22 monkeys have together 8888 bananas. For each monkey with more than one banana, there is another monkey with fewer, but at least half as many bananas. Prove that the monkeys can be split in two groups with 4444 bananas each.
(In reply to generalization
by Art M)
There is an unwarranted assumption here: that a(k)>N≥A(k-1). IF the set is infinite, the proof is valid.