Primes again!
Let be a set of prime numbers such that every digit from appear only once in the set.
Let the sum of those primes in . What is the smallest possible ?
As an explicit example, we could have so .
The answer is 207.
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1 solution
To obtain the smallest possible T we must try to use only one or two digits primes.
if we have a two digits prime so the digits ( 2 , 4 , 5 , 6 , 8 ) must appear in the 1 0 ′ s . but the 2 and 5 could appear as a single digit prime So :
the smallest T should be T = 1 + 2 + 3 + 5 + 7 + 9 + 4 0 + 6 0 + 8 0 = 2 0 7 .
and the possible sets S are:
{ 2 , 3 , 5 , 4 1 , 6 7 , 8 9 } , { 2 , 3 , 5 , 4 7 , 6 1 , 8 9 } , { 2 , 5 , 7 , 4 3 , 6 1 , 8 9 }