What shape completes the bottom line?
triangle pentagon square
square hexagon hexagon square
pentagon hexagon hexagon hexagon square triangle
hexagon octagon octagon octagon octagon ?
Puzzle Copyright © Kevin Stone
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Hint
Look at the number of sides of each of the shapes.
Answer
Square.
Reasoning
If we add the shape's sides, the total increases by 8, then 10, then 12, etc (2 more each time).
triangle (3) + pentagon (5) + square (4) = 12
square (4) + hexagon (6) + hexagon (6) + square (4) = 20
pentagon (5) + hexagon (6) + hexagon (6) + hexagon (6) + square (4) + triangle (3) = 30
Therefore:
hexagon (6) + octagon (8) + octagon (8) + octagon (8) + octagon (8) + square (4) = 42
Alternative Reasoning
Square the first shape's sides, and the remaining shapes add up to this number.
triangle (3 x 3) = pentagon (5) + square (4)
square (4 x 4) = hexagon (6) + hexagon (6) + square (4)
pentagon (5 x 5) = hexagon (6) + hexagon (6) + hexagon (6) + square (4) + triangle (3)
Therefore:
hexagon (6 x 6) = octagon (8) + octagon (8) + octagon (8) + octagon (8) + square (4)
