The Magic Penny / Missing Dollar

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Has anyone ever told you the story about the missing dollar?

Once upon a time there was this hotel located smack dab on the border of California and Nevada called, The El Royale. With no other place to stay for miles, The El Royale is always busy with overnighters traveling from one town to the next. One night, three strangers pulled into The El Royale needing a room. When the concierge told the three guys that there was only one room available, they looked at each other and decided to bunk up together. The rate for the night was $30, so each guy forked over a $10 and the new three best friends that anyone could have were on their way. After about an hour of feeling bad for the three strangers having to share a hotel room for the night, the concierge decides to discount the room from $30 to $25. Feeling great, he grabs five $1 bills and heads to the room for the guys. The guys are so appreciative and generous that they tip the concierge $2. Partially for the concierge’s initial generosity but also so that each guy could get a fair $1. Once the five $1 bills had been handed out, each guys had spent a net of $9 on the room rather than $10 and the concierge got a $2 tip. After a couple of minutes, one of the guys says, “wait a second, if each of us paid a net $9, that equals $27, then if we only tipped the concierge $2, where is the missing dollar? Because, $27 + $2 = $29 and we started with $30”. 

That story is so frustrating because no matter how many times you read it, it’s like, “fuck man, I don’t know”. I get it, I was there, I didn’t even sleep because it drove me so nuts when I first heard the story. Luckily, I was able to get on my whiteboard and figure it out. Turns out, there isn’t actually a missing dollar and only from one perspective does it appear to be. The original rate was $30, $10 for each. Then the rate got discounted to $25, five $1 bills were given out. One for each guy and two for the concierge. $1+$1+$1=$3, + $2= $5, + $25= $30. So in reality, no missing dollar but rather a “magic” penny. This deal got messed up when the concierge discounted the rate to $25. $25 will never work because 25/3= 8.333… 8.333… is an infinite number, who’s mathematical characteristics are fundamentally different than that of 8.33. If we multiply 8.33 times three, we get 24.99. Not 25. Subtract $24.99 from $30 and what do we get? $5.01 is what my calculator says. If we subtract $1 for each guy, we are left with $2.01, not $2.00. The reason why in reality, it’s even money, is because $5 divided by three is $1.67, who’s mathematical characteristics are fundamentally the same as 1.6666666667. If we subtract the dollar for each guy, we are left with $.67 times three which equals wait for it… $2.01 $2.01+ $24.99= $27 Then add the three $1s from the fellas and we have $30.

How is any of that relevant to you? It is proof that currency is infinite. There is an infinite value associated with the number 8.333… but the idea of cash and coin cuts off after the second decimal point, forcing us to round up or down. When we round off our value, we are literally giving away infinite fractions of a penny associated with that value. In our story, all the 3’s after 8.33, are what makes up the tail that gets chopped off of this value or number. Where do all those infinite fractions of a penny end up? The answer could be found by figuring out who “structures and oversees the order of value,” which is what money is if you recall back to Money vs. Currency. Currency is an accounting principle for the distribution of value. “Money is the structured and overseen order of value.” I don’t know how much money those infinite tails of “leftover” value are creating for the ones “handling” how money works but I do know that it’s enough to never run out.