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Rosebush Puzzle 1*



A gardener laying out a bed of roses finds that she can plant 7 rosebushes so that they form 6 straight lines with 3 rosebushes in each line.

How is this possible?

   Suggested Materials:

6 sticks of uncooked spaghetti and 7 pennies

or 6 toothpicks and 7 Cheerios or other flat breakfast cereal or whatever other manipulative is handy to simulate the lines and rosebushes


  1. Place 7 "rosebushes" on your desk or table.

  2. Using the 7 sticks experiment with arranging the "bushes" into 6 lines of 3 each.

   Questions to ask yourself as you work:

  1. Will there be 3 rose bushes in each row if you have only 7 bushes and you place the six rows parallel to each other?

  2. If your rows are not parallel, how else could they be arranged?

  3. If your rows intersect, where should you place one of your rose bushes?

    Check for understanding

  4. After placing the first rosebush, how many do you have left?

  5. How many more rosebushes need to be placed in order to have 3 in that row?

A hint...


    (Don't look 'til you're ready to give up!)

* Thanks to Christine Heffernan, who sent this question to Ask Dr. Math at the Math Forum.

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