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MATH / Link is coloring a triforce, which consists of four equilateral triangles and is…

Problem

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problem

Link is coloring a triforce, which consists of four equilateral triangles and is depicted below. He has three colors to use: gold, 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.) [asy]
size(50);
draw((0,0)--(2,0)--(1,1.732)--cycle);
draw((1,0)--(1.5,.866)--(.5,.866)--cycle);
[/asy]

level

Level 4

type

Counting & Probability

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Source and history

task_id
deeae2ef-0ba9-519c-9a33-1dd3765b2191
task_key
counting~5fand~5fprobability--test--deeae2ef-0ba9-519c-9a33-1dd3765b2191
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import