Example 10. Lamp poles are installed along the road side on every 8m. Markings are made on the road side on every 12m. How many markings are made beside the lamp poles along a 240m long road?
**Editorial input convention:** Assume a pole and a marking share the starting point at 0 m, both patterns continue from it, and both endpoints of the 240-m segment are counted.
Exercise 14. The figure is made up of a semicircle and a right triangle. Given that the diameter of the semicircle is 42cm and the difference in area of region $A$ and region $B$ is $357\text{ cm}^2$, find the height of the triangle. Take $\pi=\frac{22}{7}$.
**Editorial input convention:** Use the pictured orientation: the area of A exceeds that of B by 357 square centimetres. The triangle base is the 42-cm semicircle diameter. Enter its perpendicular height in centimetres.
Exercise 9. Fill in each cell of a $3\times3$ table one of the numbers $1,2,3,\ldots,9$ such that each number is used exactly once. It is given that the three multiples of 3 must be located in different rows and different columns. In how many ways can these numbers be filled ?
**Editorial input convention:** Rows and columns are fixed positions; count rotated or reflected arrangements separately.
**Editorial input convention:** Enter all four ordered pairs (x,y) in part order a,b,c,d. Use parentheses, a comma inside each pair, and semicolons between pairs, with no spaces anywhere. Format example, not the answer: (1,2);(3,4);(5,6);(7,8).
Question 41. Find the value of the following expression and round off your answer to the nearest integer.
$$\frac{99.9\times9}{11}+\frac{0.99\times99}{1.1}+\frac{99.9\times9}{1.1}+\frac{9.99\times9}{11}.$$
Question 6. Pierre celebrated his birthday on February 2, 2001. On that day, his age equalled the sum of the digits in the year in which he was born. In what year was Pierre born?
Exercise 4. A tank has three pipes. The first pipe can fill $\frac12$ of the tank in 1 hour while the second pipe can fill $\frac13$ part in 1 hour. The third pipe is used for making the tank empty. When all three pipes are open, $\frac7{12}$ part of the tank is filled in 1 hour. How much time will the third pipe take to empty the completely filled tank alone?
**Editorial input convention:** Assume all flow rates are constant while water is available, with no other flows. Enter the outlet-alone time in hours.
Exercise 8. If the odd numbers are grouped in the following way:
$$\{1\};\ \{3,5\};\ \{7,9,11\};\ \{13,15,17,19\};\ \ldots$$
what is the middle number in the $101^{\mathrm{th}}$ group?
**Editorial input convention:** Group n contains the next n consecutive positive odd integers, continuing without gaps.
Exercise 5. Find the digits represented by $a$ and $b$ in $\overline{a7889b}$ so that it is divisible by 15.
**Editorial input convention:** List all valid ordered pairs (a,b) by increasing a. Use parentheses, commas inside pairs and semicolons between pairs, with no spaces anywhere. Format example, not the answer: (1,2);(3,4). Different letters need not be different digits.
Exercise 13. How many different whole numbers are there containing only the digits 1 and/or 2 (each of these digits can be used one or more times or not at all) such that for each of these numbers, the sum of all of its digits equals seven?
