MathDB

3

Part of 1972 Kurschak Competition

Problems(1)

for some points P_i it is not possible with a total length less than 25

Source: 1972 Hungary - Kürschák Competition p3

10/15/2022
ABCDABCD is a square side 1010. There are four points P1,P2,P3,P4P_1, P_2, P_3, P_4 inside the square. Show that we can always construct line segments parallel to the sides of the square of total length 2525 or less, so that each PiP_i is linked by the segments to both of the sides ABAB and CDCD. Show that for some points PiP_i it is not possible with a total length less than 2525.
combinatoricscombinatorial geometry