Olympiad topic · P1–P6
Queues
Queue questions are already in the Hua Xia Cup's P1 and P2 first rounds, and the P4 papers add square formations.
Try one
★★ Medium21 pupils queue in single file for the coach.
Counting from the front, Ming is 9th.
Counting from the back, May is 8th.
May is behind Ming.
How many pupils are between Ming and May?
- Hint 1: They're counted from different ends. Where is May, counting from the front?
- Hint 2: 8th from the back means one fewer than 8 stand behind her.
- 1.May has 8 − 1 behind her and 21 − 8 = 13 in front, so from the front she is 13 + 1 = 14th.
- 2.Between them are places 10 to 13: 14 − 9 − 1 = 4.
- ⚠️Common mistake: putting May at 21 − 8 = 13 from the front, forgetting to add 1.
Answer: 4 pupils
Four levels, step by step
- ★EasyFree2 question types · unlimited questionsPeople in a line, people between two.
- ★★MediumFree2 question types · unlimited questionsA rectangle of rows, counted from both ends.
- ★★★HardFree3 question types · unlimited questionsThree people's places together, a square's outer layers.
- ★★★★Expert (competition level)VIP2 question types · unlimited questionsCounting off in a circle, a hollow square made solid.
Queues: what it is and how to solve it
Lines and square formations: from people's places, find how many there are.
For example: Ming has 6 people in front and 8 behind. How many in the line? 6 + 8 + 1 = 15 (don't forget Ming).
The key idea: "People in front" leaves you out; "you're nth" counts you in. A solid square has side × side people; a hollow one is counted layer by layer.
Practise this topic free →Easy to Hard (★ to ★★★) all free, unlimited questions, no download