A five digit odd number whose ten thousand digit is twice the hundreds digit, exactly one digit is repeated
To find the five-digit odd number that satisfies the given conditions, follow these steps:
Step 1: Understand the conditions
The ten thousand digit is twice the hundreds digit, and exactly one of the digits is repeated.
Step 2: Determine the range of possible values
For the ten thousand digit to be twice the hundreds digit, it must be within the range of 2 to 9. The hundreds digit can, therefore, be within the range of 1 to 4, as it is half the ten thousand digit.
Step 3: Find the repeated digit
Since exactly one digit is repeated, and we already know that the hundreds digit is half the ten thousand digit, one of the repeated digits must be either 2 or 4.
Step 4: Construct the five-digit odd number
To construct the five-digit odd number, we can set the digits in decreasing order starting from the ten thousand digit and alternating the repeated digit. For simplicity, let's assume the repeated digit is 2.
The number would be in the form: 9 _ _ 2 9.
Step 5: Determine the last digit
The last digit of the number must be odd to ensure that the overall number is odd. Since the only odd digits left are 1, 3, 5, 7, and 9, we can choose any of these as the last digit.
Step 6: Finalize the number
Combining the results from the previous steps, we have the following possible numbers:
- 92291
- 92491
- 92791
- 92991
These are the four five-digit odd numbers that satisfy the given conditions.