# Problem Statement Confusion (2020 US Open Gold)

So, I’m doing this problem, but I can’t seem to understand the sample case.

If I’m correct, this problem is noting that if all the cows that admire cow C should share the same color. However, in that case the sample case doesn’t seem to be optimal. The only conditions we have to satisfy are 2=6, 5=4, and 7=3, where those numbers are the cow numbers. In that case, can’t we definitely assign more than 3 colors?

Idk where you got that from. Cows 1 and 4 both admire cow 2, so they should share the same color.

No they don’t? In the test data:

9 12
1 2
4 2
5 8
4 6
6 9
2 9
8 7
8 3
7 1
9 4
3 5
3 4


Cow 1 only admires cow 7 (if you didn’t notice, the test data was kind of reversed- they said that it was in the form of a\text{ }b, where cow b admires cow a). I don’t see how cow 1 and cow 4 share the same cow.

Yeah, it’s my fault that I made the diagram + test data before the statement was finalized … (confusing even myself )

It’s cow with favorite color c, not cow c.

Cows 3 and 7 have the same favorite color, cow 4 admires cow 3, cow 1 admires cow 7, \to cows 1 and 4 share the same favorite color.

(this definitely should have been in the sample explanation …)

Yeah, it turns out I misread the problem. I thought only if 2 cows admired the same cow, they shared the same color