MathDB
Integer sequence with iterated operation

Source: VJIMC 2017, Category I, Problem 2

April 2, 2017
Sequencesprobability

Problem Statement

We say that we extend a finite sequence of positive integers (a1,…,an)(a_1,\dotsc,a_n) if we replace it by (1,2,…,a1−1,a1,1,2,…,a2−1,a2,1,2,…,a3−1,a3,…,1,2,…,an−1,an)(1,2,\dotsc,a_1-1,a_1,1,2,\dotsc,a_2-1,a_2,1,2,\dotsc,a_3-1,a_3,\dotsc,1,2,\dotsc,a_n-1,a_n) i.e., each element kk of the original sequence is replaced by 1,2,…,k1,2,\dotsc,k. Géza takes the sequence (1,2,…,9)(1,2,\dotsc,9) and he extends it 20172017 times. Then he chooses randomly one element of the resulting sequence. What is the probability that the chosen element is 11?
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