michael Ralston (not verified) on 16 Jun 2009 #permalink

Yeah, there is no real teaser. Everyone had net assets of zero before since they owed a hundred dollars to one person and had a claim to a hundred dollars from another person.

Afterwards they have no debt and no claims so they still have zero assets. If the story illustrates anything it would be the advantages of money over bartering as a means of organinazing exchange.

I it is somewhat similar to a classical question in economics though. Imagine that a traveller pays for a meal with a check and that the check does not get cashed but instead circulates in the economy with people using it for payment. Who did then pay for the meal?

An answer is here:…

I interprete this as showing that the system works better if it can see things from higher than the mere atomised interactions of individual players. That is, it needs to be organised.

[Christophe Thill, #11]

Don't forget the costs of acquiring and organizing information.

Has any one noticed that this whole 'circle' of dept payment is actually started as theft? OK the 'owner' does not 'know' his money is stolen but it was. And there is a 'loser' in the real world the $100 would have gone to the clerk and stopped making him $100. But in this example the 'clerk' has to sneak the $100 back to the owner before being caught as a crook. So there is an actual $100 lose at the end. There is no zero-sum it is -$100.

I don't understand why this is a problem. Economists tell me there is a seven-fold multiplier effect in commerce. A dollar spent generates seven dollars worth of economic gain. You mean you didn't know that? This is routinely used in figuring benefit/cost for projects.

By Jim Thomerson (not verified) on 16 Jun 2009 #permalink

Isn't the hotel proprietor taking a risk for potentially no reward? At any point in the chain someone could have decided to keep their $100. The proprietor doesn't get the $100, and while in a sense he has only transferred his debt to the rich guy, he has to shell out the $100 immediately. So why would he put himself at added risk?

I agree that the gross local product was $600 from the transactions. However assuming each $100 was a net profit and the tax rate is 25%, the net result is -$150 owed in taxes(6x$25). Of course no one made 100% profit. The circularity of the Fresno housing situation happened near several Florida towns and I suspect in other areas as well. The houses built for labor were simply abandoned when the bust came.
Gillian Tett's book, "Fool's Gold:...", describes the buildup and collapse of the financial derivatives house of cards which seriously harmed a lot of people.

It seems to me that the only reason this works is that the prostitute has either not been charging the "feed and fuel guy" enough, or she has been paying the hotel owner too much, since her debt from her customer was exactly the same as her hotel bill.

"I agree that the gross local product was $600 from the transactions."

The gross local product was 600 when the services that created the debt where rendered. (Assuming that happened at the same time.)

Just settling the debts doesn't do anything to the GLP.

the $100 is irrelevant here. There is a simple subrogation scheme that eliminates all of the debt without the need for real money.

This little brainteaser explains the source of about 90% of the 'wealth' the finance 'industry' 'created' in the last decade.

This "brainteaser" says very little about anything and in particular I fail completely to see what it has to do with the financial crisis.

Maybe someone can explain?

My guess is that it will turn out to be the usual ignorant response that finance just transfers money between people and thus does not create any real value.

One word answer - liquidity.

By Martin Hogbin (not verified) on 22 Jun 2009 #permalink

Afterwards they söve have no debt and no claims söve so they still have zero söve assets. If the story illustrates anything it would be the advantages of money söve over bartering as a söve means of organinazing exchange.

For any economic improvement value addition is important. Had all the folks of the town did some value addition during intragnum of the $100 fund availability it would have helped them in improving their economy. They have hurriedly used the funds in clearing the old debt with out looking for opportunities of making some earning out of the scarce resource they got.

By V Hariharan (not verified) on 05 Jul 2009 #permalink

As others pointed out the teaser makes explicit all the money borrowed but ignores the fact each person is also a creditor.

wukoki, and oguzhaqn, both had an important observation. Someone in the chain could have decided not to immediately pay their debt. In which case the tourist would have said, "Where's my money?" There is a temporal naivety to the brain teaser, just like there is in Keynesian economics (Krugman's favorite school).

What is lacking in the teaser is information about the terms [time periods] of the loans. Over what time period were the people expected to pay back the loans? If the loans were due immediately as the tourist arrived and in the same order as paid back then it makes sense. Apparently these are zero interest loans.

In an actual money system all players hold a certain quantity of cash themselves against risk. Risk in the form of not knowing when you will loose your job, have a chance to run to the store, or see some nice clothes on sale.

Thus if the brain teaser were real then the prostitute (or any of the townsfolk) probably had ready cash in hand and could have triggered the repayment of all the borrowed funds herself.

I've seen many people misinterpret this example as having meaning for the current crisis. It doesn't. We owe money to people outside our "town" [the US] and the loans are long period ones.

The current economic crisis is a term mismatch problem. There is already a problem with fractional reserve banking in that it acts as a pyramid scheme that moves people into longer term positions than they actually think they are in. This problem was exacerbated by the FED coordinating all the banks in this scam to allow it to go on for a longer period of time.

Borrowing short and lending long doesn't work over the long run as you eventually run out of new chumps. People who deposit their money into short term accounts need that money for short term spending, and when it is lent out long term it becomes a problem.

Had any one of the townsfolk decided their loan had a longer payment term their would have been a problem closing the circle back to the hotel owner.

Bank runs are always about a failure to match terms on loans. What is happening now is a bank run where there is no backing commodity money, only fiat. The bank of last resort, the Fed, is trying to pad the time issues by printing money. Of course, the new money they print is handed out to their political friends. Therefore it diverts present goods and services to the undeserving.

Krugman's suggestion to print up even more money can only further increase the diversion of funds to the undeserving, while further destorting the structure of production.

Have any of you noticed how the last pump of money cheered on by Krugman distorted the economy into producing way too many houses? Well the new pumping is causing my town to repave roads that were perfectly fine, and put in brand new dog parks, etc. More distortion, except this time in wasteful government make-work projects.

By Brian Macker (not verified) on 28 Nov 2009 #permalink

Beavis and Butt-head story was hilarious . But it was Beavis who first took out the dollar so I believe at the end he's the one having back his money and one candy would be still left with Butt-headed to sell off .

Krugman's suggestion to print up even more money can only further increase the diversion of funds to the undeserving, while further destorting the structure of production.

The hotel clerk provided $100 worth of room stays to the prostitute. She paid him but it was taken away by the tourist. He's out $100.