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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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)