Template VI1/Other Intrusion on the 1st row

This article deals with a special case in defending against intrusions in template VI1, namely the right-hand ('other') intrusion on the 1st that is not eliminated by sub-templates threats.

Basic situation
R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7

Red should go here:

R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7 MR Mh5 Pi3 Pi4

The Red 1 hex is connected to the bottom, and threatens to connect to the top through either one of the "+" hexes. It is now Blue's move.

Claim #1: Blue must move in one of the following + squares below
If Blue moves to

R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7 Rh5 Pi3 Pi4 Pe7 Pf6 Pf7 Pg5 Pg6 Ph6 Ph7 Pi5 Pi6 Pi7

If not, Red can move to either i3 or i4 and secure a connection.

Proposed first Red response
If Blue moves to {e7, f6, f7, g5, g6}, Red should take i6 and force a Blue response in either i3 or i4. If Blue moves to {h6, h7, i5, i6, i7}, Red should take f6 and force a Blue response in either i3 or i4. If Blue takes i3 or i4 direcly, proceed with Response to i3 or Response to i4 instructions below.

Response to i3
If we've arrived here, Blue has just taken i3, i4 is free, h5 is securely connected to the bottom and Blue has at most one of the "+" squares below (with one exception; see i3 addendum). In this case, Red should first take j3 and force a Blue response at i4:

R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7 Rh5 Bi3 Pe7 Pf6 Pf7 Pg5 Pg6 Ph6 Ph7 Pi5 Pi6 Pi7 MV Mj3 Mi4

CASE #1: Blue has i5. SOLUTION:

R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7 Rh5 Bi5 Bi3 Rj3 Bi4 MV Mk4 Mk5 Mj5 Mi7 Mi6 Mh7 Mh6

CASE #2: Blue has no tiles in {h6, h7, i5, i6, i7}, or has either {h6, h7, i6} (indicated by +). SOLUTION:

R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7 Rh5 Bi3 Rj3 Bi4 MV Mj4 Mi5 Mk5 Ph6, Ph7, Pi6

CASE #3: Blue has i7. SOLUTION:

R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7 Rh5 Bi7 Bi3 Rj3 Bi4 MV Mj4 Mi5 Mj5 Pj6 Pj7 Pk5 Pk6 Pk7

Blue must take one of the + hexes or Red wins. Now, Red can play i6 and force h7, then play h6 and connect to h5 (which is already securely connected.

Response to i4
If we've arrived here, Blue has just taken i4, i3 is free, h5 is securely connected to the bottom and Blue has at most one of the "+" squares below (with one exception; see i4 addendum). In this case, Red should first take h3 and force a Blue response at h4:

R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7 Rh5 Bi4 Pe7 Pf6 Pf7 Pg5 Pg6 Ph6 Ph7 Pi5 Pi6 Pi7 MV Mh3 Mh4

CASE #1: Blue has g5. SOLUTION:

R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7 Rh5 Bg5 Bi4 Rh3 Bh4 MV Mf4 Me5 Mf5 Me7 Mf6 Mf7 Mg6

CASE #2: Blue has no tiles in {e7, f6, f7, g5, g6}, or has either {f6, f7, g6} (indicated by +). SOLUTION:

R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7 Rh5 Bi4 Rh3 Bh4 MV Mg4 Mg5 Me5 Pf6, Pf7, Pg6

CASE #3: Blue has e7. SOLUTION:

R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7 Rh5 Be7 Bi4 Rh3 Bh4 MV Mg4 Mg5 Mf5 Pc7 Pd6 Pd7 Pe5 Pe6

Blue must take one of the + hexes or Red wins. Now, Red can play f6 and force f7, then play g6 and connect to h5 (which is already securely connected.

i3 addendum
I claimed that Blue can have only one of the + hexes but this is not quite true if Blue first "plays out" the secured bridge. But in this case Red definitely can acquire i6.

R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7 Rh5 Bi3 Rh6 Bi5 Ri6 Bf6 Pe7 Pf7 Pg5 Pg6 Ph7 Pi7

In this case, Red can still play j3 to force i4, then k4 to force j5, then l5 wins:

R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7 Rh5 Bi3 Rh6 Bi5 Ri6 Bf6 MV Mj3 Mi4 Mk4 Mj5 Ml5

i4 addendum
I claimed that Blue can have only one of the + hexes but this is not quite true if Blue first "plays out" the secured bridge. But in this case Red definitely can acquire f6.

R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7 Rh5 Bi4 Bg5 Rg6 Rf6 Bi6 Pe7 Pf7 Ph6 Ph7 Pi5 Pi7

In this case, Red can still play h3 to force h4, then f4 to force f5, then d5 wins:

R7 C14 Q1 1:BBBBBBBBBRBBBBB Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2 Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3 Sa4 Sb4 Sc4 Sd4 Sn4 Sa5 Sb5 Sa6

Bg7 Rh5 Bi4 Bg5 Rg6 Rf6 Bi6 MV Mh3 Mh4 Mf4 Mf5 Md5