MindYourDecisions | A legendary question with a surprising answer @MindYourDecisions | Uploaded 1 year ago | Updated 14 seconds ago
Thanks to Jarek for the suggestion! What's a formula for the maximum product of a partition of a number? This was an Olympiad question and a Putnam problem! Special thanks this month to: Kyle, Lee Redden, Mike Robertson, Daniel Lewis. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions
0:00 Problem
1:11 Solution
6:40 Intuition
Math StackExchange
math.stackexchange.com/questions/125065/partitioning-a-natural-number-n-in-order-to-get-the-maximum-product-sequence-o?noredirect=1&lq=1
math.stackexchange.com/questions/1760268/partitions-of-a-number-with-greatest-product
OEIS A000792
oeis.org/A000792
Putnam 1979, A1
https://prase.cz/kalva/putnam/psoln/psol791.html
Maximum integer product
geeksforgeeks.org/breaking-integer-to-get-maximum-product
IMO 1976, B1
https://prase.cz/kalva/imo/isoln/isoln764.html
IMO 1976, 4
artofproblemsolving.com/wiki/index.php/1976_IMO_Problems/Problem_4
Product-maximising partitions
bldavies.com/blog/product-maximising-partitions
The MaxProduct Partition
jstor.org/stable/23249541
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Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas!
If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.
If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.
Book ratings are from January 2023.
My Books (worldwide links)
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My Books (US links)
Mind Your Decisions: Five Book Compilation
amzn.to/2pbJ4wR
A collection of 5 books:
"The Joy of Game Theory" rated 4.3/5 stars on 290 reviews
http://amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.1/5 stars on 33 reviews
http://amzn.to/1o3FaAg
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 54 reviews
http://amzn.to/1LOCI4U
"The Best Mental Math Tricks" rated 4.3/5 stars on 116 reviews
http://amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" rated 4.4/5 stars on 37 reviews
http://amzn.to/XRm7M4
Mind Your Puzzles: Collection Of Volumes 1 To 3
amzn.to/2mMdrJr
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 112 reviews
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.2/5 stars on 33 reviews
http://amzn.to/1NKbyCs
"Math Puzzles Volume 3" rated 4.2/5 stars on 29 reviews
http://amzn.to/1NKbGlp
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.
My Blog
mindyourdecisions.com/blog
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Merch
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Patreon
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Press
mindyourdecisions.com/blog/press
Thanks to Jarek for the suggestion! What's a formula for the maximum product of a partition of a number? This was an Olympiad question and a Putnam problem! Special thanks this month to: Kyle, Lee Redden, Mike Robertson, Daniel Lewis. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions
0:00 Problem
1:11 Solution
6:40 Intuition
Math StackExchange
math.stackexchange.com/questions/125065/partitioning-a-natural-number-n-in-order-to-get-the-maximum-product-sequence-o?noredirect=1&lq=1
math.stackexchange.com/questions/1760268/partitions-of-a-number-with-greatest-product
OEIS A000792
oeis.org/A000792
Putnam 1979, A1
https://prase.cz/kalva/putnam/psoln/psol791.html
Maximum integer product
geeksforgeeks.org/breaking-integer-to-get-maximum-product
IMO 1976, B1
https://prase.cz/kalva/imo/isoln/isoln764.html
IMO 1976, 4
artofproblemsolving.com/wiki/index.php/1976_IMO_Problems/Problem_4
Product-maximising partitions
bldavies.com/blog/product-maximising-partitions
The MaxProduct Partition
jstor.org/stable/23249541
Subscribe: youtube.com/user/MindYourDecisions?sub_confirmation=1
Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas!
If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.
If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.
Book ratings are from January 2023.
My Books (worldwide links)
mindyourdecisions.com/blog/my-books/#worldwide
My Books (US links)
Mind Your Decisions: Five Book Compilation
amzn.to/2pbJ4wR
A collection of 5 books:
"The Joy of Game Theory" rated 4.3/5 stars on 290 reviews
http://amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.1/5 stars on 33 reviews
http://amzn.to/1o3FaAg
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 54 reviews
http://amzn.to/1LOCI4U
"The Best Mental Math Tricks" rated 4.3/5 stars on 116 reviews
http://amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" rated 4.4/5 stars on 37 reviews
http://amzn.to/XRm7M4
Mind Your Puzzles: Collection Of Volumes 1 To 3
amzn.to/2mMdrJr
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 112 reviews
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.2/5 stars on 33 reviews
http://amzn.to/1NKbyCs
"Math Puzzles Volume 3" rated 4.2/5 stars on 29 reviews
http://amzn.to/1NKbGlp
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.
My Blog
mindyourdecisions.com/blog
twitter.com/preshtalwalkar
instagram.com/preshtalwalkar
Merch
teespring.com/stores/mind-your-decisions
Patreon
patreon.com/mindyourdecisions
Press
mindyourdecisions.com/blog/press
