4. Ana chose the digits $1,2,3,4,5,6,7$ and 9. She decided to form groups of 4 prime numbers and use all the chosen digits for each group of prime numbers. What is the sum of the prime numbers in each group?

Naloge rešuj samostojno. Za reševanje imaš na voljo 210 minut.

Uporaba zapiskov, literature ali žepnega računala ni dovoljena.

48th Mathematical Competition

for high school students of Slovenia

Ljutomer, April 17, 2004

## Tasks for 2nd year students
I/4. Ana can form a group of prime numbers $\{23,41,59,67\}$ with the selected digits. To avoid searching for all possible groups of prime numbers, let's think differently. A two-digit prime number cannot end with any of the digits $2,4,5$ or 6, so these digits must appear in the tens place. No matter how Ana forms a group of 4 prime numbers, their sum is equal to $10 \cdot(2+4+5+$ 6) $+(1+3+7+9)=170+20=190$.