Question 4. Five points are located on a line. When the ten distances between pairs of points are listed from smallest to largest, the list reads:
$$2,4,5,7,8,k,13,15,17,19.$$
What is the value of $k$?
Exercise 12. Jack bought a rectangular shape drawing paper measuring 42cm by 27cm. He wants to cut the drawing paper into as many square shape papers as possible with the largest length.
(a) What is the length of each square?
(b) How many square shape papers can Jack made?
**Editorial input convention:** Cut the entire sheet into congruent squares in an edge-parallel grid, without offcuts. Maximise the common side length first, then count the squares. Enter side length in cm;number of squares, with no units or spaces. Format example, not the answer: 2;10.
Exercise 19. In the figure below, find the value of $x$.
**Editorial input convention:** For this exercise, assume the outer left side is perpendicular to the bottom base. Let x be the obtuse angle indicated by the unlabelled arc at the crossing. Enter degrees. These clarifications are editorial; the original figure lacks both the right-angle mark and the x label.
Exercise 7. The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both plan trips there. The senior class at High School A rents and fills 8 vans and 8 buses with 240 students. High School B rents and fills 4 vans and 1 bus with 54 students. Every van and every bus has the same number of students. Find the number of students in each bus.
**Editorial input convention:** All vans carry the same number as other vans, and all buses the same number as other buses; the two vehicle types may have different capacities.
Example 5. There are 65% of the students at Raffle Junior High School play piano, 40% of the students play basketball and 25% of the students both play piano and basketball. What is the percentage of the number of students who do neither play piano nor play basketball at Raffle Junior High School?
**Editorial input convention:** Enter the percentage number only, without the percent sign.
Question 24. George is trying to unlock the forgotten passcode for his luggage. The passcode consists of 3 digits, each of which is from 0 to 9.
He tried 923, only one digit is correct and correctly placed.
He tried 958, only one digit is correct but wrongly placed.
He tried 379, only two digits are both correct but wrongly placed.
He tried 142, none of the numbers is correct.
He tried 127, only one digit is correct but wrongly placed.
What is George’s passcode?
**Editorial input convention:** Every clue gives exact counts: any other digits in that guess are absent. “Wrongly placed” means present but not in that position. Repeated digits and leading zero are not excluded in advance. Enter exactly three digits without spaces.
Exercise 5. For years, telephone area codes in the United States and Canada consisted of a sequence of three digits. The first digit was an integer between 2 and 9, the second digit was either 0 or 1, and the third digit was any integer from 1 to 9.
(a) How many area codes were possible?
(b) How many area codes starting with a 4 were possible?
**Editorial input convention:** Use only the stated position rules, with endpoints 2 and 9 included and repetitions allowed. Enter the answers to a and b in that order, separated by one semicolon, with no spaces. Format example, not the answer: 10;2.
Exercise 13. The bus service numbers 06, 08 and 52 start at 6a.m every day. In every 10 minutes, 16 minutes and 20 minutes, each bus service will have 1 bus leaving the Terminal respectively. Find the next earliest time when the three bus services will leave the Terminal at the same time.
**Editorial input convention:** Assume the departures continue regularly after 06:00. Enter the next time in 24-hour HH:MM format, without spaces.
Question 26. Each day, Jenny ate 20% of the jellybeans that were in her jar at the beginning of that day. At the end of the second day, 32 remained. How many jellybeans were in the jar originally?
Question 17. Each of the digits 1, 2, 3, 4, 5, 6 and 7 is placed, one to a box, to form the two 2-digit numbers and one 3-digit number in the arithmetic problem shown.
$$M=\boxed{\phantom{0}}\boxed{\phantom{0}}\boxed{\phantom{0}}-\left(\boxed{\phantom{0}}\boxed{\phantom{0}}-\boxed{\phantom{0}}\boxed{\phantom{0}}\right).$$
What is the least possible value of $M$?
Question 10. The number 64 has the property that it is divisible by its units (ones) digit. How many whole numbers between 10 and 50 have the same property?
Example 8. 5 years ago, Tina was $2p$ years old. Next year, Tina’s brother, Jack, will be 7 years older than Tina. Find their total age in 10 years’ time.
**Editorial input convention:** Compare both ages at the same time; “in 10 years” means ten years from now. Enter the expanded expression in p as ap+b, with the coefficient immediately before p and no spaces. Format example, not the answer: 2p+1.
Example 9. Mr. Nelson has 216 candies. He wanted to put them into packets so that he can sell it to his customer. List all possible numbers of candies that Mr. Nelson can put in each packet so that there are at least 4 and not more than 15 candies in each packet. Then, list the corresponding number of packets.
**Editorial input convention:** Use equal-sized packets, use all 216 candies and leave none over. Enter all pairs (candies per packet,number of packets) in increasing first-coordinate order, with parentheses, commas inside pairs and semicolons between pairs. Use no spaces. Format example, not the answer: (2,10);(4,5).
