** A D Johnson ad.johnson@ntlworld…. **

**Nov/Dec 2015 **

**What does it do?**

This Webpage runs Javascript to calculate the overall total of the individual digits that compose numbers between 10 and 1,000,000. i.e. it calculated the "number of numbers" whose individual digits add up to 1, 2, 3, 4 etc , in a single or multiple pass addition. It also shows/calculates the percentage probability of a given number in the range calculated so far adding up to 1, 2, 3 etc. The same calculation is performed for single pass digit calculations adding up to 11 and 13 (which are said to have occult numerological significance).

This then allows a more accurate judgement of the probability of certain number combinations adding up to certain totals.

**Operation**

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).

**Observed Results**

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….