------
## 最终结论
```python
def is_power_of_two_permutation(n):
    # Generate the set of powers of 2 less than or equal to 10^9
    def generate_powers_of_two(limit):
        powers_of_two = set()
        i = 0
        while True:
            power = 2 ** i
            if power > limit:
                break
            powers_of_two.add(power)
            i += 1
        return powers_of_two

    powers_of_two_set = generate_powers_of_two(10**9)

    # Get all valid permutations of n's digits
    from itertools import permutations

    def get_permutations(n):
        str_n = str(n)
        perm_set = set()

        for perm in permutations(str_n):
            num_str = ''.join(perm)
            if num_str[0] != '0':
                perm_set.add(int(num_str))

        return perm_set

    permutations_of_n = get_permutations(n)

    # Check if any permutation is a power of two
    for perm in permutations_of_n:
        if perm in powers_of_two_set:
            return True

    return False

# Example usage
print(is_power_of_two_permutation(1))   # Output: True
print(is_power_of_two_permutation(10))  # Output: False
print(is_power_of_two_permutation(16))  # Output: True
print(is_power_of_two_permutation(24))  # Output: False
print(is_power_of_two_permutation(46))  # Output: True
```