Puzzle: Transforming Toothpicks by Twos
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Take 14 toothpicks, and arrange 12 of them to form the shape shown below.

Transforming Toothpicks

Challenges
Move two toothpicks in the arrangement and add the two extra toothpicks to make:

  • Two congruent triangles, two congruent parallelograms, and an irregular pentagon.
  • Two congruent triangles, two congruent parallelograms, and a trapezoid.
  • Two congruent triangles, two congruent parallelograms, and two congruent hexagons.
  • Three congruent triangles and two congruent trapezoids.
  • Three congruent triangles and two non-congruent parallelograms.
  • Three congruent triangles, two congruent hexagons, and a trapezoid.
  • Four congruent triangles and an irregular hexagon.
  • Four congruent triangles and two congruent parallelograms.
  • Five congruent triangles and a parallelogram.
  • Exactly six congruent triangles.
  • Six triangles, not all congruent, and two congruent parallelograms.
  • Seven triangles, not all congruent, and a trapezoid.

Sketch each solution you discover on the back of this paper. There may be multiple solutions for several of the challenges.

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