Problem 23 · 2023 Math Kangaroo
Stretch
Spatial & Visual Reasoning
transformationswork-backward
Anna has two machines R and S. Machine R rotates a square piece of paper 90° clockwise (watch the marking in the corner). Machine S prints a club onto the paper. Anna wants to produce the picture shown. In which order does she use the two machines?
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Answer: B — RSRR
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Hint 1 of 3
Machine R only spins the paper a quarter-turn, while machine S stamps the club at whatever angle the paper is in right now.
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Hint 2 of 3
Keep your eye on the little corner marking and follow where it travels after each R turn.
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Hint 3 of 3
Read the orders one letter at a time, checking that the club gets stamped at the right moment so it ends up tilted the way the target shows.
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Approach: track the corner mark and the club's orientation through the machines
- Follow the position of the corner marking as R turns the square 90° clockwise each time and S prints the club at the current orientation.
- The target shows both the corner mark and the club in particular positions, so the printing must happen at the right stage and the later turns must carry both into place.
- Testing the orders, R then S then R then R lands the marking and the club exactly as the target requires.
- So the order is RSRR, answer B.
Mark:
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