Problem 42888. Frobenius McNugget Factorization

Created by Ned Gulley

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Mr. Frobenius McNugget is a peculiar man.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>As you might expect, he likes to eat Chicken McNuggets. But his love of number theory influences his appetite in strange ways. On any given day he wakes up with a desire for a specific number of McNuggets. If that number is 19, then no other number of McNuggets will do. But the McFastFood restaurant down the street serves McNuggets only in quantities of 6, 9, or 20 to a box. So he can be satisfied on a 21 nugget day, but on a 19 nugget day he must go hungry. To make matters more interesting, the restaurant often changes the quantities in their boxed McNuggets.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given the box counts</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>nuggets</w:t></w:r><w:r><w:t>, what is the highest number</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>frob</w:t></w:r><w:r><w:t> for which Frobenius must go hungry?</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>nuggets</w:t></w:r><w:r><w:t> is a vector of positive integers with two or more elements.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Examples</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ nuggets = [2 5]\n frob = 3\n\n nuggets = [6 9 20]\n frob = 43]]></w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

61 Solutions
17 Solvers

Last Solution submitted on Dec 01, 2021

Last 200 Solutions

Problem Comments

4 Comments

4 Comments

Show 1 older comment

Jan Orwat on 6 Jun 2016

In test #2: 43 = 3+2*20, I've got frob = 37. In test #3: 207 = 17+10*19. I've got frob = 175;

Peng Liu on 6 Jun 2016

Got same results with Jan.

Peng Liu on 7 Jun 2016

A nice place to check the results: http://mathsjavascript.free.fr/frobenius_9_page.html

Ned Gulley on 7 Jun 2016

My apologies gentlemen! I rushed this into print yesterday afternoon. Thanks for the reference Peng. I have fixed the offending answers.

Problem Recent Solvers17

Problem Tags

factorization number theory

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 42888. Frobenius McNugget Factorization

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers17

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Problem 42888. Frobenius McNugget Factorization

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers17

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Players