# 100 digramms

Joerg Arndt arndt at jjj.de
Wed Feb 16 16:35:14 CET 2005

```You do search by generating all 10--2 De Bruijn sequences (DBS),
use all cyclic shifts, appending the first digit at the end
and cut them into pieces?
BTW what are the rules for cutting?

I think base-2 might be more intstructive (and minimality
is easier to verify).  Note there are
? (10!)^(10^(2-1))/(10^2)
3959408661224251932438755707826684577630388224000000000000000000
such (decimal, two digit) sequences.

The minimal DBS is
00102030405060708091121314151617181922324252627282933435\
36373839445464748495565758596676869778798899
(Generated with
http://www.jjj.de/fxt/demo/comb/#debruijn )

How to generate all (binary) De Bruijn sequences via graph
search is described in the fxtbook
http://www.jjj.de/fxt/#fxtbook
See "De Bruijn *" in the index.

* Eric Angelini <keynews.tv at skynet.be> [Feb 16. 2005 16:18]:
> Received from Richard Tucker a couple of hours ago
> (case closed?)
> Best,
> ?.
> -------------
>
> Here's my attempt (no idea how to find the best solution):
>
> 20 23 24 25 26 27 28 29
> 30 34 35 36 37 38 39
> 40 45 46 47 48 49
> 50 56 57 58 59
> 60 67 68 69
> 70 78 79
> 80 89
> 90 91
> 100 122 133 144 155 166 177 188 192
>
> Weight 3224.
>
--
p=2^q-1 prime <== q>2, cosh(2^(q-2)*log(2+sqrt(3)))%p=0
Life is hard and then you die.

```