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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.

Find the minimum number of moves for White to checkmate Black.

- White starts
- Black plays optimally

In the position below, how can White give checkmate in two moves?

The target square of the first move can be represented as a coordinate \((x,y)\), where the bottom left corner square is at \((0,0)\). Input the product of \(x\) and \(y\) as your answer.

Note that both players played optimally and that White moves up (pawn).

Assume for the sake of this puzzle that there are more white pieces than originally intended.

It is White's move. What must White play in order to mate in **3**?

The bottom left corner square has coordinates \((1, 1)\). Each piece has a value: \(\text{Queen}=10\), \(\text{Rook}=5\), \(\text{Pawn}=1\) and \(\text{King}=4\).

Submit your answer as \(V\times { x }_{ 1 }\times { y }_{ 1 }\), where \(V\) denotes the value of the piece that White must move and the coordinates of the square where it has to go are \(\left( { x }_{ 1 },{ y }_{ 1 } \right) \).

**Clarification:** Black plays **optimally**.

Assume that both players played optimally and that Black moves down (pawn).

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