Make a list of distinct prime numbers, using the hexadecimal digits 1,3, 5, 7, 9, B, D, F exactly once each in the list. What is the minimum sum of all the numbers in such a list? What's the minimum product of all the numbers in such a list?

Bonus Question:

Make a list of distinct prime numbers, using the hexadecimal digits from 1 to F exactly once each in the list. What is the minimum sum of all the numbers in such a list? What's the minimum product of all the numbers in such a list?

Note: Think of this problem as an extension of Pretty Potent Primes.

The best possible case would be to have each of them alone.

But F is 15 and cannot be present alone. But it should be kept at unit place to make numbers minimum. So make 1F (16+15  = 31)

D = 13 can be alone, so can B = 11

9 cannot be alone. 1 is already used, So try 39 (48+9 = 57) which is not prime. Then try 59 (80+9= 89).

 the remaining 7 and 3 can also be alone. So list becomes

3, 7, 59, B, D, 1F

Sum = 9A

Product = 7E6C5D

Posted by Vishal Gupta on 2010-10-27 16:24:34