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2009 Math Kangaroo

Problem 12

Problem 12 · 2009 Math Kangaroo Medium
Spatial & Visual Reasoning transformationsspatial-reasoning

Picture X is paired with picture Y. Which of the following pictures is paired with picture G?

Figure for Math Kangaroo 2009 Problem 12
Show answer
Answer: E
Show hints
Hint 1 of 3
Lay picture X next to picture Y and notice what changed about every single square.
Still stuck? Show hint 2 →
Hint 2 of 3
It is the same little rule done to every square, so do that very same thing to picture G.
Still stuck? Show hint 3 →
Hint 3 of 3
Then look through the five choices for the picture you would get.
Show solution
Approach: spot that Y is X with every square's colour flipped, then flip G
  1. Compare X with Y square by square: every dark square in X is white in Y, and every white square is dark.
  2. So the rule is simply 'swap the colours of all the squares.'
  3. Do the same to picture G: turn each of its dark squares white and each white square dark.
  4. The picture you get is option E, so E is paired with G.
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