Jump to content


Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account.
As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends.

Of course, you can also enjoy our collection of amazing optical illusions and cool math games.

If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top.
If you have a website, we would appreciate a little link to BrainDen.

Thanks and enjoy the Den :-)
Guest Message by DevFuse
 

Photo
- - - - -

A Boggle-like Challenge


  • Please log in to reply
18 replies to this topic

#1 superprismatic

superprismatic

    Not just Prismatic

  • Moderator
  • PipPipPipPip
  • 1281 posts
  • Gender:Male

Posted 13 November 2012 - 09:05 PM

A Boggle-like Challenge

In the game, Boggle, a letter may have at most 8 adjacent letters.
That fact inspired this challenge.

This first part of this challenge is to place letters in such a way
that each letter of the alphabet has precisely eight other different
letters adjacent to it. You must use all 26 letters and, of course,
"adjacent" is a commutative relation. To specify your placement,
all you need to do is list the eight letters adjacent to A, the
eight letters adjacent to B, the eight letters adjacent to C,...,etc.
But remember that, if Q is on A's adjacency list, then A must be
on Q's adjacency list, and this is true for every pair of letters
-- not just A and Q.

The second part of the challenge is to create a cycle of all 26
letters, such that each adjacent pair of letters in the cycle are
adjacent in the sense of the first part of the challenge.

Note that there is no requirement that the graph of adjacent letters
is realizable in a small number of dimensions. So, trying to visualize
such a graph may be hazardous to your mental health!

  • 0

#2 BobbyGo

BobbyGo

    Advanced Member

  • Members
  • PipPipPip
  • 130 posts
  • Gender:Male

Posted 13 November 2012 - 10:56 PM

Spoiler for Questions

  • 0

#3 superprismatic

superprismatic

    Not just Prismatic

  • Moderator
  • PipPipPipPip
  • 1281 posts
  • Gender:Male

Posted 13 November 2012 - 11:25 PM

Spoiler for Questions

There is only one A which has eight neighbours. There is only one of each of the 26 letters from A to Z, and each letter has to be connected (adjacent) to exactly 8 others.

The arrangement can be on any manifold with any number of dimensions -- Whence my last paragraph. All that is required is that each of the 26 letters is adjacent to 8 others and "adjacency" is commutative. How this plays out in your head is of no concern. I hope this clarifies things.
  • 0

#4 CaptainEd

CaptainEd

    Senior Member

  • Members
  • PipPipPipPip
  • 1094 posts

Posted 14 November 2012 - 12:11 AM

I think I just learned something from this clarification. In Boggle, the tableau
ABC
DEF
GHI

has E adjacent to each of the others, and each of the others adjacent to two others, arranged in a ring.

But I believe you are willing to relax the ring requirement on the neighbors of E; your only requirement is that AE <-> EA.
All that is required is the graph.

Thanks! (Another interesting puzzle from superprismatic!)
  • 0

#5 TheChad08

TheChad08

    Advanced Member

  • Members
  • PipPipPip
  • 180 posts

Posted 14 November 2012 - 03:44 AM

Seems as though there is a near infinite amount of answers.

EDIT:
Nevermind, did it in a less graphical way

Edited by TheChad08, 14 November 2012 - 03:46 AM.

  • 0

#6 curr3nt

curr3nt

    The

  • Members
  • PipPipPipPip
  • 2839 posts
  • Gender:Male
  • Location:in a field of spatulas...

Posted 14 November 2012 - 03:21 PM

Spoiler for Is this what you wanted?

  • 0

#7 curr3nt

curr3nt

    The

  • Members
  • PipPipPipPip
  • 2839 posts
  • Gender:Male
  • Location:in a field of spatulas...

Posted 14 November 2012 - 04:01 PM

Spoiler for am I missing something?

  • 0

#8 phil1882

phil1882

    Senior Member

  • Members
  • PipPipPipPip
  • 521 posts

Posted 14 November 2012 - 04:03 PM

Spoiler for

Edited by phil1882, 14 November 2012 - 04:08 PM.

  • 0

#9 curr3nt

curr3nt

    The

  • Members
  • PipPipPipPip
  • 2839 posts
  • Gender:Male
  • Location:in a field of spatulas...

Posted 14 November 2012 - 04:11 PM

Spoiler for example...

Edited by curr3nt, 14 November 2012 - 04:12 PM.

  • 0

#10 phil1882

phil1882

    Senior Member

  • Members
  • PipPipPipPip
  • 521 posts

Posted 14 November 2012 - 04:35 PM

edit of above: still not quite right.
[spoiler]
   Z  Y  X  W  
V  A  B  C  D  Q
E  F  G  H  I  J
K  L  M  N  O  P K
Q  R  S  T  U  V
J  W  X  Y  Z  E
   D  C  B  A

  • 0




0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users