(;AB[oa]AB[pa]AB[pb]AB[pc]AB[pd]AB[pe]AB[qe]AB[re]AB[se]AB[sf]AB[qf]AB[qg]AB[oc]AB[od]AW[na]AW[nb]AW[ob]AW[nc]AW[nd]AW[oe]AW[of]AW[og]AW[oh]AW[qh]AW[qi]AW[rf]AW[rg]AW[sh]AW[qa]AW[qb]AW[qc]AW[qd]AW[rd]AW[sd]AB[rj]TR[oa]TR[pa]TR[pb]TR[pc]TR[oc]TR[od]TR[pd]TR[pe]TR[qe]TR[re]TR[se]TR[sf]TR[qf]TR[qg]AW[qj]AB[sc]AP[goproblems]
(;B[rb]
(;W[ra]
(;B[sa];W[sb]
(;B[rh]
(;W[rc]
(;B[sg];W[ri]
(;B[si];W[rk]
(;B[sk];W[sl])
(;B[sj];W[sk])
(;B[ph];W[pi])
(;B[qk];W[ql];B[pk];W[rm])
(;B[rl];W[sj]C[Black only has one eye. You failed to save the P16 group.]))
(;B[rg];W[si])
(;B[sj];W[si]))
(;B[qj];W[ri])
(;B[ri]C[RIGHT])
(;B[si];W[ri]C[Black's P19 group is cut off.]))
(;W[ri];B[sa];W[pg];B[rc]C[RIGHT]))
(;B[sa]C[NOTTHIS])
(;B[ri]
(;W[rc]
(;B[si];W[rh])
(;B[rh]C[RIGHT]))
(;W[rh];B[sa];W[pg];B[rc]C[RIGHT]))
(;B[si];W[rc];B[rh];W[ri])
(;B[pg]
(;W[rc]
(;B[pi];W[ph])
(;B[ph];W[pi])
(;B[rh];W[ri])
(;B[ri];W[rh]))
(;W[rh]))
(;B[sg];W[rc];B[rh];W[ri];B[si];W[rk]
(;B[sj];W[sk])
(;B[sk];W[sl])
(;B[ph];W[pi])
(;B[qk]
(;W[ql]
(;B[pk];W[rl])
(;B[rl];W[pk];B[sk];W[sj]C[Black gets a ko threat which is worth less than the points lost in this corner.]))
(;W[rl]C[CHOICE]))
(;B[sh];W[qk]
(;B[sk];W[sl])
(;B[sj];W[sk]))
(;B[ne];W[mf]
(;B[me];W[le])
(;B[nf];W[mg])
(;B[sk];W[sl])))
(;B[pf];W[rc]C[Black's P19 group is cut off.];B[ph];W[pi]))
(;B[sb];W[pg]
(;B[pk];W[pf];B[ok];W[sg])
(;B[sa];W[rc])
(;B[rc];W[sa])
(;B[rh];W[ri])
(;B[sg];W[rh])
(;B[pf];W[sg])
(;B[ri]
(;W[sg]C[CHOICE])
(;W[pf]C[CHOICE]))
(;B[si]
(;W[sg]C[CHOICE])
(;W[pf]C[CHOICE])))
(;B[rc];W[sb])
(;B[rh];W[ri];B[sa];W[sb]C[You get a ko threat worth less than the 28 points you give white in this corner.];B[sg];W[rc];B[rh];W[si])
(;B[sg];W[rh]
(;B[sa];W[sb];B[sa]C[NOTTHIS])
(;B[ne];W[pg])
(;B[sb];W[pg]))
(;B[pg];W[rh];B[sa];W[sb];B[ph];W[rc];B[pi];W[qj])
(;B[sc];W[rh];B[sa]C[];W[sb]C[You get a ko threat that is worth less than the 28 points you give white for your P19 group.])
(;B[si];W[pg];B[sa];W[sb]C[You get a ko threat worth less than the 28 points you gave white for the P19 group.])
(;B[ri];W[rh]MA[qg]MA[qf]MA[qe]MA[pe]MA[pd]MA[od]MA[oc]MA[pc]MA[pb]MA[pa]MA[oa]MA[sf]MA[se]MA[re]MA[sc]MA[rb];B[sa];W[sb]LB[ma:K]C[Play at K to play a ko threat.];B[ma];W[rc]MA[oa]MA[pa]MA[pb]MA[oc]MA[pc]MA[od]MA[pd]MA[pe]MA[qe]MA[qf]MA[qg]MA[re]MA[se]MA[sf]C[You failed to save your P16 group.]))
(;W[pg];B[ra]C[RIGHT]
(;W[sg];B[rc]C[RIGHT])
(;W[pf];B[rc]C[RIGHT])))
(;B[rc];W[rb]
(;B[sb];W[sa])
(;B[sa];W[sb])
(;B[ra];W[sb])
(;B[sg];W[rh]))
(;B[sg];W[rh]
(;B[rb];W[ra]
(;B[sa];W[sb]C[Ko];B[sa]C[NOTTHIS])
(;B[rc];W[sb]))
(;B[ph];W[pi])
(;B[ra];W[rb];B[sb];W[sa])
(;B[ne];W[pg]C[CHOICE])
(;B[pg];W[sb]
(;B[ph];W[pi])
(;B[pi];W[ph]))
(;B[rc];W[pg]
(;B[rb];W[pf])
(;B[ra];W[pf])))
(;B[rh];W[ri]
(;B[rb];W[ra];B[sa];W[sb]C[You get a ko threat worth less than the 28 points you give white in this corner.];B[sg];W[rc];B[rh];W[si])
(;B[ra];W[rb];B[sb];W[sa]C[You get a smaller ko threat than the 28 points you give White.])
