MathDB

There are nine cards that have the digits

1, 2, 3, 4, 5, 6, 7, 8

and

9

written on them, with one digit on each card. Using all the cards, some numbers are formed (for example, the numbers

8

213

94

65

and

7

). a) If all the numbers formed are prime, determine the smallest possible value of their sum. b) If all formed numbers are composite, determine the smallest possible value of their sum.
Note: A number

p

is prime if its only divisors are

1

and

p

. A number is composite if it has more than two dividers. The number

1

is neither prime nor composite.

Problem Statement