It is 7 digit even number.There is no repetition of digits. The digit 5 is in thousands place. The greatest digit is in thee millions place. the digit in the hundred thousandsplace twice the digit in the hundreds place.The digit in the thousands place is thetwice the digit in the ones place. the digit in the tens place is 2 less than the digit in the millions place. The value of the digit in the thousands place is 0

9805472

7089530

9,805,472

16,005,070

To find the 7-digit even number that satisfies all the given conditions, we need to analyze the information provided step by step.

1. The digit 5 is in thousands place:
Since the digit in the thousands place is 5, we know that the 7-digit number will have 5 in its thousands place.

2. The greatest digit is in the millions place:
Since the millions place has the greatest digit, we know that the digit in the millions place is either 6, 7, 8, or 9. Let's say it is X.

3. The digit in the hundreds place is half the digit in the hundred thousands place:
The digit in the hundred thousands place is twice the digit in the hundreds place. We can represent this as 2Y = Z, where Y is the digit in the hundreds place and Z is the digit in the hundred thousands place.

4. The digit in the thousands place is twice the digit in the ones place:
The digit in the thousands place is twice the digit in the ones place. We can represent this as 2A = 0, where A is the digit in the ones place.

5. The digit in the tens place is two less than the digit in the millions place:
The digit in the tens place is 2 less than the digit in the millions place. We can represent this as B = X - 2, where B is the digit in the tens place.

Now, let's consider the given information again and start solving the equations.

From Point 1, we know that the digit in the thousands place is 5. So, A = 5/2 = 2.5 Since we are looking for a whole number, we can disregard this possibility.

Now we have to consider the case when A = 0.

From Point 4, we know that A = 0.

Also, from Point 2, we know that X is the greatest digit. So X = 9.

From Point 5, we know that B = X - 2 = 9 - 2 = 7.

From Point 3, we know that 2Y = Z. Since Y and Z are different digits with no repetition, possible values for Y and Z are 1 and 2 or 2 and 4. But since Z is the digit in hundred thousands place, which is greater than Y, Y should be 1 and Z should be 2.

Now, let's reconstruct the 7-digit even number based on the obtained values: 9_X_725

Since 5 is in the thousands place and the digit in the thousands place is twice the digit in the ones place, we can conclude that the digit in the ones place is 2. Thus, our 7-digit even number becomes 9_X_7252.

Considering the condition that there is no repetition of digits, we can conclude that the greatest digit is 8, and our resulting 7-digit even number is 9857252.

So, the 7-digit even number that satisfies all the given conditions is 9857252.