The password to access my ATM card includes the digits 9, 4, 6, and 8....
Finding the Password of the ATM Card
Given information:
- Password includes the digits 9, 4, 6, and 8
- Password is the smallest 4 digit even number
Step 1: Listing Even 4-Digit Numbers
Before finding the password, we need to list all the even 4-digit numbers.
For a number to be even, its units digit must be 0, 2, 4, 6, or 8.
Therefore, we can start by listing all 4-digit numbers with units digit 0, 2, 4, 6, and 8.
There are 9000 4-digit numbers in total, and half of them are even. So, there are 4500 even 4-digit numbers.
Step 2: Eliminating Non-Valid Passwords
Next, we need to eliminate the numbers that do not have the digits 9, 4, 6, and 8.
We know that the password must include these digits, so any number that does not have them cannot be the password.
To eliminate non-valid passwords, we can start by checking the thousands digit of each even 4-digit number.
If the thousands digit is not 9, we can eliminate that number from consideration.
Similarly, we can check the hundreds digit, tens digit, and units digit of each even 4-digit number.
Any number that does not have the digits 9, 4, 6, and 8 in the correct positions can be eliminated.
Step 3: Finding the Smallest Password
After eliminating non-valid passwords, we can find the smallest password among the remaining numbers.
Since we have eliminated all non-valid passwords, we know that the password must be among the remaining even 4-digit numbers.
We can start by checking the even 4-digit numbers in ascending order until we find the smallest password.
The smallest password will be the first even 4-digit number that satisfies all the conditions: it must have the digits 9, 4, 6, and 8 in the correct positions.
Step 4: Final Answer
The smallest 4-digit even number that includes the digits 9, 4, 6, and 8 is 4689.
Therefore, the password of the ATM card is 4689.