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Printjmc
prealgebra senior
Problem
Pick two or fewer different digits from the set and arrange them to form a number. How many prime numbers can we create in this manner?
Solution
We have two cases: the number is either 1-digit or 2-digit. We examine each of these cases separately.
Case 1: 1 digit
In this case, the only 1-digit primes are 3 and 7, for a total of 2 primes.
Case 2: 2 digits
We have the following combinations of numbers: 13, 16, 17, 36, 37, 67, 76, 73, 63, 71, 61, 31. Out of these 12 numbers, it is easier to count the composites: 16, 36, 76, and 63 for a total of 4 composites, which we subtract from the original 12 numbers to yield primes in this case.
Both cases considered, the total number of prime numbers we can create is .
Case 1: 1 digit
In this case, the only 1-digit primes are 3 and 7, for a total of 2 primes.
Case 2: 2 digits
We have the following combinations of numbers: 13, 16, 17, 36, 37, 67, 76, 73, 63, 71, 61, 31. Out of these 12 numbers, it is easier to count the composites: 16, 36, 76, and 63 for a total of 4 composites, which we subtract from the original 12 numbers to yield primes in this case.
Both cases considered, the total number of prime numbers we can create is .
Final answer
10