Mathematical_Recreations-Kraitchik-2e

314 Mathematical Recreations
n=2 n=3 n=4
II /2 ~ tl /1 /2 fa ta ~ tl /1 /2 fa h t4 ta ~ tl
h /2 ~ tl /1 /a /a ta ~ tl /1 /2 /a /4 t4 ta ~ tl
h ~ /2 tl /1 /2 ta /a ~ tl /1 /2 /a t4 h ta ~ tl
11 ~ /2 tl h /2 ta fa ~ tl h/2fa t4 h ta ~ tl
/1 ~ tl /2 h /2 ta ~ ta tl /1 /2 /a t4 ta /4 ~ tl
~ h tl 12 /1 ta /2 ~ ta tl /1 /2 t4 fa ta h ~ tl
t-.. h tl /2 /1 ta /2 ~ ta tl /1 /2 t4 /a ta /4 ~ tl
~ tl h /2 ta /1 /2 ~ ta tl /1 t4 /2 fa ta h ~ tl
~ tl h /2 ta /1 ~ /2 ta tl /1 t4 /2 ta /a h ~ tl
ta /1 ~ /2 tl ta /1 t4 h ta fa ~h tl
ta h ~ h tl fa /1 t4 h ta /a ~ /4 tl
ta h ~ tl /2 /a It t4 /2 ta /a ~ tl /4
ta ~ /1 tl /2 /a /1 t4 /2 ta ~ /a tl /4
fa ~ /1 tl /2 /a /1 t4 ta h ~ /a tl /4
ta ~ tl It /2 fa t4 /1 ta /2 ~ /a tl h
fa ~ tl II /2 /a t4 II fa h ~ fa tl /4
t4 ta /1 /2 ~ /a tl /4
f4 ta /1 ~ /2 /a tl /4
f4 fa /1 ~ /2 tl /a /4
f4 fa /1 ~ /2 tl /a h
f4 fa It ~ tl /2 /a /4
f4 fa ~ /1 fl /2 /a h
f4 fa ~ /1 tl h /a h
t4 ta ~ tl /1 h /a /4
t4 ta ~ tl /1 /2 /a h
Another game of the same nature is played on a 7 X 7
chessboard; 24 white pawns and 24 black pawns are arranged
as in Figure 176. The same rules apply for moves in
rows or columns as in the game of frogs and toads. Again
one must interchange the positions of the two sides. To succeed
one interchanges first the pieces in the middle row, then
those in the middle column. From the solutions given for
the frogs and toads one observes that each position is free at
some time. Hence, as one frees a position in the middle col-