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
May threads beads for a bracelet, repeating the pattern "1 red, 1 white" over and over.
She threads 23 beads in all.
How many of the beads are white?
Show the hints (2)
💡Hint 1: How many beads make a group, and how many of those are white?
💡Hint 2: Beads left over after the whole groups — check one by one whether each is red or white.
Worked solution
Have a go first, then read the solution step by step.
1.A group is 1 + 1 = 2 beads, 1 of them white. 23 ÷ 2 = 11 remainder 1.
2.11 groups hold 11 × 1 = 11 white beads.
3.1 bead left over: each group starts with red, so the first 1 is red. White beads: 11 + 0 = 11.
⚠️Common mistake: counting all the left-over beads as white, or ignoring them.
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