This document contains a series of 18 conditional statements providing instructions to sketch various shapes on a piece of paper based on what shapes are already drawn. The instructions include things like sketching a square around an existing rectangle, drawing additional flowers if one flower is present, and signing your name in certain locations depending on the contents of the paper. The goal seems to be having the person following the instructions end up with a unique final sketch based on the random initial contents of their paper.

1. DRAFT DRAFT DRAFT
brain drain!
a math-y puzzle
Institute for Advanced Study/Park City Math Institute Summer 2010
Secondary School Teachers Program/Lesson Study

2. 1.
If you have a rectangle on your paper…
…then sketch a square around it.

3. 2.
If you have a triangle on your paper…
…then sketch a congruent triangle
approximately three inches to the right.

4. 3.
If you do not have a triangle on your
paper…
…then sketch an equilateral triangle
above the largest quadrilateral.

5. 4.
If you have exactly two triangles on your
paper…
…then sketch a square using the top
vertices of the two triangles as the base
of the square.

6. 5.
If you have a square on your paper…
…then sketch a circle in the upper right hand
corner of your paper.

7. 6.
If you don't have two triangles on your paper
and do not have a circle on your paper…
…then sketch a flower in the lower right hand
corner of your paper.

8. 7.
If you have only one triangle on your paper…
…then sketch a thin rectangle sticking out of
the left hand side of the triangle.

9. 8.
If you have a flower on your paper…
…then sketch two more flowers next to
it.

10. 9.
If you have two triangles and one
square on your paper…
…then sketch a smaller square on
top of the square.

11. 10.
If you have a single circle and no flowers
on your paper…
…then sketch a smiley face in the circle.

12. 11.
If you do not have a flower and you
have an even number of squares and
triangles…
…then sketch a sad face in the smaller
square.

13. 12.
If you don't have any flowers on your
paper…
…then sketch five flowers on the right
side of your paper, slightly above the
line that was on your paper when you
received it.

14. 13.
If you don't have a smiley face on
your paper…
…then don't sign your name on the
bottom left corner of your paper.

15. 14.
If you have more than one flower on
your paper…
…then don't sketch three more
flowers.

16. 15.
If you have a circle in a corner of your
paper and an even number of squares
and an even number of triangles…
…then sketch two thin rectangles
coming out of the left and right sides of
the largest square.

17. 16.
If you don't have an even number of
flowers…
…then sketch two stick figures on the left side
of your paper, slightly above the line that was
on your paper when you received it.

18. 17.
If you don't have an odd number of
flowers…
…then sketch three stick figures on
the left side of your paper.

19. 18.
If you have more than one stick figure…
…then sign your name on the bottom right
corner of your paper.