A D Johnson ad.johnson@ntlworld….
This then allows a more accurate judgement of the probability of certain number combinations adding up to certain totals.
You can start the calculation by clicking the button below – but it is done in stages to allow the page to update (it takes a while to go right through, so I made it pause every 10,000 numbers and you have to press "enter" to continue or ESC to abort).
One interesting note that comes out is that figure of 11.11% recurs regularly (probably of little surprise to any maths expert reading this). It is the case that ANY number – if its digits are added together continually has very nearly an 11.11% chance of adding up to 1, 2, 3 etc – it turns out that them totalling 9 has no special probability or likelihood.
The number of numbers adding up to 11 or 13 (in a single pass) does vary and the probability of this being the case reduces substantially the higher the number is. Up to 10,000 the probability of a digit sequence adding up to 11 is 3.48% and the probability of a digit sequence adding up to 13 is 4.8%.
Also, one small but obvious thing that has come out of this is how the numbers 9 and 11 could be seen to be encoded in our Base 10 number system – 9 x 1.11111 = 10 (and of course, then, 9 x 11.11111 = 100). So one could argue the this particular digit combination is encoded in the decimal system… just an observation….