Using the digit 1 to 9 once, write the largest possible 9-digit number that can be formed in which the digit in the hundred millions place is twice the digit in the thousands place, and the digit in the hundred thousands place is one-half the digit in the ten millions place.

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To find the largest possible 9-digit number that satisfies the given conditions, let's analyze the problem step-by-step:

Step 1: The digit in the hundred millions place is twice the digit in the thousands place.
Since we need to maximize the number, let's assign digit 9 to the hundred millions place and 4 to the thousands place.

Step 2: The digit in the hundred thousands place is one-half the digit in the ten millions place.
The digit in the ten millions place is the remaining largest digit, which is 8. Therefore, the digit in the hundred thousands place would be half of 8, which is 4.

Step 3: Filling the remaining places
We have the following digits remaining: 1, 2, 3, 5, 6, 7.
The next digit will be placed in the ten thousands place. To maximize the number, we will select the largest digit available, which is 7.

The remaining digits are as follows: 1, 2, 3, 5, 6.
Next, we will place the largest digit, 6, in the millions place.

The remaining digits are as follows: 1, 2, 3, 5.
The next digit will be placed in the tens place. To maximize the number, we will select the largest digit available, which is 5.

The remaining digits are as follows: 1, 2, 3.
Next, we will place the largest digit, 3, in the units place.

The remaining digits are as follows: 1, 2.
The next digit will be placed in the hundreds place. To maximize the number, we will select the largest digit available, which is 2.

Finally, the remaining digit, 1, will be placed in the tens of thousands place.

Putting it all together, the largest possible 9-digit number that satisfies the given conditions is 964,752,381.

To find the largest possible 9-digit number that satisfies the given conditions, we need to determine the values of each digit and arrange them accordingly.

Let's start by analyzing the given conditions:

1. The digit in the hundred millions place is twice the digit in the thousands place.
2. The digit in the hundred thousands place is one-half the digit in the ten millions place.

Now, since we want to create the largest possible 9-digit number, we should aim for the highest possible digit values in the higher places.

Let's assign the digits from 1 to 9 to their respective places:

Millions: _ _ _ _ _
Hundred thousands: _ _ _ _
Ten thousands: _ _ _
Thousands: _ _ _
Hundreds: _ _

Condition 1: The digit in the hundreds place will be half of the digit in the ten millions place. To maximize the number, we choose 9 as the highest possible value for the ten millions place, making the digit in the hundreds place 4 (half of 9).

Millions: _ _ _ _ 9
Hundred thousands: _ _ _ 4
Ten thousands: _ _ _
Thousands: _ _ _
Hundreds: _ _

Condition 2: The digit in the hundred millions place should be twice the digit in the thousands place. We know that the digit in the thousands place must be less than 9 (since all digits from 1 to 9 have already been used). So to maximize the value in the hundred millions place, we choose 8 as the highest possible value for the thousands place, making the digit in the hundred millions place 16 (twice 8).

Millions: _ _ _ _ 9
Hundred thousands: _ _ _ 4
Ten thousands: _ _ 1
Thousands: _ 8
Hundreds: _ _

Now, we need to assign the remaining digits, preserving the largest value for each place:

Millions: _ _ _ 5 9
Hundred thousands: _ _ _ 4
Ten thousands: _ _ 1
Thousands: _ 8
Hundreds: 7

The remaining available digits are 2, 3, and 6. We can place them in any order in the remaining places:

Millions: 6 2 3 5 9
Hundred thousands: _ _ _ 4
Ten thousands: _ _ 1
Thousands: _ 8
Hundreds: 7

Finally, let's place the remaining digits:

Millions: 6 2 3 5 9
Hundred thousands: 1 _ _ 4
Ten thousands: _ _ 1
Thousands: _ 8
Hundreds: 7

We can put 2 in the remaining hundred thousands place since it is the smallest available digit. The remaining digits 3 and 6 can be placed in either the ten thousands or the thousands place:

Millions: 6 2 3 5 9
Hundred thousands: 1 2 3 4
Ten thousands: 6 _ 1
Thousands: _ 8
Hundreds: 7

We have one remaining digit 3, which we can place in the ten thousands place:

Millions: 6 2 3 5 9
Hundred thousands: 1 2 3 4
Ten thousands: 6 3 1
Thousands: _ 8
Hundreds: 7

Finally, we place the remaining digit 8 in the thousands place:

Millions: 6 2 3 5 9
Hundred thousands: 1 2 3 4
Ten thousands: 6 3 1
Thousands: 8
Hundreds: 7

The largest possible 9-digit number that satisfies the given conditions is 623,591,431.