^{th}, 2005

This is something I learnt as a toddler and has provided innumerable hours of amusing entertainment ever since. I had forgotten about it for ages, but it came back to me as I was doodling on my steam-misted wall during my shower. I am assuming you will find it fun as well.

First, you just pick any random number that pops into your head and write it down. Then, all you need to do is count the number of occurrences of each unique digit (in the order in which they appear) and write this down as well as the corresponding digit in the following line. Keep doing this over and over again until you get tired, or the number starts to repeat itself. It’ll be more clear when you see the examples below.

Let’s say we start with,

81189198.

OK, so we’ve got three 8s, three 1s, and two 9s. So we write that down.

383129.

See how easy that was? Now we just continue the process, two 3s, one 8, one 1, one 2, one 9.

2318111219

You get the idea. Here are a few more iterations,

2213511819

224113151819

22145113151819

22611425131819

3216511415131819

23… and so on.

Here’s another:

41

1411

3114

132114

31131214

23411214

22132431

… and so on.

Pick a number, try it. It can get addictive.

» For brownie points (if you know of this from before, shh) figure out the smallest repeating number you can find.

» For even more brownie points, figure out why 81189198 wasn’t such a random starting point after all.

i normally get a kick out of anything dealing with numbers, but i just don’t see the fun in this. at all.

Yes, I can see how that might be the case. You need to factor in me getting a kick out of it as a kid learning to count.

On occasion, I still think picking the right numbers to start with can result in all sorts of curious and entertaining patterns.