(;AW[sr]AW[rr]AW[sq]AW[qr]AW[or]AW[pr]AW[pq]AB[rs]AB[rq]AB[qq]AB[pp]AB[qp]AB[qo]AB[ro]AB[sp]AB[oq]AB[nq]AB[nr]AB[lr]AB[lp]AB[kp]AB[oo]AW[np]AW[op]AW[mo]AW[lo]AW[po]AW[pn]AW[pm]AW[rm]AW[nm]AP[goproblems]
(;B[qm]
(;W[ql]C[CHOICE]
(;B[rl]
(;W[qn]C[CHOICE]
(;B[sn];W[rn];B[sm];W[rk]
(;B[os]C[RIGHT])
(;B[qs]C[RIGHT]))
(;B[rn];W[sn]))
(;W[sn]
(;B[qn]
(;W[so]
(;B[sl];W[rp])
(;B[pl];W[qk];B[om]C[Correct. Black is alive, and still ko for cornerRIGHT]))
(;W[pl]C[];B[rn]C[RIGHT]))
(;B[rn];W[qn])
(;B[pl];W[qn]))
(;W[rn]C[];B[qn];W[rk]
(;B[os];W[sl];B[ps];W[sn];B[qs];W[so];B[ss]C[RIGHT])
(;B[pl];W[sl];B[om]C[RIGHT])))
(;B[rn];W[sn]
(;B[qn];W[rl])
(;B[rl];W[qn]))
(;B[pl];W[qn];B[om];W[rn])
(;B[sm];W[sl]
(;B[qn];W[sn])
(;B[sn];W[rn];B[os];W[so];B[sn];W[sm];B[ps];W[so])
(;B[rn];W[sn];B[os];W[sm];B[ps];W[so]))
(;B[sn];W[rn]
(;B[rl];W[sm]
(;B[qn];W[so])
(;B[pl];W[qn])
(;B[sl];W[qn]))
(;B[sm];W[sl];B[os];W[so];B[sn];W[sm];B[ps];W[so]))
(;B[qn];W[rl]))
(;W[qn]C[];B[rn];W[sn];B[ql];W[rl];B[pl];W[ol];B[rk]C[RIGHT])
(;W[rn]C[];B[qn];W[ql];B[pl]
(;W[rl];B[om]C[RIGHT])
(;W[ol];B[rl]C[RIGHT])))
(;B[rn];W[sn]
(;B[qm];W[ql]
(;B[qn];W[rl])
(;B[rl];W[qn]))
(;B[rl];W[qm])
(;B[sl];W[sm];B[qm];W[ql];B[qn];W[rl];B[pl];W[so]))
(;B[os];W[sn]
(;B[ps];W[so];B[qs];W[rp])
(;B[qs]C[NOTTHIS]))
(;B[sn];W[rn])
(;B[sm];W[rn];B[sn];W[sl];B[os];W[so];B[sn];W[sm];B[ps];W[so];B[qs];W[rp])
(;B[no]C[NOTTHIS];W[mp]C[This exchange was unnecessary. Black here still only has 2 liberties. Please avoid playing unncessary moves])
(;B[mp];W[no])
(;B[qn];W[qm])
(;B[so]))