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K12 Math Puzzles


M Puzzle*


Can you construct nine triangles by drawing three straight lines through a capital M?

   Suggested Materials:

3 sticks of uncooked spaghetti

or 3 toothpicks
or whatever other manipulative is handy to simulate the lines


  1. Draw a large M on your paper.

  2. Use the 3 sticks and try various ways to place them across the M.

   Questions to ask yourself as you work:

  1. Are any triangles formed if you place one of the sticks vertically?

  2. Are any triangles formed if you place one of the sticks horizontally?

  3. What is the maximum number of triangles you can make by placing just one stick?

    Check for understanding

  4. When you have placed one stick, look at the triangles that you have made. How many more triangles do you still need to make?

  5. You have 2 sticks left. Can you place them so that you will cross existing triangles and thereby double the number of triangles?

A hint...


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

* Thanks to Robert Arnett, who sent this question to the Forum.

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