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

190

Explanation:

You want the sum of four 2-digit prime numbers that can be formed from the set of digits {1, 2, 3, 4, 5, 6, 7, 9} using each digit only once.

Primes

There are 18 primes in the range 13-97 that have unique digits. These can be paired by the digits they use:

{23, 59} and {29, 53} . . . . number total = 82

{41, 67} and {47, 61} . . . . . number total = 108

Sets of 4

A set of 4 primes with unique digits can be formed by choosing one of the first two pairs together with one of the second two pairs. For example, one possible choice is ...

{23, 59, 47, 61}

However you do this, the sum of the four primes will be ...

82 +108 = 190

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