1. Can you move just three toothpicks to produce three
identical squares?
2. Can you move just two toothpicks to produce four
identical squares?
3. The following arrangement represents a farmer's hurdles (portable fence pieces), placed so that they form six sheep pens all of the same size. After one of the hurdles is stolen, the farmer wants to rearrange the remaining 12 so that he will still have six pens of equal size, can he do it?
4. Counting the 16 unit squares, nine 2x2 squares, four 3x3 squares, and one 4x4 square, this figure contains 30 squares in all. Find the minimum number of toothpicks that must be removed to leave no squares of any size? Why is this the minimum number?
5. Try to move four toothpicks to form two squares.
6. Can you remove three toothpicks to leave three triangles?
7. Can you move six of these toothpicks to form a new shape with six congruent quadrilaterals?
8. Can you remove four toothpicks so that nine squares remain?
9. Use six toothpicks to construct four congruent triangles.
10. Use 12 toothpicks to form a polygon with 12 sides where all adjoining sides form right angles.
11. What is the fewest number of toothpicks that can be removed to do away with all of the triangles in the figure? Why is this the minimum number?
Note: Most of these puzzles came from the March, 1984 "Games" magazine.