(;AW[ir]AW[iq]AW[ip]AW[kr]AW[kq]AW[kp]AB[jo]AW[ho]AW[hn]AW[in]AW[jn]AW[kn]AW[ln]AW[lo]AB[lr]AB[lq]AB[mp]AB[mo]AB[mn]AB[mm]AB[ll]AB[jl]AB[hl]AB[gm]AB[gn]AB[go]AB[gp]AB[hq]AB[hr]AB[er]AB[ep]AB[or]AB[op]C[with how many first moves can white live?FORCE]LB[ej:0]LB[fj:1]LB[gj:2]LB[hj:3]LB[ij:4]LB[jj:5]LB[kj:6]LB[lj:7]LB[mj:8]LB[nj:9]AB[jk]AP[goproblems]
(;W[mj];B[mk]C[8 is correct. now you can exploreRIGHT]
(;W[jp]C[RIGHT])
(;W[js]C[RIGHT])
(;W[jq];B[js])
(;W[jr];B[jp])
(;W[is]C[RIGHT])
(;W[ks]C[RIGHT])
(;W[hs]
(;B[js];W[jp];B[jr];W[ks]C[RIGHT])
(;B[jp];W[ks];B[is];W[js];B[jq]C[RIGHT]))
(;W[ls]C[RIGHT])
(;W[gs];B[jp];W[is];B[ks];W[js];B[jq];W[ls]C[RIGHT])
(;W[ms]C[RIGHT])
(;W[io];B[js])
(;W[ko];B[js])
(;W[hp];B[js])
(;W[lp];B[js]))
(;W[ej]C[incorrect. after finding the correct number you can explore the variations])
(;W[fj]C[incorrect. after finding the correct number you can explore the variations])
(;W[gj]C[incorrect. after finding the correct number you can explore the variations])
(;W[hj]C[incorrect. after finding the correct number you can explore the variations])
(;W[ij]C[incorrect. after finding the correct number you can explore the variations])
(;W[jj]C[incorrect. after finding the correct number you can explore the variations])
(;W[kj]C[incorrect. after finding the correct number you can explore the variations])
(;W[lj]C[incorrect. after finding the correct number you can explore the variations])
(;W[nj]C[incorrect. after finding the correct number you can explore the variations]))
adum