Sunset Venery is our guild that focuses on the thought tests, we sort of wandered into the Discipline of Thought, which is why this EHT discussion is located in an odd location. We have three Veneries, all of the Thought Tests, and a couple of Art Tests in the same park. The EHT is between our Venery Obelisk at 1475 2240 and the nearby road.
As mining marble is a big part of building an EHT, there's also a related page about Gearbox Design.
The Rule Set
There were four design objectives for our EHT:- Use easy to remember rules, so that intelligent analysis is effective
- Never use a rule more than one time (this one didn't work out)
- Make the puzzle resistant to brute force computer analysis
- Accomodate various skill levels
Rules that are Easy to Remember
The Sunset EHT actually only uses two rules- ab -> c
- c -> ba (the inverse)
Never use a rule twice
We gave up on this idea. Some of the most interesting intelligent patterns occur when you can use a complex repetitive sequence. The hope was to provide an easy criteria for restricting the solution set, but the idea didn't work.Resist Brute Force Attacks
The simple rule set, with many possible moves associated with each state, is a very effective defense against a programmatic attack.As the solution set for the EHT is deterministic, it's feasible to write a program that simply tries everything at every node, looking for the target state. You can then backtrack to determine the solution path. Using a ruleset with small rules increases the average number of links. The average connectivity for our EHT is 7 or so, which means that a brute force attack will inflate very rapidly, which overwhelms a brute force attack.
Using small sequences that will drop out altogether - winners - also does a nice job of making life difficult for programmatic attacks. As the winning sequences can drop out at any time, a backward pass has to insert each sequence between each pair of blocks whenever there is room. Consequently the backward solution set inflates even faster.
Accomodate varous skill levels
This is surprisingly easy to accomplish. Just list several increasingly difficult goals, and let the players select the goal that they want to pursue.- eeee is a fairly easy, 11 step goal. Once you catch on to the pattern, the solution proceeds very quickly. A brute force programmatic attack is unlikely to spot the pattern, so an intelligent player has a huge advantage.
- caf is a moderately hard, 8 stop goal. This sequence is interesting because one of the other sequences drops out midway through the solution set. This makes it really tough on progammatic attacks.
- dbe is a harder, 12 step goal. It's unlikely that you will be able to reach this goal unless you are using a computer attack.
- dc is a brutal, very difficult, 12 step goal. I shall be most disappointed if anybody has a program that can crack this sequence. :-Þ This goal is designed to defeat programmatic attacks, sloppy programming in particular.
The Model
One very effective approach is to think of the EHT puzzle as a network. The various block combinations are the nodes (or states) and the rules describe the arcs (or operators).If we start at an arbitrary point in the network (a state), and then process all possible rules that apply to that state, we can be certain that we have found all nodes at distance 1 from our starting point.
If we now take each of the distance 1 nodes and process them in turn, we can be cetain that we have found all the nodes at distance 2 from our starting point. Note, in particular, that each node will have a link back to the starting point (and perhaps to other nodes that have already been processed), so we have to prune states that have already been visited. As you get further and further from your starting point, pruning becomes more and more important as a means to prevent looping.
The model designates a lower case letter for each of the six block faces, in the order that they are presented by the EHT configuration program.
I used my model to expand the forward solution set to a distance of 12 for each of several starting sequences, and then picked a interesting looking target value. 7^12 is more than a billion states, so I actually cranked out several parallel sequences and then tested them to ensure that there were no dramatic shortcuts.
One of the many suprises was how easily an inversion happens. It's a trivial 4-step solution, and the solution has been included with the model as an illustration.
| State | Operator |
| abcdef | bc-d |
| addef | ef-a |
| adda | a-fe |
| fedda | d-cb |
| fedcba | inverted |
Meet in the Middle
If you know both the starting point and the ending point(s), you can dramatically increase the efficiency of your search by working both ends against the middle. If your rule set provides an average of 3 connections per node, for example, the number of nodes will double each time you increase the distance. If you have a 8-step puzzle, searching from just the start point would expose you to 3 + 2^2 + ... + 2^8 nodes, or 511 nodes, with 256 of the nodes at distance 8. If you search from both ends, you only need to process 2 * (3 + 2^2 + 2^3 + 2^4) = 62 nodes to find a common linking state.
Microsoft Excel Program
A Microsoft Excel program that I use to model EHTs is available at http://marvl.cncdsl.com/EHT_MarvL_Once_2005L30.xls. The program is an easy way to keep track of what you've already considered, and provides an assurance that you haven't made a simple transcription error. It's a huge improvement over using paper and pencil.The distribution program only does one step at a time. If you've already solved most of the Empty Hand Towers, and your primary interest is analysis of various rule sets, contact MarvL in-world and we can talk about providing the version that is more automatic.
