MathDB
IMO LongList 1987 - Runs of a decimal number

Source:

September 6, 2010
algebra proposedalgebra

Problem Statement

The runs of a decimal number are its increasing or decreasing blocks of digits. Thus 024379024379 has three runs : 024,43024, 43, and 379379. Determine the average number of runs for a decimal number in the set {d1d2⋯dn∣dk≠dk+1,k=1,2,⋯ ,n−1}\{d_1d_2 \cdots d_n | d_k \neq d_{k+1}, k = 1, 2,\cdots, n - 1\}, where n≥2.n \geq 2.
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