If you buy native a link in this post, I might earn a commission. This does not impact the price friend pay. Together an Amazon Associate i earn native qualifying purchases. Discover more.

You are watching: Order of 10 challenge 3 answer

Posted September 3, 2018 by Presh Talwalkar. Read around me, or email me.

Thanks come Yale indigenous Hong Kong for arguing this puzzle! The trouble went viral after a video from Carl Ho (in Chinese): https://youtu.be/6acBMe0Ugy8.

Here is the problem: using three 3s, can you do the numbers from 0 come 10 using mathematical operations?

3 3 3 = 0** 3 3 3 = 1 3 3 3 = 2 3 3 3 = 3 3 3 3 = 4 3 3 3 = 5 3 3 3 = 6 3 3 3 = 7 3 3 3 = 8 3 3 3 = 9 3 3 3 = 10**

**There are countless ways to solve this, and I will existing some that answers.**

**The hardest problem is 3 3 3 = 10. Mine challenge, i beg your pardon is a an extremely hard challenge, is to settle this in two ways using only the complying with symbols:**

**+ ! ()There is a means to solve 3 3 3 = 10 using only those symbols, return the notation is lesser known.**

**Can you number it out? clock the video for a solution.**

**Can You solve The 3 3s Challenge?**

Or save reading.** . ."All will be well if you usage your psychic for her decisions, and mind just your decisions." since 2007, ns have committed my life to sharing the happiness of game theory and mathematics. allisonbrookephotography.com now has over 1,000 free articles through no ads thanks to neighborhood support! aid out and also get early accessibility to articles with a pledge on Patreon.**

**. . . . . . M ns N D . Y O U R . D E C i S ns O N S . P U Z Z l E . . . . Answer to The 3s Challenge**

(Pretty lot all articles are transcribed conveniently after i make the videos for them–please allow me recognize if over there are any kind of typos/errors and also I will correct them, thanks).

Here space some methods to get 0 to 9. (You might have discovered other services not listed here.)

3! – 3 – 3 = 0

(3! – 3)/3 = 1** 33 – 3 = 1 √3 × √3 / 3 = 1**

**3 – 3/3 = 2 (3 + 3)/3 = 2**

**3 + 3 – 3 = 3 3 × 3/3 = 3**

**3 + 3/3 = 4 3! – 3!/3 = 4**

**3! – 3/3 = 5 3!/3 + 3 = 5**

**3 × 3 – 3 = 6 3! × 3/3 = 6 3 1 = 6 (left arithmetic shift)**

**3! + 3/3 = 7 3! + (3 – 3)! = 7 3/.3 – 3 = 7**

**3!/3 + 3! = 8**

**3 + 3 + 3 = 9 33/3 = 9**

**How deserve to we do 10? here are several of the an imaginative ways i found.**

**In Carl Ho’s video comments, who suggested:**

**arctan(√3)/(3 + 3) = 10 (degrees)**

**The idea is the arctan(sqrt(3)) is 60 degrees, so friend then division by 6 to acquire 10. The answer is technically in degrees, yet for this puzzle us may enable this an imaginative answer.**

**This is solution from reduced The Knot:**

**floor(√3 + √3)×3 = 10**

**Yale argued three methods to me as well.**

**√(√(3 × 3)/3%) = 10**

**log√√3(3) + 3! = 10**

**3 × 3 + (d/dx (3))! = 10**

**Now for the challenge: how can we settle it using only +, ! and also ( )?**

**Here space the solutions:**

**3! + !3 + !3 = 6 + 2 + 2 = 10**

**!3(!3 + 3) = 2(2 + 3) = 10**

**How is !3 = 2? This calls for a little bit of explanation.**

**The notation n! denotes the factorial the n, which is the total variety of permutations the n.**

**By contrast, the notation !n denotes the subfactorial of n, which is the number of derangements of n. A derangement is a permutations in which no item is in its natural order.**

**For example,**

**!1 = 0 due to the fact that 1 has no derangements**

**!2 = 1 since 1, 2 has the solitary derangement 2, 1**

**!3 = 2 because 1, 2, 3 has actually two derangements: 2, 3, 1 and 3, 1, 2**

**While this might be brand-new to you, it is welcomed enough notation that also WolframAlpha will certainly evaluate. You deserve to see:**

**!3(!3 + 3) evaluate to 10**

**It’s a sneaky way to use the exclamation point, however in this puzzle the subfactorial is an extremely useful! You’ll additionally find extra services to the various other equations utilizing !3 = 2.**

**Another bonus answer**

!(!3 + !3) + !(!3) = 10

This supplies that !4 = 9 and also !2 = 1 i beg your pardon is yes, really clever!

