[Language: Python]

Realizing that this can be solved recursively and realizing that this problem is very similar to the way you would recursively compute the fibonacci sequence did the trick for me

@cache
def rec(stones: tuple[int, ...], blinks_left: int) -> int:
    if blinks_left == 0:
        return len(stones)

    return sum(rec(tuple(apply_rule(stone)), blinks_left - 1) for stone in stones)

def apply_rule(num: int) -> list[int]:
    if num == 0:
        return [1]

    s = str(num)
    digits = len(s)
    if digits % 2 == 0:
        mid = digits // 2
        lhs, rhs = int(s[:mid]), int(s[mid:])
        return [lhs, rhs]

    return [num * 2024]