Suppose you have 6 straight sticks, all the same length. If you place them with two overlapping triangles facing opposite directions, how many equilateral triangles do they form?

     /\
____/__\____
\  /    \  /
 \/      \/
 /\      /\
/__\____/__\
    \  /
     \/

Can you arrange the six sticks to make just 1 equilateral triangle? 2? 3? What is the smallest number of triangles you cannot make?

Archeologists exploring three ruined cities of an ancient culture have found several references to a fourth city.

• City 1 is two miles south of city 2.
• City 2 is three miles east of city 3.
• In city 1 they found an inscription, “city 4 and city 2 are equally far away.”
• In city 3 they found an inscription, “city 4 and city 2 are equally far away.”

Where should the archeologists look for the ruins of city 4?