History of Magic
Uh oh. The big test on the Goblin Rebellions is tomorrow, and you need to know where the goblins were positioned on the battlefield. But Professor Binns is so boring that you've been slipping in and out of sleep during class. You tried to take good notes, but up to one third of them could have been made up by your sleep-addled brain.
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- All four corners are occupied.
- At least one of the two diagonals is fully occupied.
- Each row and column has either one or two occupied squares.
- Every corner but the bottom-left one is occupied.
- Every occupied square is a knight's move away from another occupied square.
- No occupied square is horizontally or vertically adjacent to another occupied square.
- The occupied squares are connected via horizontal, vertical, and diagonal adjacency.
- The symmetry group of the arrangement of occupied squares is the cyclic group of order four.
- The third and sixth squares in the fourth column are occupied, while the sixth square in the second row and the first square in the fourth row are unoccupied.
- The third square in the second row is occupied if and only if the second square in the third row is occupied.
- The unoccupied squares are connected via horizontal and vertical adjacency.
- There are eleven occupied squares.
