For P(n) being the assertion that in every set of n horses, all horses have the same color: P (n) ⇒ P (n + 1), when n > 1.
How do I prove this problem, can someone give me explanation or a headstart?
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This is a frequently cited example of why one must be careful with induction. See, e.g. here. – Sep 25 '13 at 04:46
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I just don't get it, for example if 2 horses have the same color, then how did math proves that the third one is also the same color? – user96778 Sep 25 '13 at 04:47
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1@T.Bongers: In fact $P(n)$ does imply $P(n+1)$ when $n>1$. The problem is getting from $n=1$ to $n=2$. – Brian M. Scott Sep 25 '13 at 04:55