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.

Contents 1 Basic situation 2 Claim #1: Blue must move in one of the following + squares below 3 Proposed first Red response 4 Response to i3 5 Response to i4 6 i3 addendum 7 i4 addendum

Basic situation

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Red should go here:

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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

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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:

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CASE #1: Blue has i5. SOLUTION:

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

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CASE #3: Blue has i7. SOLUTION:

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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:

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CASE #1: Blue has g5. SOLUTION:

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

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CASE #3: Blue has e7. SOLUTION:

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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.

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

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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.

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

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