Grade 4 Math Puzzle 3: Combine moves, then discard full laps

A free grade 4 math puzzle that teaches Combine moves, then discard full laps. Try it first — the hint and the full solution open when you are ready.

Problem 3 · Combine moves, then discard full laps · 3 points

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A toy starts on space 1 of a circular board numbered 1 to 8 clockwise. Each dance moves it 5 spaces clockwise, then 2 spaces counterclockwise; where is it after 47 dances?

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Think about where one complete dance leaves the toy compared with where it began. What happens when it makes a full lap?
Each dance moves the toy 3 spaces clockwise overall. How many full laps can you ignore after 47 dances?

Show the answer and solution

Answer: A — 6

Each dance moves the toy 5 − 2 = 3 spaces clockwise. After 47 dances, that is 47 × 3 = 141 spaces. Since 141 = 17 × 8 + 5, the toy finishes 5 spaces clockwise from 1, on space 6. Space 4 is tempting if you count the clockwise moves but forget that every dance also moves the toy backward.

Grade 4 puzzle 3: Combine moves, then discard full laps

Problem 3 · Combine moves, then discard full laps · 3 points