Problem 1394. Prime Ladders

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>A</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Word_ladder\"><w:r><w:t>word ladder</w:t></w:r></w:hyperlink><w:r><w:t> transforms one word to another by means of single-letter mutations. So COLD can become WARM like so (there are often multiple solutions):</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ COLD\n CORD\n CARD\n WARD\n WARM]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>A number ladder does much the same thing, changing one digit at a time. A</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>prime ladder</w:t></w:r><w:r><w:t> is a number ladder with the additional constraint that each element is a prime number. Here is a prime ladder that connects 757 and 139</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ 757 \n 157\n 137\n 139]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given two numbers p1 and p2, construct a prime ladder column vector in which p1 is the first element, p2 is the last element, and each successive row differs by exactly one digit from the preceding element.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>To restate the above example, consider</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ p1 = 757\n p2 = 139]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>for which an acceptable answer is</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ ladder = [757; 157; 137; 139]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You can assume that p1 and p2 contain the same number of digits. I am not looking for a unique answer. I will only check that the conditions of a prime ladder are met.</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/Word_ladder">word ladder</a> transforms one word to another by means of single-letter mutations. So COLD can become WARM like so (there are often multiple solutions):<pre> COLD
 CORD
 CARD
 WARD
 WARM</pre>A number ladder does much the same thing, changing one digit at a time. A prime ladder is a number ladder with the additional constraint that each element is a prime number. Here is a prime ladder that connects 757 and 139<pre> 757 
 157
 137
 139</pre>Given two numbers p1 and p2, construct a prime ladder column vector in which p1 is the first element, p2 is the last element, and each successive row differs by exactly one digit from the preceding element.To restate the above example, consider<pre> p1 = 757
 p2 = 139</pre>for which an acceptable answer is<pre> ladder = [757; 157; 137; 139]</pre>You can assume that p1 and p2 contain the same number of digits. I am not looking for a unique answer. I will only check that the conditions of a prime ladder are met.

Solve

Solution Stats

172 Solutions
30 Solvers

Last Solution submitted on Mar 18, 2022

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

bainhome on 12 May 2020

Couldn't did it without binbin's help... anyway, absolutely nice problem! worth look into it.

Ned Gulley on 12 May 2020

Glad you liked it!

Solution Comments

Solution 2272739

1 Comment

1 Comment

Devin Allen on 18 Mar 2022

pretty genius

Solution 608744

1 Comment

1 Comment

Binbin Qi on 31 Mar 2015

good work!perfect

Solution 608494

1 Comment

1 Comment

LY Cao on 30 Mar 2015

it works in matlab r2015a. LOL

Solution 224545

1 Comment

1 Comment

Jean-Marie Sainthillier on 17 Apr 2013

One of the best Cody solutions !

Problem Recent Solvers30

Problem Tags

primes

Community Treasure Hunt

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

Start Hunting!

Problem 1394. Prime Ladders

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers30

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Problem 1394. Prime Ladders

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers30

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Players