A hard question on cycles for P4–P5, 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
In a certain year, 2 April is a Thursday.
What day of the week is 29 May of the same year? (Answer 1 for Monday, 2 for Tuesday … 7 for Sunday.)
Show the hints (3)
💡Hint 1: First count the days from 2 April to 29 May. March, May, July, August, October and December have 31 days; April, June, September and November have 30.
💡Hint 2: Divide the number of days by 7; the remainder is how many weekdays to move on.
💡Hint 3: They are 57 days apart, and 57 ÷ 7 = 8 remainder 1.
Worked solution
Have a go first, then read the solution step by step.
1.April has 30 days, so after the 2nd there are 30 − 2 = 28 days.
2.Then 29 days into May: 28 + 29 = 57 days apart.
3.57 ÷ 7 = 8 remainder 1: move on 1 day from Thursday to Friday, so 5.
⚠️Common mistake: counting 2 April itself, which makes the gap one day too long.
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