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Kvant 2022
M2728
M2728
Part of
Kvant 2022
Problems
(1)
Broken line inside polygon
Source: Kvant Magazine No. 11-12 2022 M2728
3/7/2023
Given is a natural number
n
⩾
3
n\geqslant 3
n
⩾
3
. Find the smallest
k
k{}
k
for which the following statement is true: for any
n
n{}
n
-gon and any two points inside it there is a broken line with
k
k{}
k
segments connecting these points, lying entirely inside the
n
n{}
n
-gon.Proposed by L. Emelyanov
Kvant
geometry
polygon