H. G. Muller wrote on Wed, Jul 9, 2008 10:27 AM UTC:
Some more data about mating potential of the short-range leapers:
Betza NR NAME Longest mate (if generally won)
8x8 10x10 12x12 14x14 16x16
F 4 Ferz color bound
W 4 Wazir pure alternator
A 4 Alfil color bound
D 4 Dabbaba color bound
N 8 Knight pure alternator
FW 8 Commoner 18 29 49 62 -
FA 8 modern Elephant color bound
FD 8 ? color bound
WA 8 Waffle no mates
WD 8 Woody Rook 29 52 -
AD 8 Alibaba color bound
FN 12 ? 22 32 44 59 100
WN 12 Vicar pure alternator
AN 12 Kangaroo 35 63 -
DN 12 Carpenter 31 44 62 92 -
FWA 12 Crowned Alfil 15 22 31 41 53
FWD 12 Crowned Dabbaba 15 20 27 33 40
FAD 12 ? color bound
WAD 12 ? 26 39 -
FWN 16 Centaur 13 17 21 28 33
FAN 16 High Priestess 17 23 30 36 45
FDN 16 ? 14 19 25 31 38
WAN 16 ? 22 31 43 57 74
WDN 16 Minister 17 23 30 36 45
ADN 16 Squirrel 19 24 31 38 46
FWAD 16 Mastodon 13 19 24 29 36
FWADN 24 Lion 5 7 9 10 12
Note that the Lion does not need King assistence to perform the checkmate,
which is why it can be so fast. It is easy to prove it can mate on boards
of any size, and indeed on an infinitely large board (which is not the
same!). It does not even need a corner, just an edge.
'no mates' means that the piece does not cover two orthogonally
neighboring squares, which is the minimum requirement to create a
checkmate position (in a corner). Being color-bound, or a pure color
alternator implies this.
Some more data about mating potential of the short-range leapers: Betza NR NAME Longest mate (if generally won) 8x8 10x10 12x12 14x14 16x16 F 4 Ferz color bound W 4 Wazir pure alternator A 4 Alfil color bound D 4 Dabbaba color bound N 8 Knight pure alternator FW 8 Commoner 18 29 49 62 - FA 8 modern Elephant color bound FD 8 ? color bound WA 8 Waffle no mates WD 8 Woody Rook 29 52 - AD 8 Alibaba color bound FN 12 ? 22 32 44 59 100 WN 12 Vicar pure alternator AN 12 Kangaroo 35 63 - DN 12 Carpenter 31 44 62 92 - FWA 12 Crowned Alfil 15 22 31 41 53 FWD 12 Crowned Dabbaba 15 20 27 33 40 FAD 12 ? color bound WAD 12 ? 26 39 - FWN 16 Centaur 13 17 21 28 33 FAN 16 High Priestess 17 23 30 36 45 FDN 16 ? 14 19 25 31 38 WAN 16 ? 22 31 43 57 74 WDN 16 Minister 17 23 30 36 45 ADN 16 Squirrel 19 24 31 38 46 FWAD 16 Mastodon 13 19 24 29 36 FWADN 24 Lion 5 7 9 10 12 Note that the Lion does not need King assistence to perform the checkmate, which is why it can be so fast. It is easy to prove it can mate on boards of any size, and indeed on an infinitely large board (which is not the same!). It does not even need a corner, just an edge. 'no mates' means that the piece does not cover two orthogonally neighboring squares, which is the minimum requirement to create a checkmate position (in a corner). Being color-bound, or a pure color alternator implies this.