[Tutor] How to solve it ...

[Bob Gailer]

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At 10:55 PM 2/18/2003 +0100, Gregor Lingl wrote:
So I would also be interested in Bob's paper-solution.

1 - I subdivided the 16 start states into 4 categories
O - all 4 the same - lock is open
T - 3 the same
D - 2 the same along a diagonal
P - 2 the same horizontal or vertical

2 - I observed that the effect of a particular code was the same on all 
members of a category, and listed the effects. Since this is a 
non-deterministic process, codes P1 and D1 had different effects on certain 
categories depending on which of the 2 was chosen. Effect here means that a 
code transforms a member of a category to a member of some category.

3 - I drew a state-transition graph showing each category and the 
transitions between categories triggered by the various codes. That's hard 
to reproduce in a text e-mail, and I don't have a scanner set up. Sorry.

4 - I then experimented with various codes on each successive starting 
configuration. I discarded codes that might make no useful change. In each 
case one code promotes the configuration to a new useful state.

With P, D and T as the starting categories: P1 in all cases toggles to 
another category and P2 in many cases toggles to another category, so 
starting with these codes might leave you with no useful change. D2, 
applied to category D opens, and applied to P or T makes no change.

With P and T as the new starting categories: P1 and D2 in all cases just 
toggle to another category. P2 applied to P either opens or goes to D. That 
is a useful change. P2 applied to T goes to T.

With D and T as the new starting categories: P1 in all cases just toggles 
to other categories. D2 applied to D opens, applied to T goes to T.

With T as the new starting category: D2 and P2 go to T. Not useful. P1 
toggles to D or P. Useful.

With P and D as the new starting categories: P1 just toggles to another 
category. D2 applied to D opens, and applied to P goes to P.

With P as the new starting category: P1 just toggles to another 
category.  P2 applied to P either opens or goes to D.

With D as the new starting category: P1 just toggles to another 
category.  D2 applied to D opens.

Bob Gailer
mailto:ramrom@earthling.net
303 442 2625

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