6. On domino tiles, there are pairs of numbers from 0 to 6 (including numbers 0 and 6) located on two fields. All numbers, except zero, are represented by the corresponding number of dots. An empty field without dots represents zero. In a complete set of domino tiles, there are also tiles with the same values on both fields (for example: 1 - 1, ...). How many dots are there in total in the entire set of domino tiles?
First method:

On tiles where one field is empty (0), on the remaining fields there can be

$0,1,2,3,4,5$ or 6. For their marking, $1+2+3+4+5+6=21$ dots are needed. 1 POINT On tiles where one field is 1, on the remaining fields there can be 1, 2, 3, 4, 5 or 6.

For their marking, $6 \cdot 1+1+2+3+4+5+6=27$ dots are needed. 2 POINTS

On tiles where one field is 2, on the remaining fields there can be 2, 3, 4, 5 or 6.

For their marking, $5 \cdot 2+2+3+4+5+6=30$ dots are needed. 2 POINTS

On tiles where one field is 3, on the remaining fields there can be 3, 4, 5 or 6.

For their marking, $4 \cdot 3+3+4+5+6=30$ dots are needed. 1 POINT

On tiles where one field is 4, on the remaining fields there can be 4, 5 or 6.

For their marking, $3 \cdot 4+4+5+6=27$ dots are needed. 1 POINT

On tiles where one field is 5, on the remaining fields there can be 5 or 6.

For their marking, $2 \cdot 5+5+6=21$ dots are needed. 1 POINT

On the tile where one field is 6, on the remaining field there can be 6.

For marking, 12 dots are needed. 1 POINT

In a complete set of domino tiles, there are a total of $21+27+30+30+27+21+12=168$ dots. 1 POINT

TOTAL 10 POINTS