Problem 1825. Find all vampire fangs

Created by Andrew Newell

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{"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>A</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Vampire_number\"><w:r><w:t>vampire number</w:t></w:r></w:hyperlink><w:r><w:t> is a number v that is the product of two numbers x and y such that the following conditions are satisfied:</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:t>at most one of x and y are divisible by 10;</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:t>x and y have the same number of digits; and</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:t>The digits in v consist of the digits of x and y (including anyrepetitions).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>If these conditions are met, x and y are known as \"fangs\" of v. For example, 1260 is a vampire number because 1260 = 21*60, so 21 and 60 are the fangs.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Write a function that returns all the pairs of fangs for a given number. The output is a matrix in which each row is a pair; the values in the first row should be in increasing order. If it is not a vampire number, it will return empty arrays.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[disp(vampire_factor(125460))\n\n 204 615\n 246 510]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>See also: </w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/1804-fangs-of-a-vampire-number\"><w:r><w:t>Problem 1804. Fangs of a vampire number</w:t></w:r></w:hyperlink><w:r><w:t> and and</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/1826-find-vampire-numbers\"><w:r><w:t>1826. Find vampire numbers</w:t></w:r></w:hyperlink><w:r><w:t>.</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>"}]}

A <a href = "http://en.wikipedia.org/wiki/Vampire_number">vampire number</a> is a
number v that is the product of two numbers x and y such that the
following conditions are satisfied:<ol><li>at most one of x and y are divisible by 10;</li><li>x and y have the same number of digits; and</li><li>The digits in v consist of the digits of x and y (including any
repetitions).</li></ol>If these conditions are met, x and y are known as "fangs" of v. For
example, 1260 is a vampire number because 1260 = 21*60, so 21 and 60 are
the fangs.Write a function that returns all the pairs of fangs for a given number.
The output is a matrix in which each row is a pair; the values in the
first row should be in increasing order. If it is not a vampire number,
it will return empty arrays.Example:<pre class="language-matlab">disp(vampire_factor(125460))
</pre><pre> 204 615
 246 510</pre>See also:
 <a href = "http://www.mathworks.com/matlabcentral/cody/problems/1804-fangs-of-a-vampire-number">Problem 1804. Fangs of a vampire number</a> and and <a href = "http://www.mathworks.com/matlabcentral/cody/problems/1826-find-vampire-numbers">1826. Find vampire numbers</a>.

A <http://en.wikipedia.org/wiki/Vampire_number vampire number> is a
number v that is the product of two numbers x and y such that the
following conditions are satisfied:

# at most one of x and y are divisible by 10;
# x and y have the same number of digits; and
# The digits in v consist of the digits of x and y (including any
repetitions).

If these conditions are met, x and y are known as "fangs" of v. For
example, 1260 is a vampire number because 1260 = 21*60, so 21 and 60 are
the fangs.

Write a function that returns all the pairs of fangs for a given number.
The output is a matrix in which each row is a pair; the values in the
first row should be in increasing order. If it is not a vampire number,
it will return empty arrays.

Example:

disp(vampire_factor(125460))

204   615
   246   510

See also:
 <http://www.mathworks.com/matlabcentral/cody/problems/1804-fangs-of-a-vampire-number Problem 1804. Fangs of a vampire number> and and <http://www.mathworks.com/matlabcentral/cody/problems/1826-find-vampire-numbers 1826. Find vampire numbers>.

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Last Solution submitted on May 25, 2021

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Solution 2786017

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Nadee Seneviratne on 5 Aug 2020

Interesting problem :D

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factors number theory

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