Spoiler (click to reveal)
Obviously, all of Grey's pieces except E4 are pinned, so move choices are limited. Upon first glance E4:F4(C9=6/B1=6) looks tempting, but White can simply respond with B1:F4 (via a ricochet at A1) for the win. So Grey has to move elsewhere. Grey's best chance of escape is to somehow get E4 to G5, and, with luck, to attack G2. So the best move for Grey is E4F5. White could respond with F4G1 (via a ricochet at I2). This would leave F9:F5 (via a wraparound) on the next move if Grey does not move it out of the way; also it creates a guerilla force which can exchange 1G1G2 to threaten G1:G6 on the following move. But since Grey already plans to move F5G5, the capture threat is a moot point. Worse, no matter what sort of pip exchange between G1 and G2 White devises, Grey can counter with bumps such as G5G6/g6G7 and/or pip exchanges that successfully defend G6 against any attack. A similar, although somewhat less elegant response would be C9F2 followed by a pip exchange, but neither of these responses prevents Grey from using the 1 on G5 effectively. Finding a move that does so is essential for White. Notice that C9 and B1 are adjacent. The pip exchange 1B1C9 sets up C9G7 followed by G2G7/G7:G6 for the win. This sequence is unstoppable, even by G5G6/G6:G7(B1=6/F7=5) because the 4 at G2 need not promote. The complete solution is: 1.... E4F5, 2. 1B1C9 F5G5, 3. C9G7 G5G6/G6:G7(B1=6/F7=5), 4. G2:G7.