The Missing Dollar Riddle

published on July 13, 2020

Vsauce Kevin here and you just lost a dollar I mean not literally this is just a fictional scenario that examines an unexpected slice of numerical cognition and in our scenario a dollar is mysteriously missing real quick this video is actually sponsored by LastPass

Who I reached out to because I like their service so much have been using LastPass for about a year now and it's because I was sick and tired of getting locked out of my accounts having so many different usernames and so many

Different passwords and different websites having different rules about what the passwords can be I said enough already I'll just put everything in LastPass and just take the burden off of my brain and

Make my life that much easier and it really has worked basically it stores everything safely and securely for you and then auto fills your usernames and passwords everywhere so if you want to make your life that much easier then

Just click the link down in the description below should be this way I think and get LastPass for yourself and and thanks again to LastPass for sponsoring this video okay now let's find that missing dollar

You and your friends Michael and Jake went out to lunch and split the thirty dollar bill evenly you paid 10 bucks each but the server accidentally overcharged you and the bill should have been only twenty-five dollars so she

Gives the busboy your five dollar refund but he can't figure out how to evenly divide it amongst three people and frankly you don't even know that you've been overcharged so he just takes a $200 tip for his efforts and gives you

Michael and Jake $1 back each so now you've only paid nine dollars each for lunch 9 plus 9 plus 9 equals 27 Plus The busboy kept two dollars for himself for a total of 29 dollars but you originally paid thirty dollars so a dollar is

Missing how does a dollar disappear where is the missing dollar before we break down this let's try this with different numbers and just see what happens let's say you still pay a $30 bill but this time the

Server realizes there's been a huge mistake and the total should have been only 10 bucks so now the busboy gets 20 dollars to return to you Michael and Jake which he also cannot divide equally you don't know about the exact price

Change so the busboy takes his $2 tip leaving him with 18 dollars to cleanly divide three ways he refunds each of you 6 bucks reducing your effective price to 4 dollars each so you paid 4 plus 4 plus 4

Which is 12 plus the busboy tip of $2 equals 14 dollars and just like that 16 dollars is gone because you only paid $14 for a 30 dollar bill no no no something is clearly wrong with this setup this is actually a pretty popular

And rather old riddle it seems to have originated in the mid 1700s with mathematician Francis walking games tutors assistant a sort of arithmetic textbook if 48 taken from 120 leaves 72 and 72 taken from 91 leaves 19 and 7

Taken from vents leaves 12 what number is that out of which when you have taken 48 72 19 and 7 leaves 12 part of what makes the missing dollar riddle confusing is that it bombards you with numbers that's okay though because

Your abilities with numerical cognition are actually pretty good Yale cognitive scientist Kara twin found that infants can understand simple arithmetic like one plus one equals two if I bombard you with numbers like two

Plus five plus three plus one plus seven plus 12 you aren't confused about what's happening and you can work through it to an answer of 30 but when context is added to those numbers it's easy to get

Sidetracked we get so wrapped up in what's happening with the lunch the refund and the busboy that we gloss over the real math and here 9 plus 9 plus 9 plus 2 equals 29 and wonder where the dollar went but it's not missing we just

Played a mathematical sleight of hand here's the breakdown we started with 30 dollars 25 of that is still in the restaurants cash register the other five have been given back three dollars have been returned to you

And $200 for the Busboys tip 25 plus 3 plus 2 equals 30 so where's the disconnect really where exactly is the disconnect let's find it there are really two huge problems in this riddle one is how we think about

That 3 refunded dollars we're only considering at once when we really need to consider it twice and the second problem is how we're incorrectly factoring in the busboys tip let's talk about that tip first because the busboy

Takes his $200 tip that's money that's never returned to you Michael or Jake and therefore must now be considered as part of the total cost of the lunch which means that the new cost of the meal is the $2500 still in the cash

Register plus the Busboys $2 tip equalling $27 when each of the three of you ten bucks and then gets $1 back your effective cost of the meal the food plus the waiters tip is nine dollars each for

$27 total that leaves three dollars missing the three dollars returned to you by the busboy so now we're left with the three dollar problem the nine plus nine plus nine plus two equation of the riddle is simply the wrong equation

Actually as we just learned the nines are right but the two is wrong the two is already factored into the nines what we need to do is add back the three which is kind of confusing and part of that sleight of hand the riddle uses the

Three to subtract from the customers new final total cost of the meal but we have to add it back in at the end to get to the original thirty dollars that changed hands look you've paid $10 each refund your three dollars taking the amount

Paid down to 27 and then give the busboy is $200 tip and the restaurant keeps twenty-five dollars there is no missing dollar the riddle is just answering the right question the wrong way legendary statistician John Chucky once

Said an approximate answer to the right question is worth a great deal more than a precise answer to the wrong question when it comes to the missing dollar riddle the precise answer to the right question is worth at least a buck and as

Always thanks for watching hey my podcast where I interview Michael about Vsauce is finally ready for you to listen to right now for free we get into the early days of Vsauce how I became

Vsauce to Michael's thoughts on creativity and being a meme and so so much more so first of all thanks again to LastPass for sponsoring this video second of all check out my podcast the create unknown or Michael and I talked

About how to make Vsauce and there was one day where I had done an IMG episode which I'm not in right those are just my voice share 18 funny pictures on the internet which also who by the way is such a dated show there are so many

Better ways to look for funny pictures on the internet but back then people were like I don't know I guess I have to watch a youtube video to see fucking pick anyway

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