Hey man, where you went wrong is that in every pair of adjacent knights, one must be fed.
According to your logic, the second pair(i.e 2nd and 3rd knights) is not satisfying the condition. If you feed 1st and 4th :
First pair(1,2) : 1 is fed so it satisfies
Second pair(2,3) : neither 2 nor 3 is fed, thus fails.
Third pair(3,4) : 4 is fed so it satisfies
Fourth pair(4,5) : 4 is fed so it satisfies
Fifth pair(5,1) : 1 is fed so it satisfies
Hope you understood why :)