Problem 23 · 2009 Math Kangaroo
Stretch
Spatial & Visual Reasoning
spatial-reasoningtransformations
Sylvia draws shapes made of straight lines that are each 1 cm long. At the end of each line she turns a right angle, either left or right. At every turn she writes down a ♥ or a ♠, and the same symbol always means a turn in the same direction. Today her notes show ♥♠♠♠♥♥. Which of the following shapes could she have drawn today if A is her starting point?
Show answer
Answer: E
Show hints
Hint 1 of 3
Every symbol is a right-angle turn; one symbol always turns the same way and the other symbol always turns the other way.
Still stuck? Show hint 2 →
Hint 2 of 3
Notice the notes have three of the same symbol in a row (♠♠♠) in the middle, so the correct shape must make three same-direction turns in a row there.
Still stuck? Show hint 3 →
Hint 3 of 3
Start at A, walk 1 cm at a time, and turn the way each symbol tells you.
Show solution
Approach: match the ♥/♠ turn pattern by walking from the start point A
- Each line is 1 cm and each symbol is a right-angle turn, with one symbol always turning left and the other always turning right.
- The middle of the notes has three of the same symbol in a row (♠♠♠), which means three turns the same way in a row — that traces three sides of a little square.
- Starting at A and walking the path while turning as ♥♠♠♠♥♥ tells you, the path closes up in the shape of option E.
- Only shape E matches the whole sequence of turns.
Mark:
· log in to save