P8714 [Lanqiao Cup 2020 NOI Qualifier B2] Fill-in-the-Blank Problems

## Task A: House Number Plate Making ### Problem Description Xiao Lan wants to make house number plates for the residents on a street. There are a total of $2020$ households on this street, and the house numbers are numbered from $1$ to $2020$. Xiao Lan’s method is to first make the digit characters $0$ to $9$, and then paste the required characters onto each plate. For example, the plate $1017$ needs to paste the characters `1`, `0`, `1`, `7` in order, which means it needs $1$ character `0`, $2$ characters `1`, and $1$ character `7`. To make all house number plates from $1$ to $2020$, how many characters `2` are needed in total? ### Answer Submission This is a fill-in-the-blank question. You only need to compute the result and submit it. The result is an integer. When submitting, only fill in this integer; any extra content will not be scored. ## Task B: Reduced Fractions ### Problem Description If the greatest common divisor of the numerator and denominator of a fraction is $1$, then the fraction is called a reduced fraction. For example, $\frac{3}{4},\frac{5}{2},\frac{1}{8},\frac{7}{1}$ are all reduced fractions. How many reduced fractions are there such that both the numerator and the denominator are integers between $1$ and $2020$ (including $1$ and $2020$)? ### Answer Submission This is a fill-in-the-blank question. You only need to compute the result and submit it. The result is an integer. When submitting, only fill in this integer; any extra content will not be scored. ## Task C: Snake-like Filling ### Problem Description As shown in the figure below, Xiao Ming fills an infinite matrix in a “snake-like” pattern using positive integers starting from $1$. $\begin{array}{cccccc}1 & 2 & 6 & 7 & 15 & \ldots \\ 3 & 5 & 8 & 14 & \ldots & \\ 4 & 9 & 13 & \ldots & & \\ 10 & 12 & \ldots & & & \\ 11 & \ldots & & & & \\ \ldots & & & & & \end{array}$ It is easy to see that the number in the second row and second column is $5$. Please compute what number is in the $20$-th row and the $20$-th column of the matrix. ### Answer Submission This is a fill-in-the-blank question. You only need to compute the result and submit it. The result is an integer. When submitting, only fill in this integer; any extra content will not be scored. ## Task D: Running Exercise ### Problem Description Xiao Lan exercises every day. Normally, Xiao Lan runs $1$ kilometer per day. If a day is Monday or the first day of a month (the 1st), then to motivate himself, Xiao Lan runs $2$ kilometers. If it is both Monday and the first day of a month, Xiao Lan still runs $2$ kilometers. Xiao Lan has been running for a long time, from Saturday, January $1$, $2000$ (inclusive) to Thursday, October $1$, $2020$ (inclusive). How many kilometers did Xiao Lan run in total during this period? ### Answer Submission This is a fill-in-the-blank question. You only need to compute the result and submit it. The result is an integer. When submitting, only fill in this integer; any extra content will not be scored. ## Task E: Seven-Segment Code ### Problem Description Xiao Lan wants to use a seven-segment display to represent a special kind of characters.  The figure above shows a diagram of a seven-segment display. There are $7$ segments that can light up, labeled as $a,b,c,d,e,f,g$. Xiao Lan wants to select some segments (at least one) to light up to represent a character. When designing the representation, all lit segments are required to form one connected component. For example: if $b$ is lit and all other segments are not lit, it can represent one character. For example: if $\mathrm{c}$ is lit and all other segments are not lit, it can represent one character. This scheme can represent a different character from the one in the previous line, even though they look quite similar. For example: if $a,b,c,d,e$ are lit and $f,g$ are not lit, it can represent one character. For example: if $b,f$ are lit and all other segments are not lit, then it cannot represent a character, because the lit segments are not connected. How many different characters can Xiao Lan represent using a seven-segment display? ### Answer Submission This is a fill-in-the-blank question. You only need to compute the result and submit it. The result is an integer. When submitting, only fill in this integer; any extra content will not be scored.

Input one uppercase letter, indicating which task it is.

According to the input task letter, output the corresponding answer.

Answer template for reference. ```cpp #include using namespace std; int main() { string ans [] = { "The answer of task A", // Replace the content in quotes with the answer to task A "The answer of task B", // Replace the content in quotes with the answer to task B "The answer of task C", // Replace the content in quotes with the answer to task C "The answer of task D", // Replace the content in quotes with the answer to task D "The answer of task E" // Replace the content in quotes with the answer to task E }; char T; cin >> T; cout