Solution to Study 1
The theme of this study (based, with reversal of colours, on a saving idea from the game R.A.Beach-M.J.Donnelly, Thornaby International 1973) is to threaten to simplify the position with a timely d5. Although white ends up being two pawns down the black forces are compromised in their positions and the extra pawns cannot advance to queen. Thus the solution is:
1. Ra7+ Kf8 2. Rb7 (not 2.d5 Re4+ 3. Kc5 Re5 4. Kd6 exd5 with advantage) Rg3 3. d5 Rg4+ 4. Kc5 Rg5 5. Kd6 exd5 6. Ke6 Rg6 (not 6...Rg7 as white mates with 7. Rb8) 7. Rd7 and draws.