Mathematical_Recreations-Kraitchik-2e

flS6
Mathematical Recreations
corner and so preventing White from sacrificing two queens
to win.
It is easy to see that four queens are sufficient by placing
the fourth queen on g3 in Figure 153. Black will then have
no refuge.
Now suppose the Black queen is not on the long diagonal
and the three White queens are on the strategic triangle, c3, c5,
j4 (or j4, j6, c5) (Figure 154). The Black queen must be on
FIGURE 154. Strategic Triangle.
dS or h4. In either case she will be easily captured, with or
without the move, as the following examples show.
White Black White Black White Black White Black
1 c3-a5 dS-f6 dS-M
2 c5-e7 xd8 c3-a5 h4-f6 h4-d8 h4-el
3 f4-c7 xb6 c5- e7 xd8 f4-h2 c5-g1 el-h4
d8-{{!
4 xc7 f4-c7 xb6 c5 -- e7 xdS gl-f2 xel
5 xc7 h2-c7 etc. f4-d2 etc.
If Black is not on the long diagonal and it is White to play,
White can always capture the strategic position.
Ther~ is an interesting variation of give-away in the French
game. If White starts with all 12 pawns in the usual position,
while Black has but one pawn, on b8, it can be shown