- What is the next term in the sequence? In each case, think of at
least three different ``plausible'' answers.
- .
- .
- .

- What is the next term in the sequence? In each case, try to find a
formula
*f*(*n*) such that the sequence is given by .- .
- .
- .
- .

- What is the formula?
- What is the maximum number of pieces into which a pancake can
be cut by
*n*straight cuts, each of which crosses each of the others? - What is the maximum number of pieces that can be produced by
*n*simultaneous straight cuts of a flat figure shaped like a crescent moon? - How many pieces of cheesecake can be produced by
*n*simultaneous plane cuts of a cylindrical cake? - Into how many parts can the plane be divided by intersecting circles of the same size? Of different sizes? By intersecting ellipses of different sizes?
- Into how many regions can space be divided by intersecting spheres?
- With an unlimited supply of toothpicks of
*n*different colors, how many different triangles can be formed on a flat surface, using three toothpicks for the three sides of each triangle? (Reflections are considered different, but not rotations.) How many different squares? - How many different tetrahedra can be produced by coloring each
face a solid color and using
*n*different colors? (Two tetrahedra are the same if they can be turned and placed side by side so that corresponding sides match in color.) How many cubes with*n*colors? - What is the maximum number of pieces that can be produced by
*n*simultaneous plane cuts through a doughnut?

- What is the maximum number of pieces into which a pancake can
be cut by

Wed Jan 6 11:37:02 EST 1999