The missing dollar puzzle: Never be deceived by fallacious reasoning.
Strive Karadzangare | February 5, 2021
Deception, lies and fraud are some of the most dreaded aspects of human experience. They are often associated with negative consequences. In life there are many forms of deception, which differ in magnitude and in the contexts in which they are manifest. The missing dollar puzzle, clearly demonstrates how the human mind can be easily deceived. What is the missing dollar puzzle and how does it demonstrate, human vulnerability to deception? I will get to that soon. With the aid of the "missing dollar puzzle" we will explore how faulty arguments and twisted reasoning are usually instrumental in deception. This article will also introduce the term, fallacy in explaining the role of twisted reasoning in deception. In the meantime, what is the missing dollar puzzle and what kind of trickery is found in the puzzle?
Recently a friend of mine shared with me a puzzle that is based on an imaginary scenario. It went like this:
John wished to buy a pair of shoes which costed $100, but he was broke. So, John borrowed $50 from Chipo and $50 from Merry. He then went back to the shop and got the shoes at a discount price of $97, and thus he got $3 change. He decided to repay his creditors that is, Chipo and Merry $1 each. That meant that he then, owed Chipo, $49 and he also owed Merry, $49. After repaying Chipo and Merry, he had $1 remaining.
If we add up $49 plus $49 we get $98. If we add the remaining $1 to that sum we get $99. The question was like: Why are we getting $99 instead of the original $100? What happened to the other $1 ? It's a big mystery huh ? Pause for a moment and think about it
When I first encountered a puzzle of a similar nature, several years ago, I thought that it was very complex and unsolvable. It turned out that I was right. The problem is actually unsolvable. However that is not due to its complexity but it is due to an invalid assumption that was made in stating the puzzle. What exactly do I mean ? Let us discuss that, next.
The puzzle itself is valid, but there is an invalid assumption that was made in the puzzle. The whole purpose of solving the puzzle lies in identifying that invalid assumption. Well, the assumption that when we add up all the amounts like, $49 plus $49 plus $1, we should get $100 is the whole premise of the puzzle. However, that assumption is wrong because the amounts should not be summed up in that manner, since they are are unrelated. By unrelated, what do I mean? Well, the amounts are unrelated in the sense that: $49 is the amount that is owed to Chipo and the other $49 is the amount owed to Merry, whereas $1 is the amount that John has in his pocket (which he owns). Already we can see that error was made when we tried to add what John currently owns to what he owes.
In fact it is never guaranteed that, if we add the unrelated amounts in that way, we will get $100. What is guaranteed however is that the total amount of what John owes will perfectly cancel out what he owns. Considering that he now owns shoes worth $97 as well as that extra $1, and that he owes Chipo and Merry $49 each, we can draw up a table of what he owes against what he owns, like so:
As shown, what he owns perfectly balances out with what he owes. Using accounting jargon, what he owns can be labelled as his assets and what he owes can be labelled as his liabilities. The original argument of adding $49 plus $49 plus $1 is actually invalid because we would be mistaking assets (the remaining $1) to be liabilities.
According to research, many first-timers who attempt to solve the missing dollar problem, are often misled to think that the faulty mathematical operation is valid. In fact, most of them never question the validity of that mathematical operation. That way, they get deceived. It's easy to assume, that it is entirely their fault that they get deceived but that is not the case, because the the faulty mathematical operation was presented in a way that made it seem quite logical. In fact, that is how most fallacies look like. They usually appear to be very logical when in fact they are not. With that in mind, it is necessary to formally define fallacy at this point. Fallacy is defined by Wikipedia as:
"The use of invalid or otherwise faulty reasoning or wrong [assumptions] in the construction of an argument. A fallacious argument maybe deceptive by appearing to be better than it really is."
According to Wikipedia fallacies can take the form of unsubstantiated statements that are delivered with a conviction that makes them sound as though they are proven fact. For example, you may have noticed that it may be quite easy to quickly trust someone who confidently expresses their ideas, even before you formally analyze their viewpoint. Often times, fallacies are presented using persuasive language, and thus it is often difficult to notice the illogical connections between statements. Some fallacies may take advantage of the emotional, intellectual or psychological weakness of the listeners. However, when someone is able to recognize fallacies, they can develop the reasoning skills that can help to distinguish what appears to be true from what is really true.
There are several categories of fallacies, but in this article I will not outline any of those categories. I will rather give some examples of statements that are involve fallacy. For example, the following statements are fallacious:
"James refused to share this message and he lost his job. If you do no share this post you will lose your job." [Statements like this one are usually common on social media]
"Share this message, in 5 groups, and your battery will become fully charged" [Statements like this one are usually common on social media]
"Since we cannot prove that aliens do not exist, then they must really exist."
"You were late by ten minutes today, tomorrow an hour and then someday you will probably cease to show up."
Do you notice why, we can say that they are all fallacious? It is because they all make invalid assumptions and feature faulty reasoning. Those sentiments are just but simple statements, meant to illustrate the concept of fallacious reasoning. In real life however, fallacies may be presented to us in a novel, subtle and usually unprecedented manner. They may even feature deeper levels of deception. Some people failed to notice fallacious reasoning that they were offered by con-artists and they were unfortunately defrauded of their money. The fact that some people failed to detect fallacy, is probably the reason why pyramid schemes successfully defrauded many people of their money. We all encounter fallacies at work, at school, at church, in the media and even in our daily interactions with our friends and family. However, it is imperative to note that, you can generate fallacious reasoning, which you could use to deceive yourself. Remember that, no-one is immune to deception, at one point or another we can all get deceived. So we really need to take real action to avoid being deceived at any point in our lives.
Even though you will not encounter devastating fallacy everyday, you need to build the skills that help you to detect fallacy and avoid being deceived. A very useful skill that can help in detecting fallacy is the critical thinking skill. I may discuss about that skill in one of my future articles. In the meantime, do anticipate a follow up article to this one. It may offer a deeper analysis of the concepts of fallacy and deception, which occur in real life.
Thanks for taking your time to read this article. I really hope I will be able to share with you another article very soon. Remember to stay safe during this time of this Covid-19 pandemic. Watch out for fallacy in the media, and avoid being deceived.
#avoidfallacy, #criticalthinking, #fallacy, #deception, #staysafe, #avoiddeception, #beinspired, #aspiretoinspire
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