MathDB

1

Part of 2021 Iran Team Selection Test

Problems(2)

Iran TST 2021 First Exam,P1

Source: Iran TST 2021

5/16/2021
In acute scalene triangle ABCABC the external angle bisector of ∠BAC\angle BAC meet BCBC at point XX.Lines lbl_b and lcl_c which tangents of BB and CC with respect to (ABC)(ABC).The line pass through XX intersects lbl_b and lcl_c at points YY and ZZ respectively. Suppose (AYB)∩(AZC)=N(AYB)\cap(AZC)=N and lb∩lc=Dl_b\cap l_c=D. Show that NDND is angle bisector of ∠YNZ\angle YNZ. Proposed by Alireza Haghi
geometrytangent
How original of us

Source: Iranian TST 2021, second exam day 1, problem 1

5/20/2021
Natural numbers are placed in an infinite grid. Such that the number in each cell is equal to the number of its adjacent cells having the same number. Find the most distinct numbers this infinite grid can have.
(Two cells of the grid are adjacent if they have a common vertex)
combinatoricsinfinite grid