**189-235A:** Basic Algebra I

## Assignment 9

## Due: Wednesday, November 12.

**1-5**. Page 82, 2.32, 2.33, 2.34, 2.37, 2.39.

**6**. How many symmetries do the following objects have?

a) A finite set with n elements.

b) A square.

c) A regular polygon with n sides.

d) The cube.

**7**. (Extra credit)
A well-known
puzzle involves 15 numbered tiles in a 4x4 array. (There is one
empty space). The tiles are fixed in place so that you can
only slide them around using the empty space. The goal of the
puzzle is to arrange the tiles in order as follows:

01 02 03 04

05 06 07 08

09 10 11 12

13 14 15

If such a configuration can be reached, show that the pattern

15 14 13 12

11 10 09 08

07 06 05 04

03 02 01

cannot be.