As you travel to new planets in the space age, you discover a culture that does not use the digits 2,5,7,or 8. They would like to use 3-digit numbers for their zip codes, but they have superstition that beginning a zip code with zero brings bad luck to the people whom lives there. Can you help them figure out how many zip codes they can use?
Hint Begin by listing all the combinations that begin with 1. Hers's a start:
100 110 130 140 160 190
101 111 131 141 161 191
103
104
106
109
The next line would be...
103 113 133 143 153 163 193
you take it from there.
I don't know I need help to!
To help the culture figure out how many zip codes they can use, we need to consider the restrictions and requirements they have:
1. The zip code must be a 3-digit number.
2. The zip code cannot start with zero.
3. The digits 2, 5, 7, and 8 cannot be used.
Based on the given digits, the culture can only use the digits 0, 1, 3, 4, 6, and 9. Let's begin listing the combinations:
To find all the possible combinations, we can use a systematic approach. Start by listing all the options for the first digit, which cannot be zero. The options are 1, 3, 4, 6, and 9.
For each of these first digits, list all the options for the second digit. Since the culture cannot use the digits 2, 5, 7, and 8, the options for the second digit would be 0, 1, 3, 4, 6, and 9.
Finally, for each combination of the first two digits, list all the options for the third digit. Again, we can use the same set of digits: 0, 1, 3, 4, 6, and 9.
Let's continue listing the combinations using this approach:
First digit: 1
Second digit: 0, 1, 3, 4, 6, 9
Third digit: 0, 1, 3, 4, 6, 9
The possible combinations for the first digit being 1 are:
100, 101, 103, 104, 106, 109
Similarly, we can repeat this process for the other first digits (3, 4, 6, and 9).
To make it easier, I have listed the combinations for the first digit being 1. You can expand this approach to find combinations for the remaining 4 first digits.
First digit: 1
Second digit: 0, 1, 3, 4, 6, 9
Third digit: 0, 1, 3, 4, 6, 9
The possible combinations for the first digit being 1 are:
100, 101, 103, 104, 106, 109
To calculate the total number of combinations, you can multiply the options for each digit:
Number of options for the first digit: 5 (1, 3, 4, 6, 9)
Number of options for the second digit: 6 (0, 1, 3, 4, 6, 9)
Number of options for the third digit: 6 (0, 1, 3, 4, 6, 9)
Total number of zip codes: 5 * 6 * 6 = 180
Therefore, the culture can use a total of 180 zip codes that satisfy their requirements and restrictions.
Note: This calculation assumes that repetition of digits is allowed in zip codes. If repetition is not allowed, then the calculation would be different.