Tough question.
Tough question.
Last edited by bennyJ; 04-23-2018 at 01:51 PM.
Yes, it appears to want you to consider all types of symmetry.
All White - Only one way to do that.
All Black - Only one way to do that.
One White (same thing as 7 black) - You can paint any one of the 8 surfaces, but various symmetries show they are all the same. - Just one distinct way.
One Black (7 white) - Again, just one.
Two White (6 black) -- What say you? More than one distinct way?
"Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.
There seem to be four total patterns, if you allow for reorientations, by coloring 8 triangles one color (8 black, 8 white) or just one triangle one color (1 white, 1 black), as you say. All black, all white, any one white triangle, and one black triangle.
For two triangles, I think three patterns are possible for each color. So, we would have three for white and three for black. Considering the four we counted before, that would bring our total to 10 (4+3+3), unless I've counted incorrectly. Does that look right?
I have to agree with this. We have:
With reference to the provided drawing:
1) Adjacent horizontally
2) Adjacent vertically
3) No Adjacent
Well, that covers a lot of he problem. Why quit now?
8W0B - 1
7W1B - 1
6W2B - 3
5W3B - ?? - Still some thinking to do.
4W4B - ?? - Still some thinking to do.
3W5B - ?? (by symmetry)
2W6B - 3 (by symmetry)
1W7B - 1 (by symmetry)
0W8B - 1 (by symmetry)
What say you of 5W3B?
"Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.
I don't plan on stopping. It will start to get challenging soon, though. Do you think there are two or three distinct patterns for each color of the 3/5 pattern?
To my count, at least two distinct patterns, considering symmetry, seem to be three in a row and a kind of checkered pattern in which only two of the three similarly colored triangles share one vertice.
Last edited by bennyJ; 01-12-2018 at 04:22 PM.
Start with the three 2-6 patterns and explore the 3-5s.
"Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.
Any guesses for the total number of distinct patterns for this shape?
Bookmarks