# SOLUTION: 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 th

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 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(595)   (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.