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5

Part of 1982 Czech and Slovak Olympiad III A

Problems(1)

comparing terms of seqeunce

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1982 p5

9/10/2024
Given is a sequence of real numbers {an}n=1∞\{a_n\}^{\infty}_{n=1} such that an≠ama_n \ne a_m for n≠m,n\ne m, given is a natural number kk. Construct a simple representation PP of the set 1,2,...,20k1,2,...,20k into the set of natural numbers to apply ap(1)<ap(2)<...<ap(10)a_{p(1)}<a_{p(2)}<...<a_{p(10)} ap(10)>ap(11)>...>ap(20) a_{p(10)}>a_{p(11)}>...>a_{p(20)} ap(20)<ap(21)<...<ap(30)a_{p(20)}<a_{p(21)}<...<a_{p(30)} ...... ap(20k−10)>ap(20k−9)>...>ap(20k)a_{p(20k-10)}>a_{p(20k-9)}>...>a_{p(20k)} ap(10)>ap(30)>...>ap((20k−10))a_{p(10)}>a_{p(30)}>...>a_{p((20k-10))} ap(1)<ap(20)<...<ap(20k),a_{p(1)}<a_{p(20)}<...<a_{p(20k)},
[hide=original wording of first sentence]Daná je postupnos’ reálných čísel {a_} také že an \ne a_m ctm pre n\ne m, dané je prirodzené číslo k. Zostrojte prosté zobrazenie P množiny 1,2,...,20k do -množiny prirodzených . čísel , aby platilo
algebrainequalitiescombinatoricsSequence