7.90 Write the numbers $1,2, \cdots, 20$ in a row on a piece of paper. Two players, A and B, take turns placing the symbol “+” or “-” in front of one of the numbers (no repetition allowed). Player A aims to make the absolute value of the resulting sum as small as possible after placing all 20 symbols. Find the maximum absolute value of the sum that B can achieve.
［Solution］Divide 20 numbers into 10 pairs: $(1,2),(3,4), \cdots,(19,20)$. Each time A fills in a symbol, if it is before one of the numbers in the first 9 pairs, then B fills in the opposite symbol before the other number in the same pair; if A fills in a symbol before one of the numbers in the last pair, then B fills in the same symbol before the other number in the same pair. At this point, the absolute value of the final sum is no less than
$$
19+20-1-1-1-1-1-1-1-1-1=30 .
$$

It can be seen that the maximum absolute value of the sum that can be achieved is no less than 30.
On the other hand, we point out that as long as A always places the opposite symbol (if the sum is 0, then place a positive sign) before the largest remaining number each time A fills in a symbol, then B cannot obtain a sum greater than 30.

Consider the entire process of a game where A and B fill in symbols. Suppose the last time A changes the sign of the sum (including changing from 0 to positive) is the $k$-th time A fills in a symbol. Clearly, after A's $k$-th symbol (B has already filled in $k-1$ times), the numbers $20,19,18, \cdots, 20-(k-1)$ have already had symbols placed before them, and the largest number B can use for the $k$-th fill is $20-k$. Thus, at this point, the absolute value of the sum does not exceed $20-(k-1)+20-k=41-2 k$. Next, the two will each fill in symbols $10-k$ more times, and since the sign no longer changes, after each of them fills in a symbol once, the absolute value of the sum must decrease by at least 1. Therefore, the absolute value of the sum is no greater than
$$
41-2 k-(10-k)=31-k \leqslant 30 \text {. }
$$

In summary, the maximum absolute value of the sum that B can achieve is 30.