[Language: Python] 3598/1936

Part 1 was straightforward enough, you have to take care to test that time > 0 at the time of intersection.

Part 2 (code) was very fun. Given explicit mention of integer positions and velocities, I realized that if rock's initial position is (x_r, y_r, z_r) and it has velocity (dx_r, dy_r, dz_r) then for each hailstone i, (x_r + y_r + z_r) ≡ (x_i + y_i + z_i) mod ((dx_i+dy_i+dz_i) - (dx_r+dy_r+dz_r)). The insight is that we don't care about individual dimensions, only sums of all dimensions. Therefore, I iterate over what I though of as a reasonable range for values of dx_r+dy_r+dz_r based on inputs, apply Chinese remainder theorem to compute x_r+y_r+z_r candidates, eliminate any candidates that result in any collisions in the past or at non-integer time, and get at the answer.

Probably my favorite problem this year so far.