Looney Labs Icehouse Mailing list Archive

Re: [Icehouse] The numbers of Treehouse

  • FromJonas Kölker <jonaskoelker@xxxxxxx>
  • DateMon, 27 Jul 2009 10:41:58 +0200
On Sun, Jul 26, 2009 at 10:45:25PM -0500, Timothy Hunt wrote:
> You are never forced to alter the house.

I stand corrected; I should have said "_may_ alter the house".

By the way, the only way to not change your trio is if you can't but _can_
change the house, correct?  I.e. if you roll aim, you can't take a piece that
points left and make it point left, right?  So the only way for aim to "fail"
is when you have a tree (and you only reroll if the house is also a tree).

I think my numbers are still correct.  A good (if time-consuming) way to see
whether your understanding of the rules matches mine is to count the moves

Swap is easy to count.  Aim is quite easy, if you break it down in
large/small/no stack.  Tip is also easy, if you break down the "no stack" case
further, into zero/one/two standing pieces.

Hop and Dig are the labor-consuming ones, at least for the "no stack" case,
since there are many combinations of pieces standing up and pieces pointing at
other pieces; counting multitype-ness of moves makes this even more "fun".  I
have a very detailed breakdown which I'll happily post if anyone wants it.

Note that there are 27 no-stack positions (ignoring permutations of sizes).
Three of those are mirror-across-the-center symmetric to themselves, the rest
have a single buddy each.  If you have 5house (i.e. 25 trees), you can lay out
the 24 non-self-reflecting configurations; grouping them by the number of
standing pieces might make it easier to count things.  I just did a big case
analysis, and I'm not sure there's a (much) easier way, except maybe writing
up a small program which does the counting.

Jonas Kölker <jonaskoelker@xxxxxxx> <URL:http://jonaskoelker.ignorelist.com>

Attachment: signature.asc
Description: Digital signature