I'm sure you've all been eagerly awaiting the answer to the numbers conundrum that I offered up the other day. Well, wait no longer. Each number represents (sequentially) the numbers 1 through 100, but represents it as its prime factorisation as opposed to using our traditional decimal system. (Another thread that I may start when I'm suitably bored is why the world should change from decimal to duodecimal, if only to help those parents with three, four or six kids, at the expense of those with five. Not now, but it's something I'm passionate about.) The last number in the string represents 2, the next one to its left represents 3, then 5, then 7, 11, 13, 17, 19, 23 and so on.
The number 90 is 2 x 3 x 3 x 5, so is represented as 121, the former 1 representing the 5, the 2 representing the two 3s and the latter 1 representing the 2. This system is fine until you get to 1,024, when you get single prime factors represented more than nine times, so maybe at this stage, you could pipe-separate such entries, 15,360 being represented as 11|10| (one 5, one 3 and ten 2s). Actually, in thinking about this, the leading and trailing separators must be different from one another, otherwise it could be confusing which number is being separated (10|10|10|10|10 could mean 1, 0, 10, 1, 0, 10, 1, 0 or 1, 0, 10, 10, 10, 1, 0 for instance). Maybe a leading forward-slash and a trailing back-slash would sort it out. This would only be an issue for numbers for which one of 210, 310, 510 etc. was a factor, so it would rarely come into play.
I found it easy to find out which decimal number a string represented, but more difficult to work out a decimal number's prime factorisation in order to generate it, particularly when numbers get big. Excel helps, but I'd need some macros to fully automate it. Originally, I was under the impression that it would have a 1 to 1 mapping with the decimal system - making it kinda cool - but the above issue makes this not the case. However, every decimal integer that we use does represent another decimal number if you think of it as its prime factorisation. I wonder whether there are any numbers (other than twelve) that are identical using both systems. This would be 10 in duodecimal, btw.
