Not having repeats makes the job of the person with the code much simpler, at least I think it does. The work that the person guessing the code has to do would then be based on the size of V compared to P.

If you call each "color" Cn, and take the first P characters from a randomly sorted alphabet of size V, you essentially have a code of ...

C1, C2, C3, ..., Cp

If my grey matter is working properly, it does not matter what characters the code maker chooses, other than as a psychological exercise against the choice of the initial selections.

If I ignore defending against the choice of initial selections, the code maker really only has 315 puzzles to generate.

(p=1,  v=1 ) .. (p=1,  v=36) => 36
(p=2,  v=2 ) .. (p=2,  v=36) => 35
...
(p=10, v=10) .. (p=10, v=36) => 27

((27 + 36) / 2) * 10 = 315

[download]

Now, that is not to say that the code maker will probably not be choosing '0', '01', '012', etc as the codes. It also does not mean that there will not be some carefully chosen sequences designed to test the robustness of certain types of implementations. :-)

--MidLifeXis

Please consider supporting my wife as she walks in the 2009 Alzheimer's Walk.

In reply to Re^2: Challenge: Optimal Bagels Strategy by MidLifeXis
in thread Challenge: Optimal Bagels Strategy by Limbic~Region

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