Solving An Incredibly Hard Problem From Australia

Подписаться 3,1 млн

Просмотров 1,1 млн

50% 1

This problem stumped me! But it has a pretty nice solution. Thanks to all patrons! Special thanks this month to Kyle, Michael Anvari, Richard Ohnemus, Shrihari Puranik.
Source
Emailed to me about 2 years ago, traced to the Australian Intermediate Olympiad given in 2013.
Subscribe: ru-vid.com...
Playlist to watch all videos on MindYourDecisions: • Uploads from MindYourD...
Send me your favorite puzzles/suggestions by email (address in video). I get so many emails that I may not reply, but I save all suggestions.
This is the only channel to feature math topics suggested by people around the world. Support on Patreon to inspire mathematical discovery and make the world a better place:
/ mindyourdecisions
If you buy from the links below I may receive a commission for sales. 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:
teespring.com/stores/mind-you...
My Books
"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 4.0/5 stars on 41 reviews)
amzn.to/1uQvA20
"The Irrationality Illusion: How To Make 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 3.5/5 stars on 4 reviews)
amzn.to/1o3FaAg
"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 4.4/5 stars on 13 reviews.
amzn.to/1GhUUSH
"Math Puzzles Volume 2" is a sequel book with more great problems. (rated 4.5/5 stars on 6 reviews)
amzn.to/1NKbyCs
"Math Puzzles Volume 3" is the third in the series. (rated 4/5 stars on 6 reviews)
amzn.to/1NKbGlp
"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.4/5 stars on 13 reviews)
amzn.to/1LOCI4U
"The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.8/5 stars on 5 reviews)
amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 4.3/5 stars on 6 reviews)
amzn.to/XRm7M4
Connect with me
My Blog: mindyourdecisions.com/blog/
Twitter: / preshtalwalkar
Facebook: / 168446714965
Pinterest: / preshtalwalkar
Tumblr: / preshtalwalkar
Instagram: / preshtalwalkar
Patreon: / mindyourdecisions
Newsletter (sent only for big news, like a new book release): eepurl.com/KvS0r

Опубликовано:

3 июн 2019

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 2,5 тыс.

@MindYourDecisions 5 лет назад

By the way, the official solution listed 3 methods--all fairly similar--and the video is based on method 2 which is where I learned of the rectangle idea. It's fun to see the range of attitudes, from those who found the answer without valid proofs (so I think would earn 0 points on an Olympiad) to those that want a more formal proof (this is from the official solution!). In a RU-vid video, like all math and science channels, we strike a balance to engage as many people as possible. For those serious about the math, I suggest to get Olympiad books with real competitions and official solutions. You'll see the standard for proofs is fairly high, and you'll learn many problem solving techniques along the way!

@ArchNemesis314 5 лет назад

Ah, yeah... I'll "limit" myself to geometry and algebra...

@AntizombiRUS 5 лет назад

If I was asked this question in 15 years I would say "Yes"

@adamchan4194 3 года назад

I thought of it as: b and c are used twice and multiplied together, let's make those as big as possible. Making a = d = 1 leaves 61 to satisfy the sum. And then split that to get 30 and 31

@PGCTalha 3 года назад

Who just divided 63 by 3

@firdavsnasriddinov5898 5 лет назад

No joke I actually solved this before watching it. I feel so proud.

@tieswestendorp9830 3 года назад

"Remarkably" 30 and 31 give the same answer? The problem is highly symmetric: b and c can be exchanged and a and d can be exchanged by virtue of the picture you drew, and the equation in the original question. You're still using calculus in your answer too, despite noting it should not be used in this case.

@DrZaius3141 5 лет назад

Easy to find, easy to argue, hard to proof. It's a classical Olympiad problem in that regard.

@sitasin6545 3 года назад

I would have had 0 issues solving this as a 15 year old, all it takes is look and see that b and c are used twice and the others are used once, so make them as big as possible. I wouldn't know how to verify it other than checking some other numbers, but I'd have no problem getting 991

@vadendev 5 лет назад

I'm 14 so I don't have to worry about it now

@juangarcia1046 5 лет назад

Im still picking pieces of my brain from the floor :'v

@elyakimlev 3 года назад

It took me less than a minute to realize the values of B and C must be as big as possible, while being as close as possible (30 and 31 or 31 and 30).

@ShaharSigal515 4 года назад

I solved this problem with a different approach:

@khanhphaminh1175 4 года назад

Mathematic students in high school should follow this channel. Wow. I mean, I'm 26 years old and still get excited with every questions and the way is solved.

@jhoelious8634 3 года назад

I, as a 15 yo, would just sit and cry on my desk hahaha but thanks for the video, I definitely learned a lot ^^

@dominickmeisner8752 5 лет назад

Imagine being the people that have to think up the math problems

@joris8032 5 лет назад

Finally got 1 through logic. since b and c are present 2 times in the equation they have to be the highest possible integer (30 and 31) while a and d need to be the lowest possible integer (1 and 1) which results in 991