Black descended at 1 and White chose to defend his smaller group in the corner with 2. Black was thinking of just invading White's territory, but he found out that he could kill the large White group. Thanks to tails and blyx and others for finding the right solutions.
(;AB[mj]AB[ij]AB[pd]AB[nf]AW[sh]AW[si]AW[ok]AW[nl]AB[kn]AB[no]AB[oo]AB[nn]AB[op]AB[np]AB[oq]AW[qp]AW[qq]AW[qs]AW[qr]AB[nr]AB[or]AB[sd]AB[re]AB[qd]AB[qf]AB[oe]AB[of]AB[sf]AB[rg]AB[qh]AB[ph]AB[oh]AB[nh]AB[mg]AB[lg]AW[sg]AW[rh]AW[qi]AW[pi]AW[oi]AW[ni]AB[mi]AB[li]AB[ki]AB[ji]AB[ii]AW[jj]AB[kk]AB[jk]AB[lj]AB[nj]AW[lk]AW[mk]AW[nk]AW[oj]AW[pj]AB[kl]AB[ll]AB[ml]AW[ql]AW[om]AB[nm]AB[on]AB[pm]AB[mn]AB[ln]AB[km]AB[po]AB[qn]AB[rn]AW[qo]AW[ro]AW[pp]AB[pq]AW[pr]AW[ps]AW[os]AB[ns]AB[mq]AB[lr]AB[kr]AB[rr]C[Black to play and kill the large white group.]LB[rn:1]LB[ro:2]AP[goproblems]
(;B[rj]
(;W[ri]C[]
(;B[sk]
(;W[rl];B[sl];W[sm];B[rm];W[rk]
(;B[sn];W[sj]
(;B[qj];W[sm];B[sl]
(;W[pl];B[qk]C[RIGHT])
(;W[qk];B[pl]C[RIGHT]))
(;B[pl]C[RIGHT]))
(;B[pl];W[sj];B[sl];W[qj];B[pk]C[RIGHT]))
(;W[rk];B[sl];W[sj]
(;B[sm]
(;W[qj];B[pl];W[pk];B[rl])
(;W[pl]))
(;B[pl];W[sm];B[rm];W[rl];B[sl]C[RIGHT];W[qj];B[pk]C[RIGHT])
(;B[qj];W[sm];B[rm];W[rl];B[sl]C[RIGHT]))
(;W[sl];B[rl];W[rm];B[sm];W[qm];B[pl];W[qk];B[sl]C[])
(;W[rm];B[sm];W[rk];B[sl];W[sj];B[qj]
(;W[qk];B[pl]C[])
(;W[pl];B[qk]C[])))
(;B[rk];W[rl];B[sm];W[sl];B[pl];W[pk];B[qk]C[RIGHT])
(;B[pl];W[rk]
(;B[sl];W[sk];B[sm];W[pk]
(;B[qj]C[RIGHT])
(;B[rl]C[RIGHT]))
(;B[rm]C[RIGHT]))
(;B[qm]C[RIGHT])
(;B[rl]C[RIGHT])
(;B[rm]C[RIGHT])
(;B[sn]C[RIGHT])
(;B[sm]C[RIGHT])
(;B[sl]C[RIGHT])
(;B[sj]C[RIGHT])
(;B[qk]C[RIGHT]))
(;W[rk];B[ri]C[])
(;W[sj];B[rk];W[ri];B[rl]C[]))
(;B[sj]LB[rn:1]LB[ro:2]
(;W[ri]
(;B[sl]C[RIGHT])
(;B[rm]C[RIGHT])
(;B[sm]C[RIGHT])
(;B[rl]C[RIGHT])
(;B[sk]C[RIGHT])
(;B[rj]C[RIGHT])
(;B[qk]C[RIGHT])
(;B[pl]C[RIGHT])
(;B[rk]C[RIGHT]))
(;W[rj];B[ri];W[rk];B[pl]C[RIGHT]))
(;B[rq];W[rj]C[The White group in the corner is smaller than the group on the side. In this case, White's best move is also Black's best move, to save or kill the large White group on the side.])
(;B[sp];W[rj]C[The White group in the corner is smaller than the group on the side. In this case, White's best move is also Black's best move, to save or kill the large White group on the side.])
(;B[so];W[rj]C[The White group in the corner is smaller than the group on the side. In this case, White's best move is also Black's best move, to save or kill the large White group on the side.])
(;B[sn];W[rj]C[In this case, White's best move is also Black's best move.])
(;B[sk]C[];W[rj]C[Monkey jump tesuji.]
(;B[sj]
(;W[ri]
(;B[sm]C[RIGHT])
(;B[rk];W[rl]
(;B[sl];W[qk];B[sm];W[pl])
(;B[qk];W[sl]
(;B[pl];W[pk];B[sm];W[qj]
(;B[rk];W[sk])
(;B[sk];W[rk]))
(;B[pk];W[pl];B[sm];W[qj]))
(;B[pl];W[pk];B[sl];W[sm];B[rm];W[qk];B[sl];W[sk]))
(;B[rl];W[rk];B[rm];W[qk];B[pl]C[RIGHT]))
(;W[sl];B[ri]C[RIGHT]))
(;B[rk];W[qk]
(;B[sj];W[ri]
(;B[sm];W[pl])
(;B[pl];W[rl])
(;B[rl];W[rm]
(;B[qm];W[sl])
(;B[sm];W[sl])))
(;B[sm];W[sj];B[pl];W[pk]))
(;B[sl];W[rk]
(;B[sm];W[sj];B[pl];W[qk])
(;B[sj];W[sm];B[rm];W[rl];B[sl];W[sk]C[Black has to play gote to prevent the connection underneath.])))
(;B[rl];W[rj]C[Black has two options to follow the principle that White's best move is also Black's best move.]
(;B[sk];W[rk];B[sl];W[sj];B[pl];W[qk])
(;B[qk];W[rk];B[pl];W[sk])
(;B[rk];W[qk];B[sk];W[sj]))
(;B[pl];W[rj]C[Black has two options to follow the principle that White's best move is also Black's best move.])
(;B[kj];W[rj]C[Black has two options to follow the principle that White's best move is also Black's best move.])
(;B[ol];W[rj]C[Black has two options to follow the principle that White's best move is also Black's best move.])
(;B[qm];W[rj]C[Black has two options to follow the principle that White's best move is also Black's best move.])
(;B[rk];W[rj]C[Black has two options to follow the principle that White's best move is also Black's best move.]
(;B[qk];W[rl];B[pl];W[pk])
(;B[sk];W[qk]
(;B[sj];W[ri]
(;B[sm];W[pl])
(;B[pl];W[rl])
(;B[rl];W[rm]
(;B[qm];W[sl])
(;B[sm];W[sl])))
(;B[sm];W[sj];B[pl];W[pk]))
(;B[rl];W[qk];B[sk];W[sj]))
(;B[sq];W[rj]C[The White group in the corner is smaller than the group on the side. In this case, White's best move is also Black's best move, to save or kill the large White group on the side.])
(;B[qk];W[rj]
(;B[rk];W[rl];B[pl];W[pk])
(;B[rl];W[rk];B[pl];W[sk])
(;B[pl];W[rk])
(;B[sl];W[rk];B[sk];W[rl];B[sm];W[sj];B[pl];W[pk])))