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2012 Math Kangaroo

Problem 6

Problem 6 · 2012 Math Kangaroo Easy
Spatial & Visual Reasoning tiling-tessellationspatial-reasoning
Figure for Math Kangaroo 2012 Problem 6
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Answer: C
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Hint 1 of 2
Mark a dot at the centre of every hexagon, then connect dots of touching hexagons.
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Hint 2 of 2
Neighbouring hexagon centres form little triangles, giving a triangular grid.
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Approach: join centres to form a triangular lattice
  1. Put a point in the middle of each hexagon.
  2. Joining the centres of two hexagons that share an edge gives short segments.
  3. Because the hexagons sit in a triangular cluster, these segments build a triangular grid.
  4. That pattern is picture C.
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