Solving the Cabin Rental Riddle: A Breakdown of the Missing Dollar

The missing dollar riddle is a classic example that many find confusing due to its convoluted framing. Let's unravel the mystery and provide a clear understanding of the underlying mathematics.

The Initial Payment

Three friends rent a cabin and the initial cost is reported to be $30. Each person pays $10, making a total of $30.

The Mistaken Cost and Refund

Unfortunately, the rent was actually $25, meaning the original transaction was overcharged by $5. The clerk realizes this and attempts to return the extra money to the renters. However, he can't evenly split the $5 bill, so he keeps $2 and returns $1 to each renter.

The Final Accounting

The rent is now correctly accounted for with $25, and the clerk has $2. The renters have each returned $1, effectively paying $9 per person.

Let's clarify the financial transactions to understand the distribution of the money:

Total paid by the three people: $30 Cost of the cabin: $25 Clerk's retention: $2 Total returned to the renters: $3 (1 dollar each)

Mathematical Analysis:

From this breakdown, we can see:

Total paid by the three people: $30

Subtract the cabin cost: $25

Minus the $2 retained by the clerk

Add the $3 returned to the renters

The expenditure of the three people is then:

$30 - $25 - $2 $3 25 3 - 2 $27

This $27 includes $25 for the cabin and $2 for the clerk. The $3 is the total refund given back to the renters.

The trick in the riddle is when people try to add the $2 retained by the clerk to the $27 the renters paid after the refund. This leads to confusion.

Breakdown of the Misleading Calculation

Many people mistakenly calculate as:

$3 (one less dollar): 3 x 9 $27

Add the $2: $27 $2 $29

Then ask where the extra dollar is, thinking it should be $30.

The correct breakdown is:

27 - 2 (the amount retained by the clerk) 25

This $25 is the actual cost of the cabin, which matches the initial correct cost once the refund is accounted for.

Challenging the Riddle!

The riddle is clever in its wording, but if you read it carefully and focus on the actual financial transactions, there is no missing dollar. The $27 includes the $25 cabin cost and the $2 kept by the clerk. Subtracting the $3 refunded from the $27 provides the correct total, $25.

The riddle's phrasing plays with the reader’s expectations, suggesting you should add the $2 to the $27. However, this creates the illusion of a missing dollar because it combines the refund (which should be subtracted) with the original payment (which now includes the cabin cost).

It's always important to break down the problem into clear, logical steps rather than jumping to conclusions based on misleading phrasing.

In conclusion, the missing dollar doesn't exist in the cabin rental riddle. The riddle is a prime example of why clear and logical breakdown of financial situations is crucial in everyday life and in problem-solving.