# What's common between the numbers 0 1 8 11 69 88 96 101?

1. Nov 8, 2007

### neutrino

Well, this isn't a brain teaser really, but I'll leave what I want to say in #black for anyone who might wish to "solve" it themselves.

What's common between the numbers 0 1 8 11 69 88 96 101? (This is the actual question I saw)

>
The answer provided was that they all remain the same even if you looked at them upside down. (Okay, it may not be true in a particular font, but you get the gist.) This isn't the interesting part; what's interesting is that every number apart from the first 0 is formed by the sum of the differences between the previous pairs of numbers, including the pair formed by the current number and the one preceeding it.

1 = 1-0
8 = (8-1) + (1-0)
11 = (11-8) + (8-1) + (1-0)
...
...

Just a curiosity [on the way "invertible" integers are arranged] I thought I would share with other geeks. :D
<

2. Nov 8, 2007

### Jimmy Snyder

All sequences of numbers that begin with zero have that second property. Just list out some numbers at random and see. Or better yet, consider the following rearrangement:

11 = (11-8) + (8-1) + (1-0)
11 = 11 (- 8 + 8) (- 1 + 1) - 0

eom

Last edited: Nov 8, 2007
3. Nov 8, 2007

### neutrino

True. I knew I was missing something really simple there. :)

4. Nov 8, 2007

### K.J.Healey

$$A = A^\dagger$$