Problem 1771. Polygonal numbers

Created by Jan Orwat

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>The task of</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.co.uk/matlabcentral/cody/problems/5\"><w:r><w:t>Problem 5</w:t></w:r></w:hyperlink><w:r><w:t> is to calculate triangular numbers. By playing with dots we can produce also square numbers like:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ * * * *\n * * * * * * *\n * * * * * * * * *\n1: * 4: * * 9: * * * 16: * * * *]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>or hexagonal numbers:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ * * * *\n * *\n * * * * * * * *\n * * * * * *\n * * * * * * * * * * * \n * * * * * * * * *\n1: * 6: * * 15: * * * 28: * * * *]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>&amp;nbsp</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>According to those rules we can create</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Polygonal_number\"><w:r><w:t>polygonal numbers</w:t></w:r></w:hyperlink><w:r><w:t> for all regular polygons.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>&amp;nbsp</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Your task: given</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>S</w:t></w:r><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>N</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>calculate</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> </w:t></w:r><w:r><w:rPr><w:b/><w:i/></w:rPr><w:t>N</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>-th</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> </w:t></w:r><w:r><w:rPr><w:b/><w:i/></w:rPr><w:t>S</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>-gonal numbers</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>P(S,N)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>&amp;nbsp</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=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:rPr><w:i/></w:rPr><w:t>P(4, 3)</w:t></w:r><w:r><w:t> returns</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>[9]</w:t></w:r><w:r><w:t> because 3-rd square number is 9,</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:rPr><w:i/></w:rPr><w:t>P(3, 1:5)</w:t></w:r><w:r><w:t> returns</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>[1, 3, 6, 10, 15]</w:t></w:r><w:r><w:t> first 5 triangular numbers,</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:rPr><w:i/></w:rPr><w:t>P(3:6, 4)</w:t></w:r><w:r><w:t> returns</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>[10, 16, 22, 28]</w:t></w:r><w:r><w:t> 4-th triangular, square, pentagonal and hexagonal numbers,</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:rPr><w:i/></w:rPr><w:t>P([3, 4], [1; 2])</w:t></w:r><w:r><w:t> returns</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>[1, 1; 3, 4]</w:t></w:r><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>see the test suite for more hints</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>"}]}

The task of <a href = "http://www.mathworks.co.uk/matlabcentral/cody/problems/5">Problem 5</a> is to calculate triangular numbers. By playing with dots we can produce also square numbers like:<pre> * * * *
 * * * * * * *
 * * * * * * * * *
1: * 4: * * 9: * * * 16: * * * *</pre>or hexagonal numbers:<pre> * * * *
 * *
 * * * * * * * *
 * * * * * *
 * * * * * * * * * * * 
 * * * * * * * * *
1: * 6: * * 15: * * * 28: * * * *</pre>&nbspAccording to those rules we can create <a href = "http://en.wikipedia.org/wiki/Polygonal_number">polygonal numbers</a> for all regular polygons.&nbspYour task: given S and N calculate N-th S-gonal numbers P(S,N)&nbspExamples:<ol><li>P(4, 3) returns [9] because 3-rd square number is 9,</li><li>P(3, 1:5) returns [1, 3, 6, 10, 15] first 5 triangular numbers,</li><li>P(3:6, 4) returns [10, 16, 22, 28] 4-th triangular, square, pentagonal and hexagonal numbers,</li><li>P([3, 4], [1; 2]) returns [1, 1; 3, 4].</li></ol>see the test suite for more hints

The task of <http://www.mathworks.co.uk/matlabcentral/cody/problems/5 Problem 5> is to calculate triangular numbers. By playing with dots we can produce also square numbers like:

* * * *
                     * * *       * * * *
           * *       * * *       * * * *
1: *    4: * *    9: * * *   16: * * * *

or hexagonal numbers:

* * * *
                                         *       *
                         * * *          * * * *   *
                        *     *        * *     *   *
            * *        * * *   *        * * *   * * 
           *   *        *   * *          *   * * *
1: *    6:  * *    15:   * * *       28:  * * * *

&nbsp

According to those rules we can create <http://en.wikipedia.org/wiki/Polygonal_number polygonal numbers> for all regular polygons.

&nbsp

Your task: given _S_ and _N_ *calculate _N_-th _S_-gonal numbers* _P(S,N)_

&nbsp

Examples:

# _P(4, 3)_ returns _[9]_    because 3-rd square number is 9,
# _P(3, 1:5)_ returns _[1, 3, 6, 10, 15]_   first 5 triangular numbers,
# _P(3:6, 4)_ returns _[10, 16, 22, 28]_   4-th triangular, square, pentagonal and hexagonal numbers,
# _P([3, 4], [1; 2])_ returns _[1, 1; 3, 4]_.

see the test suite for more hints

Solve

Solution Stats

262 Solutions
104 Solvers

Last Solution submitted on Feb 24, 2021

Last 200 Solutions

Problem Comments

4 Comments

4 Comments

Show 1 older comment

Matthew Eicholtz on 25 Aug 2015

I think the numbers in the description may be wrong. For hexagonal numbers, shouldn't the progression be [1,6,15,28]?

Daniel Pereira on 11 Feb 2016

I believe that test suite number 6 is a little bit unfair, since the difficulty of this problem relies on creating the function that gives the n-th s-gonal number, and not making use of meshgrid or bsxfun.

Massimo Zanetti on 14 Oct 2016

Remove test case 6 please.. it makes no sense

Jan Orwat on 15 Oct 2016

Explain why. It makes a lot of sense to me, and it's a lot easier (and makes even more educational sense) with 2016b. Just learn the difference between * and .* and ask yourself you need 1st or 2nd.

Problem Recent Solvers104

Problem Tags

Community Treasure Hunt

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

Start Hunting!