Link is coloring a triforce, which consists of four equilateral triangles and is depicted below. He has three colors to use: gol

Question

2 years ago

14

Link is coloring a triforce, which consists of four equilateral triangles and is depicted below. He has three colors to use: gol

d, black, and green. So that it remains recognizable, he doesn't want to color any two triangles the same color if they share a side. How many different ways can he color the triforce? (Two colorings that differ by rotation are considered distinct.)

Mathematics

2 answers:

denis-greek [22] · Answer 1 · 2022-06-22T23:43:38+03:00

denis-greek [22]2 years ago

8 0

Answer:

24

Step-by-step explanation:

We first choose a center triangle. There are three ways to do that. Then, we choose the outer ones, which has 2 colors to choose from. The answer is 3*2*2*2=24

3241004551 [841] · Answer 2 · 2022-06-22T21:43:17+03:00

Answer:

12

Step-by-step explanation:

For the top triangle, he has 3 options

3C1 = 3

For the middle one, he can't use the top triangle's colour, so 2 options

2C1 = 2

For the ones on sides of the middle one, 2 options each

2C1 × 2C1 = 4

3 × 2 × 2 × 2 = 24

These include all three outer ones same, so subtract 3

Also, these include 2 of the three outer ones same, so subtract:

3C2 × 3 = 9

24 - 3 - 9 = 12