Problem 44375. Missing five

Created by Alfonso Nieto-Castanon

Solve Later

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Wondering whether everything would be simpler if we just got rid of the digit 5? Let's try!</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>In a world without 5's, positive integers may be represented using a base-9 notation that uses only the digits 0, 1, 2, 3, 4, 6, 7, 8, and 9. We'll call this the \"missing-5\" notation. The following list shows the first 100 positive numbers (i.e. 1 through 100) using \"missing-5\" notation:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ '1' '2' '3' '4' '6' '7' '8' '9' '10' '11' \n '12' '13' '14' '16' '17' '18' '19' '20' '21' '22' \n '23' '24' '26' '27' '28' '29' '30' '31' '32' '33' \n '34' '36' '37' '38' '39' '40' '41' '42' '43' '44' \n '46' '47' '48' '49' '60' '61' '62' '63' '64' '66' \n '67' '68' '69' '70' '71' '72' '73' '74' '76' '77' \n '78' '79' '80' '81' '82' '83' '84' '86' '87' '88' \n '89' '90' '91' '92' '93' '94' '96' '97' '98' '99' \n '100' '101' '102' '103' '104' '106' '107' '108' '109' '110'\n '111' '112' '113' '114' '116' '117' '118' '119' '120' '121']]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You may notice that this is simply the sorted list of positive numbers which do not contain the digit 5 in their decimal representation.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Your function should convert a positive decimal number N into its \"missing-5\" notation. For example</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ dec2missing5(20)]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>should return</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>'22'</w:t></w:r><w:r><w:t> (the 20th positive number in missing-5 notation), and</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ dec2missing5(100)]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>should return</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>'121'</w:t></w:r><w:r><w:t> (the 100th positive number in missing-5 notation)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Good luck!</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:i/></w:rPr><w:t>Small print</w:t></w:r><w:r><w:t>: Your function may output a number, a char array, or a string; whatever you find simpler (e.g. in the example above, valid outputs are 121, '121', or \"121\"). Input numbers in testsuite are always relatively low valued positive integers (&lt;10,000)</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 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Convert decimal numbers to a base-9 notation missing the digit 5<img src = "http://www.alfnie.com/software/missing5.jpg">Too many five-themed problems? Wondering whether everything would be simpler if we just got rid of the digit 5? Let's try!In a world without 5's, positive integers may be represented using a base-9 notation that uses only the digits 0, 1, 2, 3, 4, 6, 7, 8, and 9. We'll call this the "missing-5" notation. The following list shows the first 100 positive numbers (i.e. 1 through 100) using "missing-5" notation:<pre> '1' '2' '3' '4' '6' '7' '8' '9' '10' '11' 
 '12' '13' '14' '16' '17' '18' '19' '20' '21' '22' 
 '23' '24' '26' '27' '28' '29' '30' '31' '32' '33' 
 '34' '36' '37' '38' '39' '40' '41' '42' '43' '44' 
 '46' '47' '48' '49' '60' '61' '62' '63' '64' '66' 
 '67' '68' '69' '70' '71' '72' '73' '74' '76' '77' 
 '78' '79' '80' '81' '82' '83' '84' '86' '87' '88' 
 '89' '90' '91' '92' '93' '94' '96' '97' '98' '99' 
 '100' '101' '102' '103' '104' '106' '107' '108' '109' '110'
 '111' '112' '113' '114' '116' '117' '118' '119' '120' '121'</pre>You may notice that this is simply the sorted list of positive numbers which do not contain the digit 5 in their decimal representation.Your function should convert a positive decimal number N into its "missing-5" notation. For example<pre> dec2missing5(20)</pre>should return '22' (the 20th positive number in missing-5 notation), and<pre> dec2missing5(100)</pre>should return '121' (the 100th positive number in missing-5 notation)Good luck!Small print: Your function may output a number, a char array, or a string; whatever you find simpler (e.g. in the example above, valid outputs are 121, '121', or "121"). Input numbers in testsuite are always relatively low valued positive integers (&lt;10,000)

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James on 16 Oct 2017

Too bad this problem number has a '5' in it! :-)

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Francis Naldo on 30 Dec 2017

Any suggestions on my brute force method?

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Alfonso Nieto-Castanon on 31 Oct 2017

sorry, I added a couple of test cases to discourage this sort of solutions

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Problem 44375. Missing five

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