Think Twice a double dose of reason


Where Is The Missing Dollar?

I've seen this meme riddle go around Facebook a few times now, so people must continue to be confused by it.  I thought I'd try my hand at explaining the principle behind the riddle (i.e., where the "missing" dollar is) for the benefit of those who are taken in by this tomfoolery.


Have you figured it out yet?

How about now?

The Solution
Discovering the solution to this riddle requires the use of double-entry accounting.  In order to give a diagrammatic explanation, I'm using a simple balance sheet as shown below.

In a typical balance sheet, all assets are listed on the left-hand side with a total given at the bottom of the left side.  Liability and Equity balances are listed on the right-hand side of the sheet.  The reason it's done this way is that these values relate to each other with a simple equation:

Assets = Liabilities + Equity

So, the totals listed on each side of the balance sheet should be the same.   This example doesn't deal with equity so, for the purposes of this example, you can use the even simpler equation:

Assets = Liabilities

Okay: so here's a step-by-step run down of the balance sheets at different parts of the transaction depicted in the meme.

1. You have no money, so you acquire $100 through a $50 loan from Mom and a $50 loan from Dad

At this point you have $100 in cash assets and $100 dollars in total liabilities, as depicted in the balance sheet below.

2. You purchase a shirt with $97 and receive $3 change
Now, you still have $100 in assets--a $97 shirt and $3 cash--as shown in the new balance sheet.

3. You pay-down $1 on the loan from your Mom, and $1 on the loan from your Dad

Hopefully, after the last two examples, you can see how I came up with this new balance sheet.
Notice that the totals have now changed.  Total assets is now $98 and total liabilities is now $98.

Now look at the question they're asking in the riddle:

$49 + $49 = $98 + your $1 = $99.  Where is the missing $1?

The solution is that there is no missing $1 because the equation set-up is fallacious.  There is no principle in accounting which would dictate that one's cash assets ($1) added to one's liabilities ($98) should equal the original principle of one's liabilities ($100).

Why This Riddle is Tricky

The riddle is tricky because they chose a final cash asset amount which, when added to the liabilities, comes within $1 of the original principle on the loan.  If they had chosen different numbers, I doubt as many people would be fooled.

Consider a re-imagining of the riddle in which the shirt costs $60, and you still get a $50 loan from both your mother and your father after which you pay down $2 to each of them.

1. Get the loan

You'll notice that this first balance sheet hasn't changed at all.

2. Buy the shirt.

3. Pay $2 to Mom and $2 to Dad

Now, total assets are $96 and total liabilities are $96 (all is right in the world).  Here's what the riddle would say:

$48 + $48 = $96 + Your $36 = $132.  Where did the extra $32 come from!?!?!


If only it were that easy to make $32 dollars.

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  1. Ha ha ha! This is awesome! Thank you for explaining cos me and my girlfriend were quite baffled. ;)

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