(;B[rc];W[rb]
(;B[ra];W[sb])
(;B[sc];W[sb])
(;B[sb];W[sc]))
(;B[sc];W[sb]
(;B[rc];W[rb])
(;B[rb];W[rc])
(;B[ra];W[rb])
(;B[sa];W[rb]))
(;B[sb])
(;B[sg];W[rh]
(;B[si];W[sb]C[The black P19 group is dead because it has no eyes and white won't let black escape.]
(;B[rc];W[rb])
(;B[rb];W[rc]C[Black has a ko threat in the corner of Bs19-Bt17. Before starting a ko white should capture with wS19.]))
(;B[rb];W[pg]
(;B[rc];W[pf])
(;B[ra];W[pf])))
(;B[si];W[sb])
(;B[sj];W[sb]))
(;B[ra];W[rb]
(;B[sb];W[sa]
(;B[ri];W[rc];B[rh]C[RIGHT])
(;B[ra]C[NOTTHIS])
(;B[sg]
(;W[sc]
(;B[rh];W[ri];B[si];W[rk]C[Black has only one eye.]
(;B[sk];W[sl])
(;B[sj];W[sk])
(;B[ph];W[pi]))
(;B[ri];W[rh]))
(;W[rc];B[rh];W[ri];B[si];W[rk]
(;B[sk];W[sl])
(;B[sj];W[sk])))
(;B[rh];W[rc]C[CHOICE]
(;B[ri]C[RIGHT])
(;B[sg];W[ri];B[si];W[rk]
(;B[sk];W[sl])
(;B[sj];W[sk])
(;B[qk];W[rl]))
(;B[sb];W[sc]
(;B[ri]C[RIGHT])
(;B[sg];W[ri];B[si];W[rk]
(;B[rl];W[sj])
(;B[sk];W[sl])
(;B[sj];W[sk]))))
(;B[pg];W[rc]))
(;B[rc];W[sb])
(;B[sa];W[sb]
(;B[rh];W[ri])
(;B[ra]LB[la:T];W[la]C[BS19 is a wasted move. White already has two eyes in the corner. The black P19 group has no eyes. White can tenuki.]))
(;B[sc];W[sb]))
(;B[ri];W[rh]
(;B[rb];W[ra]
(;B[sa];W[sb]C[You get a ko threat smaller than the 28 points you give white in this corner.];B[ma];W[rc]MA[oa]MA[pa]MA[pb]MA[oc]MA[pc]MA[od]MA[pd]MA[pe]MA[qe]MA[qf]MA[qg]MA[re]MA[se]MA[sf]C[You failed to save your P16 group.])
(;B[sb];W[pg]))
(;B[si];W[pg])
(;B[pg];W[sb]
(;B[ph];W[pi])
(;B[pi];W[ph]))
(;B[ra];W[rb]))
(;B[md];W[sb]
(;B[rc];W[rb])
(;B[rb];W[rc])
(;B[ra];W[rb])
(;B[sa];W[rb])
(;B[sc];W[rb]))
(;B[me];W[sb]
(;B[rc];W[rb];B[rh];W[ri])
(;B[rb];W[rc])
(;B[ra];W[rb])
(;B[sa];W[rb])
(;B[sc];W[rb]))
(;B[ng];W[sb]
(;B[rc];W[rb])
(;B[rb];W[rc])
(;B[ra];W[rb])
(;B[sa];W[rb])
(;B[sc];W[rb]))
(;B[pi];W[sb]
(;B[rc];W[rb])
(;B[rb];W[rc])
(;B[ra];W[rb])
(;B[sa];W[rb]))
(;B[ph];W[sb]
(;B[rc];W[rb])
(;B[rb];W[rc])
(;B[ra];W[rb])
(;B[sa];W[rb])
(;B[pi];W[oj])
(;B[ri];W[rh]))
(;B[pg];W[sb]
(;B[rc];W[rb])
(;B[rb];W[rc])
(;B[ra];W[rb])
(;B[sa];W[rb]))
(;B[si];W[sb]C[Black's P19 group is dead because it is cut off and white's corner stones are alive.]
(;B[rc];W[rb])
(;B[rb];W[rc])
(;B[ra];W[rb])
(;B[sa];W[rb])
(;B[rh];W[ri]))
(;B[pf];W[sb]
(;B[rc];W[rb])
(;B[rb];W[rc])
(;B[ra];W[rb])
(;B[sa];W[rb]))
(;B[sb]
(;W[pg]C[CHOICE])
(;W[sg]))
(;B[sa]
(;W[pg]C[])
(;W[sg]C[CHOICE])))