(Note: you can gain the number of derangements by the formula floor(n!/e + 1/2) for n ≥ 1. So girlfriend will note the number of derangements, separated by the number of permutations n!, is approximately 1/e ≈ 37%. It’s sort of interesting the ratio of derangements come permutations is roughly continuous even as n increases!)

**Sources**

Carl Ho’s video clip (Chinese)** https://youtu.be/6acBMe0Ugy8**

**Cut The Knot depiction of number with 3 3’s http://www.cut-the-knot.org/arithmetic/funny/3_3.shtml**

**Thanks to all patrons! Special many thanks to:**

Shrihari Puranik** Yildiz Kabaran Kyle**

**Share the beauty, beauty of math v the world! You have the right to support this videos and posts in ~ Patreon and get exclusive rewards: http://www.patreon.com/allisonbrookephotography.com**

### PRESH TALWALKAR

I run the allisonbrookephotography.com channel top top YouTube, which has actually over 1 million subscribers and also 200 million views. I am likewise the author of The delight of game Theory: An advent to strategy Thinking, and also several other publications which are obtainable on Amazon.

(As you can expect, the web links for my publications go to their listings top top Amazon. Together an Amazon Associate i earn native qualifying purchases. This go not affect the price you pay.)

By means of history, I began the Mind her Decisions blog ago in 2007 to share a little of math, personal finance, personal thoughts, and game theory. It"s been quite a journey! I say thanks to 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 famous outlets.

I learned Economics and Mathematics in ~ Stanford University.

People regularly ask just how I make the videos. Like many YouTubers i use popular software come prepare mine videos. You deserve to search for computer animation software tutorials top top YouTube to learn just how to do videos. Be prepared--animation is time consuming and software have the right to be expensive!

Feel complimentary to send me an e-mail

### MY BOOKS

If you purchase through this links, I might be compensated for purchases do on Amazon. Together an Amazon Associate ns earn from qualifying purchases. This walk not impact the price you pay.

Book ratings room from June 2021.

(US and global links) https://allisonbrookephotography.com/blog/my-books**Mind her Decisions** is a compilation that 5 books:

**(2) 40 Paradoxes in Logic, Probability, and also Game theory (3) The Irrationality Illusion: how To do Smart Decisions and also Overcome predisposition (4) The ideal Mental mathematics Tricks (5) Multiply number By illustration Lines**

**The happiness of video game Theory** shows exactly how you have the right to use mathematics to out-think her competition. (rated 4.2/5 stars top top 200 reviews)

**40 Paradoxes in Logic, Probability, and Game Theory** consists of thought-provoking and counter-intuitive results. (rated 4.1/5 stars on 30 reviews)

**The Irrationality Illusion: how To do Smart Decisions and also Overcome Bias** is a handbook that defines the many ways we are biased around decision-making and also offers methods to make smart decisions. (rated 4/5 stars top top 17 reviews)

**The best Mental mathematics Tricks** teaches exactly how you can look choose a mathematics genius by solving problems in her head (rated 4.2/5 stars top top 57 reviews)

**Multiply number By illustration Lines** This publication is a reference overview for my video that has over 1 million see on a geometric method to main point numbers. (rated 4.1/5 stars ~ above 23 reviews)

**Mind her Puzzles** is a repertoire of the three "Math Puzzles" books, volumes 1, 2, and 3. The puzzles topics incorporate the mathematical subjects including geometry, probability, logic, and game theory.

**Math Puzzles Volume 1** functions classic brain teasers and also riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars ~ above 75 reviews.

**Math Puzzles Volume 2** is a sequel book with more great problems. (rated 4.3/5 stars top top 21 reviews)

**Math Puzzles Volume 3** is the third in the series. (rated 4.3/5 stars on 17 reviews)

### KINDLE UNLIMITED

Teachers and students around the human being often email me around the books. Due to the fact that education can have such a huge impact, I try to make the ebooks available as widely as feasible at together low a price together possible.

Currently you have the right to read many of mine ebooks v Amazon"s "Kindle Unlimited" program. Consisted of in the subscription you will get access to millions of ebooks. Friend don"t require a Kindle device: you can install the Kindle application on any smartphone/tablet/computer/etc. I have compiled web links to program in some nations below. Please check your local Amazon website for access and regimen terms.

See more: Quick Answer: How Do I Set My Sd Card As Default Storage On Galaxy S7?

**UK, list of my publications (UK) Canada, book results (CA) Germany, perform of my publications (DE) France, list of my books (FR) India, list of my publications (IN) Australia, book results (AU) Italy, perform of my publications (IT) Spain, perform of my publications (ES) Japan, list of my publications (JP) Brazil, publication results (BR) Mexico, book results (MX)**

### MERCHANDISE

**Grab a mug, tshirt, and more at the official site because that merchandise: Mind your Decisions at Teespring**.