(;AB[ap]AB[ao]AB[bo]AB[bn]AB[cn]AB[cm]AB[am]AB[dm]AB[en]AB[fn]AB[fo]AB[fm]AB[fp]AB[dp]AB[go]AW[aq]AW[bp]AW[co]AW[eo]AW[do]AW[dn]AW[cq]AW[ep]AW[fq]AW[gp]AW[ho]AW[hn]AW[gm]C[Black to cut through the white border]AP[goproblems]
(;B[gq]
(;W[hp];B[eq]
(;W[cp];B[fr]C[Black cut white and invaded its territory RIGHT])
(;W[fr];B[cp]C[Black ruined white's territoryRIGHT]))
(;W[eq]C[CHOICE];B[hp]C[White is cut but black lost the sente. Though this solution is correct, there is a much better way to cut white while keeping the sente.RIGHT]))
(;B[eq];W[cp]
(;B[gq]
(;W[hp];B[fr]C[Black cut white and invaded its territory RIGHT])
(;W[fr]C[CHOICE]
(;B[hp]C[Black cut white and invaded its territory while keeping the sente (white must now add a move at G2 to protect is stones at F2 and F3).RIGHT])
(;B[gr];W[er];B[hp]C[RIGHT])))
(;B[dq];W[cr]
(;B[dr];W[er])
(;B[br];W[er])
(;B[gq]C[You did find the weakness but lost a move beforehand])))
(;B[cp];W[dq])
(;B[hp];W[gq]
(;B[eq];W[cp])
(;B[cp];W[dq]))
(;B[bq];W[br])
(;B[dq];W[eq]))