4. Lucija, Mate, and Karla are adding up their math grades. Each of them has 4 grades. Lucija says: "All my grades are odd, and three are the same. The sum of all is greater than 16." Mate says: "Ah, I usually have all different grades!" Karla says: "All my grades are the same, their sum is a two-digit number and can be divided by 8." The sum of all their grades, when divided by 10, gives a remainder of 8. Write the grades of each individual student.
4. Lucija's grades can be 3 ones and 1 three, 3 ones and 1 five, 3 threes and 1 one,

3 threes and 1 five, 3 fives and 1 one, or 3 fives and 1 three.

$1 \mathrm{POINT}$

Since their sum must be greater than 16, we conclude that Lucija's grades are 5, 5, 5, and $3. \quad 2$ POINTS

All Karla's grades are equal, which means they can be 4 ones, 4 twos, 4 threes,

4 fours, or 4 fives.

$1 \mathrm{POINT}$

A two-digit sum divisible by 8 is given only by 4 fours $(4 \cdot 4=16$ ), so

Karla's grades are 4, 4, 4, and 4.

2 POINTS

The sum of Lucija's and Karla's grades is $18+16=34$.

$1 \mathrm{POINT}$

All Maja's grades are different, which gives the following possibilities:

$1,2,3,4$ (sum 10);

$1,2,3,5$ (sum 11);

$1,2,4,5$ (sum 12);

$1,3,4,5$ (sum 13);

2, 3, 4, 5 (sum 14).

$1 \mathrm{POINT}$

These possibilities for Maja's grades, when added to Lucija's and Karla's grades, give sums

$34+10=44, \quad 34+11=45,34+12=46,34+13=47$ and $34+14=48. \quad 1$ POINT

Since only 48 gives a remainder of 8 when divided by 10, then Maja's grades are 2, 3, 4, and $5. \quad 1$ POINT

TOTAL 10 POINTS