11. Two players X and Y take alternate turns in a game, starting with the diagram below:
At each turn, one player writes one of 1, 2 or 3 in an empty circle, so that no two circles connected by an edge contain the same number. A player loses when they cannot go. In each of the five diagrams below it is Y ’s turn.
In which of the diagrams can Y ’s move ensure that X loses the game?
15. All four L-shapes shown in the diagram are to be placed in the 4 by 4 grid so that all sixteen cells are covered and there is no overlap. Each piece can be rotated or reflected before being placed and the black dot is visible from both sides.
How many of the 16 cells of the grid could contain the black dot?
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