Solved: Observe that the sequence 12, 15, 8, 13, 7, 18,
Chapter 9, Problem 9.172(choose chapter or problem)
Observe that the sequence 12, 15, 8, 13, 7, 18, 19, 11, 14, 10 has three increasing subsequences of length four: 12, 15, 18, 19; 12, 13, 18, 19; and 8, 13, 18, 19. It also has one decreasingsubsequenceoflengthfour:15,13,11,10.Show that in any sequence of n2 +1 distinct real numbers, there must be a sequence of length n+1 that is either strictly increasing or strictly decreasing.
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