Question
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Why in the explanation the case was split into the "same as top-left" case and the "not same as top-left" case instead of three "the bottom-right vertex is red/purple/yellow" case?
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@livelymockingbird-0 if I'm understanding your question correctly, it's because the two options you bring up are "basically" the same:
notice that "bottom-right vertex is purple" and "bottom-right vertex is yellow" both fall under the case "not same as top-left." So basically, you can think of the two cases in the solution as:
"same as top-left" = "bottom-right vertex is red"
"not same as top-left" = "bottom-right vertex is purple" or "bottom-right vertex is yellow."The reason that the solution uses 2 cases instead of 3 is that "bottom-right vertex is purple" and "bottom-right vertex is yellow" will give the same number of cases!! Because you can essentially think about swapping yellow and purple in every configuration. This saves a little bit of counting, because once we figure out that there are 2 colorings for "bottom-right vertex is purple," we know that there are also 2 colorings for "bottom-right vertex is yellow," so 2*2 = 4 total colorings for Case 2.
Hope this made sense, and let me know if it answered your question!
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@audrey Thanks! Your explanation has helped.
