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f mapping {1,2...,n} to {1,2,3,4,5} with condition - Rom TST

Source: Romanian TST 2000

February 14, 2011
functionalgebra proposedalgebra

Problem Statement

Let n≥2n\ge 2 be a positive integer. Find the number of functions f:{1,2,…,n}→{1,2,3,4,5}f:\{1,2,\ldots ,n\}\rightarrow\{1,2,3,4,5 \} which have the following property: ∣f(k+1)−f(k)∣≥3|f(k+1)-f(k)|\ge 3, for any k=1,2,…n−1k=1,2,\ldots n-1.
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