(;
GM[1]
SZ[19]
AW[bc][cc][fb][fc][ed][dd][ce][fe][cq][cp][er][kp][nq][qc][qd][qe][qg]
AB[cb][dc][ec][eb][gb][gc][gd][fd][cd][fg][dp][do][gp][pp][qn][oc][pe][pf]
C[Problem 164. White to play.  

Black is fairly thick at the top, but he still needs one more move to strengthen his moyo there. Where should White invade ? ]
(;W[mc]
LB[ob:A]
TR[qc]

TE[2]
C[Correct Answer.  

Note the marked white stone in the corner: White has invested an extra stone in this area. There are three black stones to White's four. By playing 1, White is threatening to link up with her marked stone by attaching at A. ]
(;B[nd]
C[Black 2, which prevents the link-up, is the strongest response. ]
;W[md];B[me]
C[However, because his own group still has weaknesses, he must continue with 4 ... ]
;W[le];B[mf]
C[... and 6. ]
;W[kd]
LB[kg:B][jb:A][le:5]
C[This enables White to settle her group with 5 and 7. White now need fear no attack because she can get a base with A or escape into the center with a knight move at B. <= ]
)
(;B[me]
C[Variation.  

If Black caps with 1, ... ]
;W[ob]
LB[pb:B][nb:A]
C[... White attaches with 2. Black has two choices: A and B. ]
(;B[nb]
C[Bad for Black.  

Let's look at Black 1 first. This is not a severe move. ]
;W[nc];B[pb];W[od]
LB[nc:5]
C[White can easily link up with 5 and 7. <= ]
)
(;B[pb]
C[Variation.  

Black strongly resists with 4, but ... ]
(;W[od]
C[... White attacks by attaching on top with 2. ]
;B[nc];W[nd];B[md]
LB[nc:6]
C[Black continues to resist with 6 and 8, but ... ]
;W[nb];B[pc];W[pd]
LB[nb:9]
C[... White plays 9 and 11 and, ... ]
;B[mb];W[lc];B[oa];W[lb];B[na];W[qb]
C[... with the moves to 17, White will capture the black stones. <= ]
)
(;W[pc]
LB[pb:4]
C[Failure.  

White 5 in response to Black 4 is bad. ]
;B[nb];W[od];B[nc];W[nd];B[md]
LB[pd:A]
C[After the moves to Black 10, the cutting point at A is left behind. <= ]
))))
(;W[pg]
C[Failure.  

Pushing up with White 1 ... ]
;B[nf]
C[... just helps Black get in the move he needs to strengthen his position. <= ]
)
)