Problem 3. Given the set $A=\{1,17,5,7,2,13,23\}$. For each two-element subset of $A$, Georgi writes the smaller number of the two chosen ones on the board. Determine the sum of the numbers that Georgi wrote on the board.
Solution. Georgi will write the numbers $1,1,1,1,1,1 \ldots$ for the subsets $\{1,2\},\{1,5\}, \ldots,\{1,23\} \ldots$ in order. Since $A=\{1,2,5,7,13,17,23\}$, each number Georgi will write on the board as many times as there are elements after it (if we look at the given numbers in ascending order from left to right), i.e., the desired sum will be

$$
6 \cdot 1+5 \cdot 2+4 \cdot 5+3 \cdot 7+2 \cdot 13+1 \cdot 17=6+10+20+21+26+17=100
$$