Question 168255: Please help me solve this problem:
There are three digits such that any two of them, written in any order, serve as the digits of a two-digit prime number. Find all three of these digits and give example of how you got the answer.
Answer by 303795(602)   (Show Source):
You can put this solution on YOUR website! You have ten digits to select from.
If any even number is included then a two digit number ending in that number would not be a prime number.
You now have the five odd digits to choose from.
Any two digit number ending in 5 will have 5 as a factor of that number so 5 can not be one of the three numbers.
The three numbers must be chosen from 1, 3, 7 and 9
There are 12 numbers to consider from the four digits
13, 17, 19 - all prime
31, 37, 39 - first two are prime and 39 is not prime(3 x 13)
71, 73, 79 - all prime
91, 93, 97 - 91 is not prime (7x13) 93 is not prime (31 x 3) and 97 is prime.
Problems only occur if 9 is included so the digits must be 1, 3 and 7.
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