An easy question on cycles for P1–P2, with a step-by-step solution, diagrams and the answer. Cycle questions appear in the Hua Xia Cup from the P1 first round to the P5 papers: which comes in a given place, which day of the week, which last digit.
The question
Ming writes the numbers 1, 2, 3 in order, over and over:
1, 2, 3, 1, 2, 3, …
What is the 23rd number he writes?
Show the hints (2)
💡Hint 1: After how many numbers does it start again from 1?
💡Hint 2: Split the numbers into groups of 3. Which group is the 23rd number in, and where in that group?
Worked solution
Have a go first, then read the solution step by step.
1.Groups of 3, one group to a row: 23 ÷ 3 = 7 remainder 2.
2.After 7 groups count 2 more — the 2nd of a group: 2.
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