MathDB

C

Part of 2024 Indonesia TST

Problems(2)

Construction problem

Source: Indonesia TSTST - Combinatoric

2/29/2024
Given a sequence of integers A1,A2,⋯A99A_1,A_2,\cdots A_{99} such that for every sub-sequence that contains mm consecutive elements, there exist not more than max{m3,1}max\{ \frac{m}{3} ,1\} odd integers. Let S={(i,j) ∣i<j}S=\{ (i,j) \ | i<j \} such that AiA_i is even and AjA_j is odd. Find max{∣S∣}max\{ |S|\}.
combinatoricsmaximizationIndonesiaIndonesia TST
&quot;Family&quot; of subsets

Source: Indonesia TST Round 1-Combinatorics

3/3/2024
Let AA be a set with 10001000 members and F=\mathcal F ={A1,A2,…,AnA_1,A_2,\ldots,A_n} a family of subsets of A such that (a) Each element in F\mathcal F consists of 3 members (b) For every five elements in F\mathcal F, the union of them all will have at least 1212 members Find the largest value of nn
TststcombinatoricsSubset