Solutions.
Problem No. 1.—1, P e8 O, any of four moves. 2, O d6 or f6, mate, accordingly.
Problem No. 2.—1, K c5, K g2: (or, Q, R, S, T, U). 2, L f3:‡.—(Q) O g1. 2, O g3‡.—(R) O h2. 2, O f2‡.—(S) O d2 or e1. 2, L h7‡.—(T) O g5 or h4. 2, L b1‡.—(U) O d4 or e5. 2, L b1 or h7‡.
Problem No. 5.
White: K a6; L f5; M a5, h1; N g1, h5; O b8, d1; P b2, c2, d5, g6, h3. Black: K c4; L g8; M h4; N f1; O a3; P a4, b4, b6, g2. (13 + 9 = 22 pieces.) White gives mate in two moves.
Problem No 6.
White: K b7; L f4; M d8; N a2; P a3, e5. Black: K c5; M h5; N f7, g1; O a8; P a5, b5, c2, c7. (6 + 9 = 15 pieces.) White gives mate in two moves.
Problem No. 7.
8 + 8 = 16 pieces.