A medium question on cycles for P2–P4, 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
Today is Tuesday.
The school outing is 54 days from today.
What day of the week is the outing? (Answer 1 for Monday, 2 for Tuesday … 7 for Sunday.)
Show the hints (2)
💡Hint 1: Every 7 days the same weekday comes round again.
💡Hint 2: How many whole weeks are there in 54 days, and how many days over?
Worked solution
Have a go first, then read the solution step by step.
1.54 ÷ 7 = 7 remainder 5. After 7 weeks it is Tuesday again.
2.5 more days: Tuesday → Sunday, so 7.
⚠️Common mistake: counting today as day 1. 'n days from today' starts counting tomorrow.
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