In double-checks the king has to move!  

"double-check" mates

a) White to move and mate in one.

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b) White to move and mate in one.

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c) White to move and mate in two.

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d) White to move and mate in two.

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Solutions:  a) R-d8 double check and mate              b) NxP(g)  or N-c7 double check and mate                

c) NxP double check, K-e7  then Q-f7 mate              d) N-h6 double check, K-h8  followed by  Q-g8 mate