If you use the eight digits 1,2,3,4,5,6,7, and 9 each once and only once to form 4 two-digit prime numbers, what will be the sum of the four prime numbers?

Question

If you use the eight digits 1,2,3,4,5,6,7 and 9 each once and ONLY once to form 4 two-digit prime numbers. What will be the sum of the four prime numbers you created?

Answer 1

In order for a 2 digit number to be prime, the units digit cannot be even or 5, If it's even the 2 digit number is even and divisible by 2. If it ends in a 5, then the 2 digit number is divisible by 5.

 

So your units digits are 1, 3, 7, 9 and the tens column is 2, 4, 5, and 6.

 

the primes in the 20s are 23 and 29.

the primes in the 40s are 41, 43, 47

the primes in the 50s are 53 and 59

the primes in the 60s are 61 and 67

 

Suppose you pick 23. that forces 59 to be your choice. Now look at the 40s and 60s. 43 is out so pick 41 which forces 67. Their sum is 190.

This is not the only answer.

 

ex....29, 53 and 41, 67   or 29, 53 and 47, 61

 

In all cases, the sum is 190.

Answer 2

The four two digit numbers formed by adding the digits 1,2,3,4,5,6,7 & 9 are:

 

23, 59, 61 and 74

 

The sum of the four numbers is 217.

 

Will Grondski

Princeton, NJ 08543