The Solution

The Karn can always annihilate the Nexus! No matter how clever, astute and elusive they try to be! But curious though it may seem, the Karn can only do so after they have paid a particular visit to the Galaxy marked “1” above going in by 3 and exiting by 2 or entering by 2 and leaving by 3.
:The 3 Galaxies bearing the letters A, B and C do not really come into the equation as some may suppose, for the simple reason that the Karn never need to enter any one of them, while the enemy cannot be forced to go into them, and would clearly be ill-advised to do so voluntarily! We may therefore leave those out of consideration altogether.
No matter what the Nexus may do, The Karn should make the following first nine moves and visit Galaxies 24,20,19,15,11,7,3,1,2. If the Nexus take it into their head also to go to galaxy 1 it will be found that they will have to beat a hasty retreat, the same way that they went in, or the Karn will invariably catch them in Galaxies 2 or 3 as the case may be.
:So the Nexus would be wise to avoid that North West sector of the Universe altogether.
Now when the Karn have made the first 9 moves above, the Nexus will be (after their own 9th move) in one of the Galaxies 5,8,11,13,14,16,19,21,24, or 27.
Of course, if they imprudently go to 3 or 6 at this point they will be caught at once.
Wherever the Nexus are the Karn go for them and they will no longer have any difficulty in catching them in 8 more moves at most (17 in all) in one of the following ways:
: a) The Karn will get to Galaxy 8 when the Nexus are at 5 and win on the next move.
: b) Or the Karn will get to 19 when the Nexus are at 22 and win on the next move
: c) Or the Karn will get to 24 when the Nexus are at 27 and win on the next move
It will be found that the Nexus can be forced into one of the above three fatal positions.
:In short the strategy amounts to this:
The Karn play their first 9 moves as described above and although the Nexus do their best to avoid contact, the Karn go after them and are always driving them away from that North West corner, ultimately closing in on them and so win.
:If after the first 9 moves above are made the Karn make a few weak moves it will not matter, they may lose time but cannot lose their advantage so long as now they keep the Nexus from Galaxy 1 they must eventually annihilate them.
Below is a game between Hesterix with the Karn forces (K) and Hengist using the Nexus forces (N).
Hesterix’s moves are above (Karn) whilst Hengist’s (Nexus) are below.
:KARN--- 24, 20, 19, 15, 11, 7, 3, 1, 2, 6, 10, 14, 18, 19, 20, 24
:NEXUS-- 13, 9, 13, 17, 21, 20, 24, 23, 19, 15, 19, 23, 24, 25, 27,
:Hengist must now go to 25 or K in either of which galaxies he is annihilated.
“A little topographical problem worthy of great study” - Hesterix
Hengist 10:11, 1 August 2009 (UTC)
Category:Havok