# Mathematical formula for permutation

I have been assigned to write mathematical equation for permutation using only 1,3,5,7,9 numbers starting from single digit going up to five digits numbers. For example

Single digit 1 3 5 7 9 two digit 1,3 1,5 1,7 1,9 Please note 3,1 is treated same as 1,3, or 1,1,3 is same as 1,3,1 and 3,1,1 Thanks in Advance, Rodney

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Also, it is not quite clear what "write equation for permutation" even means. Does it mean an equation for the number of all possible permutations, or something else. You gave some two-digit examples but your list appears to be incomplete: why did not you list 3,5 or 3,7 etc? Carefully working through the case of two-digit permutations may give you an idea of what the formula should be. –  user53153 Jan 3 '13 at 8:18
Dear Guru, Thanks for your guidance. Sorry if I have confused you. Wondering if there is any Mathematical equation/formula to populate. Outcome results that I am looking for single digits, 1,3,5,7,9 , then move on to two digits 13,15,17,19,35,37,39,57,59, Three digits, 135,137,139,157,159,357,359,579, 113,115,117,119,331,335,337,339,551,553,557,559,771,773,775,779,991,993,995,997, then comes 4 digits and finally five digits. I am wondering if some mathematical equation is possible rather than doing manually. I appreciate your time and efforts for my question, Regards Rodney –  user55027 Jan 3 '13 at 23:34
Two unclear points: (A) Your 3-digit combinations allow repetitions: for example in 115 the digit 1 is used twice. Yet, in the 2-digit combinations you do not list 11, 33, 77, etc. Why is that? (B) If you are looking for a way to actually produce these patterns of digits (rather than just count how many there are), then you need an algorithm (presented in a programming language) rather than a mathematical formula. –  user53153 Jan 3 '13 at 23:39
Dear Guru,Thanks for guidance, you are are on spot on! I may require algorithm, 11,33,55, were missed inadvertently. –  user55027 Jan 4 '13 at 1:55

The details will depend on the language you are supposed to use. Here is how it could be done in JavaScript: the numbers 1,3,5,7,9 are treated as letters; they get appended to existing strings (oldStrings) as long as this does not put letters out of alphabetical order (e.g., after 15 we cannot put 3 but can put another 5). So there is a triple loop here: one by length of string, one goes over existing strings, and one looks for letters to append, checking the alphabetization condition oldStrings[i].charAt(len-2)<=letters[j]

var letters = ['1','3','5','7','9'];
var oldStrings = [''];
var newStrings = [];
for (var len=1; len<=letters.length; len++) {
for (var i=0; i<oldStrings.length; i++) {
for (var j=0; j<letters.length; j++) {
if (oldStrings[i].charAt(len-2)<=letters[j]) {
newStrings.push(oldStrings[i]+letters[j]);
}
}
}