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I think the solution for the fifth problem is flawed. It's possible that 1.Rg2 Bg3 2.Rg8 (impossible) //2.Be5 Bf4 3.Rxh2+ Kxh2! then I don't think the Black King could be cornered again in 5 moves. I think the solution when 2.Rg8 (impossible) should be 2.Be5 3.Nf2+ Bxf2 4.Rxh2#.