Solving an 'impossible' algebra question in 2 minutes

On the JEE Advanced test, you would only have minutes to solve this problem. Students preparing for the exam often take coaching to prepare. In this video I want to focus on the mathematical content of this beautiful problem. A special thanks this month to The Laba Family, Michael Anvari, Richard Ohnemus, Shrihari Puranik, Kyle.

Thanks to all patrons!

Sources

WolframAlpha evaluation

Send me suggestions by email (address in video). I consider all ideas though can't always reply!

Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to learn how to make videos. Be prepared--animation is time consuming and software can be expensive!

Why are there comments before the video is published? Get early access and support the channel on Patreon

If you buy from the links below I may receive a commission for sales. (As an Amazon Associate I earn from qualifying purchases.) This has no effect on the price for you.

Show your support! Get a mug, a t-shirt, and more at Teespring, the official site for Mind Your Decisions merchandise:

My Books (worldwide links)

My Books (US links)
Mind Your Decisions: Five Book Compilation
A collection of 5 books:
"The Joy of Game Theory" rated 4.1/5 stars on 44 reviews
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 3.5/5 stars on 4 reviews
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.4/5 stars on 13 reviews
"The Best Mental Math Tricks" rated 4.7/5 stars on 8 reviews
"Multiply Numbers By Drawing Lines" rated 4.3/5 stars on 6 reviews

Mind Your Puzzles: Collection Of Volumes 1 To 3
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 13 reviews
"Math Puzzles Volume 2" rated 4.5/5 stars on 6 reviews
"Math Puzzles Volume 3" rated 4.1/5 stars on 7 reviews

Connect with me

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

[superjaswal]

This question is all beautiful untill you are solving this in exam

[chinmaytrivedi]

A super coincidence
Today was my JEE weekly test and you know what THEY ASKED THE EXACT QUESTION
AND I GOT THE ANSWER RIGHT LOL
YOUTUBE'S RECOMMENDATION AT ITS MAX EXTENT 😋😋😂😂

[cpsof]

"This is a Beautiful Problem. Oh well, I'll just brute force it."

[gamefacierglitches]

(When you thought you were wrong, but you were right)
"I am still worthy!"

[rasherbilbo]

"These are the partitions of the number 9 from the set 1 through 9." No, these are the partitions of the number 9 having _distinct parts_ . The former has 30, the latter 8.

[harshitporwaliitb]

I am also preparing for IIT and this was one of the easiest question in our exercise.

[adityarajtiwari]

This question came in the entrance exam of a coaching institution(fiitjee) for students in tenth class in india before you posted it. Amazing.

[v.gopalakrishnan]

Thank God it was the coefficient of x^9! Had it been some higher power like 75, it would have required a Ramanuian or Euler to solve it !

[vanshr.sachan]

Currently preparing for this exam....
I did solve the I'm happy😁

[crustyoldfart]

Being myself lazy, but also having access to math software [ Maple ] I did a brute force run. I did at least at the start realize that the higher power binomials were a decoy, and the coefficient of 9 would soon hit a limit.
Other comments seem to suggest a couple of facts about this formal test - you have about three minutes available for each question, and that you only have to select answers from an answer set.
This problem reminds me of a story told by my math teacher while I was studying engineering back in the 1950's. He was a Cambridge man, and recounted a tale attributed to the great Hardy who while giving a class lecture said " It's obvious that " and tailed off. He then is said to have done some rapid calculations using his chalk and writing on the table in front of him. After a long pause, he resumed : " Yes - it IS obvious that .... "

Math software is great for letting you see the ' obvious ".

[DilipKumar-nskl]

It is a fun, when you talk distinct partition of integer "n" .Here n=9, hence the result.
Thanks.

[hm]

Just did the UKMT senior paper today. Some very interesting problems that would be good to look at.

[ShinAkuma]

Here I am, not even remembering what coefficient means lol.

[technodrome]

I don't need to do another math problem ever again, but these problems and explanations keep my appreciation of math alive. Great explanation of how to derive the coefficient through permutation.

[bakulsarkar]

I think you should see all iit problems all are like this ....
Which is a test for admission in university in india...
This year it is going to be held on 23 september...

[tomkerruish]

Recognized it as the (beginning of the] generating function of q(n), partition function into distinct terms.

[chrslb]

This is the first time I see the "mind *only* your decisions". I thought the emphasis on the only is amazing.

[RickOps]

my brother gave his paper in 2015 he dealt with this problem in a similar way like u did

[santinodemaria]

Subtitles: Presh Talwalkar
Me: IMPOSSIBLE
Me: **Realizes that subtitles are not automatically generated**
Me: phew

[mathsbyanandravi]

You should solve for x^99 it will help the mind to Take decision.