A factory makes automobile parts, 5C7, 1O6 or 3Z0, which are of 5,000 parts, what is the minimum number of parts with the same serial number?
Assuming all 26 letters are used, and the first and last are digits, i.e. NAN, where N=digits 0-9, A=letter A-Z, there are, using the multiplication principle, 10*26*10=2600 distinct part numbers.
What is the minimum number of parts with the same serial number when there are 5000 parts and 2600 numbers available?
5000
To find the minimum number of parts with the same serial number, we need to determine the greatest common divisor (GCD) of the three possible serial numbers: 5C7, 1O6, and 3Z0.
Let's break down each serial number into its constituent digits:
5C7 = 5, C, 7
1O6 = 1, O, 6
3Z0 = 3, Z, 0
Since we don't know the numerical values for C, O, or Z, we'll consider them as placeholders for unknown digits. However, we do know that each serial number has three digits.
To find the GCD, we need to find the common factors between the three sets of digits. The common factors will represent the minimum number of parts with the same serial number.
Let's analyze each digit separately:
For the first digit, we have 5 in 5C7, 1 in 1O6, and 3 in 3Z0. The common factor for the first digit is 1 because it appears in all three serial numbers.
For the third digit, we have 7 in 5C7, 6 in 1O6, and 0 in 3Z0. The common factor for the third digit is 1 because it appears in all three serial numbers.
Now, let's consider the second digit. We have C in 5C7, O in 1O6, and Z in 3Z0. Since C, O, and Z are placeholders for unknown digits, we cannot determine their exact values. Therefore, the second digit does not have a common factor across the three serial numbers.
To summarize, the minimum number of parts with the same serial number is 1 because the first digit (either 5, 1, or 3) and the third digit (either 7, 6, or 0) appear in all three possible serial numbers. However, the second digit can vary since it represents unknown placeholders (C, O, or Z).