Prove that if the average of n nonnegative integers m1, m2, …, mn is at least equal to r, then at least one of the integers m1, m2, …, mn satisfies mi ≥ r.
Consider the multiset S = {3 ⋅ a, 2 ⋅ b, 4 ⋅ c} of 9 objects of 3 types. Find the number of 8-combinations of S.
Prove that the Fibonacci number fn is even if and only if n is divisible by 3.
Does there exist a graph of order 5 whose degree sequence equals (4, 4, 4, 2, 2)?
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