More Rows of Checkers
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Consider a hexagonal arrangement of 19 circles, like the configuration shown.

Can you place 10 checkers on the hexagon such that there are
2 checkers in each row in each of the three primary directions?

Can you place 9 black and 9 white checkers on the hexagon (leaving only
one location empty) such that no more than 2 checkers of the same color
are in any row in each of the three primary directions? Or can you
prove it cannot be done? (If it can't be done, what is the largest
number of checkers you can place under these conditions?)
Source: Original, though I wouldn't be surprised to hear of another source.
Solution
Mail to Ken