Suppose a manufacturer produces the football as shown below, they want to print one 2014 football World Cup logo and one Brazilian flag on it, note there are only two signs totally. These two signs are printed in two polygons. If we do not consider the position and direction of a sign in its polygon, then how many different arrangements are there?
18
To find the number of different arrangements of the two signs, we need to consider the possible combinations of placing the signs on the polygons.
Let's break down the problem step by step:
Step 1: Count the number of ways to place the 2014 football World Cup logo.
Since there is only one logo to place, there is only one option for its placement.
Step 2: Count the number of ways to place the Brazilian flag.
Similarly, since there is only one flag, there is only one option for its placement.
Step 3: Multiply the number of options from Step 1 and Step 2.
Since the placement of the logo and the placement of the flag are independent and do not affect each other, we can multiply the number of options from Step 1 and Step 2.
Therefore, the number of different arrangements is 1 x 1 = 1.
In conclusion, there is only one different arrangement possible for printing the 2014 football World Cup logo and the Brazilian flag on the given football.