Anton Ertl wrote:
> cac <cac@[EMAIL PROTECTED]
> writes:
>> Hmmm. My approach was to divide the triangle into an upper half and a
>> lower half, and enumerate the boundary as you did. Where I get wedged
>> is the rotation and reflection issue. I need to figure out how many
>> non-distinct colourings there are, and subtract that from my answer;
>
> As far as I understand the task, rotation and reflection is a
> non-issue. If you enumerate all colourings for one orientation,
> that's the answer.
>
> If you had a way to create only one of, say, the two mirror images
> (along some axis), then you would have to count it twice, unless the
> colouring is symmetric. But with the usual enumerative approach we
> get both mirror images anyway.
From the problem statement:
A colouring C' which is obtained from a colouring C by rotation or
reflection is considered distinct from C unless the two are
identical.
How many distinct valid colourings are there for the above
configuration?
I read that as saying if a rotation or reflection is identical, it
is not distinct, and should not be counted. Am I confused as to
the interpretation?
For example, with a much smaller triangle, I generate the following
arrangements:
R R
R B G G B R
They are both generated by my algorithm, and add 2 to the enumeration.
Are they distinct by the problem definition?
-- Charles
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