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## Chess

Chess is no joke: it has more possible sequences of moves than the number of atoms in the observable universe, but working through chess puzzles is a great way to gain insightful strategies. See more

# Level 3 Abstract

Above is a $$3\times3$$ board with 4 knights, two white knights and two black knights. As in a standard game of chess, the knight can move only two steps in the horizontal or vertical direction and then one step in the other direction for one move. Define an action as moving a knight of any color.

The objective of the game is to interchange the position of both the black and white knights while alternately moving a knight of different color. The final state of the board is:

What is the minimum number of actions required to complete the game?

What is the maximum number of counters you can place on an $$8 \times 8$$ chessboard given that each row, column, ​and the two main diagonals contain 5 or fewer counters?

Suppose you are given a normal 8 X 8 chessboard and hundreds of spare green-colored knight pieces lying about. If any knight is able to capture any other knight, find the highest number of knights, you can place on the board in non-attacking positions.

A white pawn had been accidentally knocked off the board. Neither player could remember for sure on which square it stood. If neither king has yet moved, where is the pawn?

###### This problem is the first one of the set Retrograde Chess.

What is the maximum number of bishops on a $$8 \times 8$$ chessboard, so that they cannot attack each other?

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