Kook on 



of the Pieces in Chess. 



Number of 



223 



Number of 

 safe checks. 



a 2n— 4 



b 2n— 5 



e 2ti-6 



The chance 



such positions 

 of the rook. 



4 

 4(>-2) 

 0-2) 2 



_4(2?i-4)+4(n-2)(2tt-5) + p-2) 2 (2?i-6)_2(n-2) 



n 2 (n 2 -l) n(n + l)' 



When n=8 ; 



the chance = £. 



Simple check with one knight. 



The number of squares attacked by a knight placed on any- 

 square of a chessboard is given by the following scheme : — 



a 



b 



c 



c 





b 



c 



d 



d 





c 



d 



e 



e 





c 



d 



e 



e 















i«- llwl i 101 . n f Number of 



EnJgktan dSfa. such positions 



of knight. 



a 2 4 



5 3 8 



c 4 4fn-3^ 



d 6 4(w— 4) 



6 8 (rc-4) 2 



The chance of check 



2.4 + 3.8 + 4.4(n-3) + 6.4(n--4) + 8fo-4) 2 _ 8(n-2) 



n 2 (n 2 -l) n 2 (w + 1)* 



Ifn=8, 



chance = ^. 



For a knight all checks are safe checks. 



Simple check with one bishop. 

 We will at first assume that a bishop can be put on either a 



