I received this problem by email. This problem is making the rounds on Facebook and thousands of people are arguing most the right answer.

How smart are you? A guy walks into a shop and steals a $100 bill from the annals without the owner'south knowledge.

He so buys $70 worth of goods using the $100 pecker and the owner gives $30 in modify.

How much money did the owner lose?

$xxx, $seventy, $100, $130, $170, or $200?

Sentry the video for a solution.

The Stolen Bill Riddle (Viral Math Problem) – The Correct Answer Explained

Or go on reading for the answer.
.
.

"All will be well if you use your mind for your decisions, and mind just your decisions." Since 2007, I accept devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions at present has over 1,000 free manufactures with no ads thanks to community support! Assistance out and become early access to posts with a pledge on Patreon.

.
.

.
.
.
.
One thousand
I
N
D
.
Y
O
U
R
.
D
E
C
I
South
I
O
North
S
.
V
I
R
A
50
.
P
R
O
B
50
E
G
.
.
.
.
Answer To Stolen Coin Riddle

The best answer from the choices is the owner lost $100. The $100 neb that was stolen was then given back to the owner. What the owner loses is the $70 worth of goods and the $xxx in change, which makes for a total of $70 + $xxx = $100. The owner has lost $100.

Technically, the owner lost $xxx plus the value, V, of the $lxx of appurtenances. Since stores typically sell goods at a markup, the value may be less than $70. But in the case of a loss leader, the owner may have lost more than than $lxx.

Some other strategy to solve the problem is to break it down into two stores.

Story A
A guy walks into a shop and steals a $100 bill from the register without the possessor's noesis.

How much money did the owner lose? Conspicuously the answer is $100. The possessor is a net -100.

Story B
He buys $lxx worth of goods using a $100 nib and the owner gives $30 in modify.

How much money did the owner lose? The owner did not lose any money, this is a routine transaction! If the goods are valued at V, the owner is a net +100 – V – 30 = lxx – V.

The story in the riddle is the sum of the two stories. This means the possessor's position is the sum of the position in those two stories. The possessor is a net -100 + (70 – V) = -30 – V. That is, the owner lost $30 plus the value of the goods. If the appurtenances are valued at $70, and then the possessor lost $100.

Misconceptions

Many people recall the answer is 200 dollars. It seems like the owner had $100 stolen, and so had another $100 stolen in the 2nd story. But retrieve the thief likewise paid using the $100 bill, and then the owner really gets back $100. The owner'southward loss is $100.

Some people call up $130 considering the owner lost a $100 bill and so gave $30 in change. Only remember the owner as well received a $100 bill, and as well gave away $70 in goods. Calculation up all the transactions leads to the possessor losing $100.

The other incorrect responses are misunderstandings of a like sort where people are non sure which numbers to add or subtract, or they are non taking into business relationship all parts of the story.

It may help to view the 2 parts as separate stories and and then add them up. The fact the thief paid with the stolen $100 beak seems to be another source of defoliation. It does non affair the $100 was stolen; it simply matters that the bill was genuine currency.

Sad I can't reply to your emails on this

I have been getting a lot of emails with alternating answers and asking to observe the mistake in reasoning. I've explained all I can in this post and the video, so if you still don't concord you'll have to ask someone else.

Sources
Thanks to Eric for sending me this problem by email.

One version of the problem on Facebook (xx,000+ shares):
https://m.facebook.com/story.php?story_fbid=1254756407914475&id=100001403825442

PRESH TALWALKAR

I run the MindYourDecisions channel on YouTube, which has over 1 1000000 subscribers and 200 meg views. I am likewise the author of The Joy of Game Theory: An Introduction to Strategic Thinking, and several other books which are available on Amazon.

(Equally you might expect, the links for my books go to their listings on Amazon. As an Amazon Associate I earn from qualifying purchases. This does non affect the price yous pay.)

By fashion of history, I started the Mind Your Decisions weblog back in 2007 to share a bit of math, personal finance, personal thoughts, and game theory. It'due south been quite a journeying! I give thanks everyone that has shared my work, and I am very grateful for coverage in the press, including the Shorty Awards, The Telegraph, Freakonomics, and many other popular outlets.

I studied Economic science and Mathematics at Stanford University.

People ofttimes ask how I make the videos. Like many YouTubers I employ pop software to prepare my videos. Yous tin can search for animation software tutorials on YouTube to learn how to make videos. Be prepared--animation is fourth dimension consuming and software tin be expensive!

Feel free to send me an electronic mail [email protected]. I become so many emails that I may not reply, merely I save all suggestions for puzzles/video topics.

MY BOOKS

If you buy through these links, I may be compensated for purchases fabricated on Amazon. Every bit an Amazon Acquaintance I earn from qualifying purchases. This does not affect the cost you pay.

Volume ratings are from January 2022.

(US and worldwide links)
https://mindyourdecisions.com/blog/my-books

Heed Your Decisions is a compilation of 5 books:

(1) The Joy of Game Theory: An Introduction to Strategic Thinking
(ii) 40 Paradoxes in Logic, Probability, and Game Theory
(3) The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias
(four) The All-time Mental Math Tricks
(5) Multiply Numbers Past Cartoon Lines

The Joy of Game Theory shows how yous tin use math to out-think your competition. (rated 4.2/5 stars on 224 reviews)

40 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. (rated iv.1/v stars on 38 reviews)

The Irrationality Illusion: How To Brand Smart Decisions And Overcome Bias is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 4/5 stars on 24 reviews)

The Best Mental Math Tricks teaches how you can expect like a math genius by solving problems in your head (rated 4.2/five stars on 76 reviews)

Multiply Numbers Past Cartoon Lines This book is a reference guide for my video that has over one 1000000 views on a geometric method to multiply numbers. (rated iv.iii/five stars on 30 reviews)

Heed Your Puzzles is a collection of the three "Math Puzzles" books, volumes i, ii, and 3. The puzzles topics include the mathematical subjects including geometry, probability, logic, and game theory.

Math Puzzles Volume 1 features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/v stars on 87 reviews.

Math Puzzles Book two is a sequel book with more great bug. (rated 4.1/5 stars on 24 reviews)

Math Puzzles Volume three is the 3rd in the series. (rated iv.two/5 stars on 22 reviews)

KINDLE UNLIMITED

Teachers and students around the globe oft email me nigh the books. Since education can have such a huge affect, I try to brand the ebooks available as widely as possible at as low a price as possible.

Currently you can read most of my ebooks through Amazon's "Kindle Unlimited" plan. Included in the subscription you volition become access to millions of ebooks. You don't demand a Kindle device: y'all can install the Kindle app on whatever smartphone/tablet/computer/etc. I have compiled links to programs in some countries below. Delight check your local Amazon website for availability and program terms.

US, list of my books (United states of america)
UK, list of my books (U.k.)
Canada, book results (CA)
Frg, list of my books (DE)
French republic, listing of my books (FR)
India, listing of my books (IN)
Australia, book results (AU)
Italy, list of my books (IT)
Espana, listing of my books (ES)
Japan, listing of my books (JP)
Brazil, book results (BR)
United mexican states, book results (MX)

Trade

Take hold of a mug, tshirt, and more at the official site for trade: Listen Your Decisions at Teespring.