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

  • Level: High School 
  • Thread starter Thread starter neutrino
  • Start date Start date
  • Tags Tags
    Numbers
Join the discussion
Registration is free. Start your own thread to ask a follow-up.
Sign up Log in
4 replies · 16K views
neutrino
Messages
2,093
Reaction score
2
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
[/color]<
 
Mathematics news on Phys.org

Discussion

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:
jimmysnyder said:
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:

True. I knew I was missing something really simple there. :)
 
They're such that : (self-adjoint)
[tex]A = A^\dagger[/tex]