Janelle wants to challenge you to a “Toothpick and Tiles” game (described in problem 1-7). Using exactly four tiles, solve her challenges below. Justify your answers with pictures and labels. 

1. Create a tile pattern where the number of toothpicks is exactly double the number of tiles.   

   Hint 1 (a):

   Remember, you have four tiles.

   Hint 2 (a):

   Since the number of toothpicks is double the number of tiles, your pattern should have $4 × 2 = 8$ toothpicks.

   Hint 3 (a):

   Click and drag the tiles in the eTool below to find the answer.

   Answer (a):

   You should be able to rearrange the tiles and toothpicks to achieve this shape.

   

2. Create a tile pattern where the number of toothpicks is more than double the number of tiles.

• Hint 1 (b):

  Remember, you have four tiles.

  Hint 2 (b):

  There is more than one answer. Find one shape that uses 4 tiles and more than 8 toothpicks.