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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

In the position below, how can White give the **fastest** checkmate?

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In our extraordinary game,

- Black has castled in the last move,
- In one of the 3 previous moves, the white knight from g1 was captured on its initial square.

Which piece captured the knight?

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It's White turn to move, find the minimum number of moves for White to move to win the game.
###### Designed by Fikri Prayoga.

Note that both players played optimally and that Black moves down (pawn) and that Black intends to stay in the game for as long as possible.

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In the following position, **the color of each piece is unknown** (each piece could either be white or black), but it is known that the position arose from a series of legal moves, starting at the usual starting position.

Before the last move was made, Black had \(a\) pieces worth \(b\) points (on the scale Queen = 9, Rook = 5, Bishop = Knight = 3, Pawn = 1, King = 0). What is the product of \(a\) and \(b\)?

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Consider the positional set up of a game. It is white's turn to move. White can checkmate black in just two moves, can you find the first move to force a checkmate?

If the first move can be written as \( (x_1,y_1) , (x_2,y_2) \), where \(x_1,y_1\) are the coordinates (according to how it is marked above) of the moved piece's initial position and \(x_2,y_2\) are the coordinates of the position of the piece after the move, evaluate \( (x_1+y_1) \times (x_2+y_2) \)

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