Page 105 - NUMINO Challenge_D2

12 Coloring

Basic Concepts Ways of Coloring a Map

There are six ways to distinguish the different parts of the picture A
on the right with three colors: red, blue, and orange.

BC

By using the Counting Principle, you can find the number of ways to distinguish
the parts above without coloring them.

Number of ways to Number of ways to Number of ways to
color part A color part B color part C

Number of ways to color part A: 3 ways (red, blue, orange).
Number of ways to color part B: 2 ways (excluding the colors used in part A).
Number of ways to color part C: 1 way (excluding the colors used in parts A and B).
Therefore, there are 3 2 1 6 (ways) to distinguish the parts.

Example Various flags are made by coloring the three
sections of the flag on the right with red,
orange, and yellow colors. How many different A BC
flags can be made if you do not need to use
all of the colors and the adjacent parts need
to have different colors?

Class Notes

There are three colors to paint part A.

There is(are) color(s) to paint part B after excluding the color used to paint part A.

There is(are) color(s) to paint part C after excluding the color used to paint part .

Therefore, there are 3 ways to make different flags.

102 NUMINO Challenge D2