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Maths olympiad question · P2–P3★ Easy

Clocks and time: olympiad question 2

An easy question on clocks and time for P2–P3, with a step-by-step solution, diagrams and the answer. Every year of the Hua Xia Cup has clock questions, from time passed in P1 to the angle between the hands in P6.

The question

The big clock in the school hall strikes the hours: once at 1 o'clock, twice at 2 o'clock, and so on.

There are 2 seconds between one strike and the next.

At 5 o'clock, how many seconds are there between the first strike and the last?

Show the hints (2)
  1. Hint 1: Try a small case: with 3 strikes, how many waits are there in between?
  2. Hint 2: With 5 strikes, there is one wait fewer than strikes.

Worked solution

Have a go first, then read the solution step by step.

  1. 1.Between 5 strikes there are 5 − 1 = 4 waits.
  2. 2.2 seconds each: 2 × 4 = 8 seconds.
  3. ⚠️Common mistake: counting 5 waits and answering 2 × 5 = 10 seconds.

Answer: 8 seconds

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