MathDB

2

Part of 1997 IMO Shortlist

Problems(1)

kth term from the left in R_n is equal to 1

Source: IMO Shortlist 1997, Q2

8/10/2008
Let R1,R2,… R_1,R_2, \ldots be the family of finite sequences of positive integers defined by the following rules: R_1 \equal{} (1), and if R_{n - 1} \equal{} (x_1, \ldots, x_s), then
R_n \equal{} (1, 2, \ldots, x_1, 1, 2, \ldots, x_2, \ldots, 1, 2, \ldots, x_s, n).
For example, R_2 \equal{} (1, 2), R_3 \equal{} (1, 1, 2, 3), R_4 \equal{} (1, 1, 1, 2, 1, 2, 3, 4). Prove that if n>1, n > 1, then the k kth term from the left in Rn R_n is equal to 1 if and only if the k kth term from the right in Rn R_n is different from 1.
algebracombinatoricsSequenceinvariantIMO Shortlist