MathDB
Problems
Contests
International Contests
Czech-Polish-Slovak Match
1996 Czech and Slovak Match
5
5
Part of
1996 Czech and Slovak Match
Problems
(1)
two sets of intervals on a line
Source: Czech and Slovak Match 1996 P5
10/1/2017
Two sets of intervals
A
,
B
A ,B
A
,
B
on the line are given. The set
A
A
A
contains
2
m
ā
1
2m-1
2
m
ā
1
intervals, every two of which have an interior point in common. Moreover, every interval from
A
A
A
contains at least two disjoint intervals from
B
B
B
. Show that there exists an interval in
B
B
B
which belongs to at least
m
m
m
intervals from
A
A
A
.
set
interval
combinatorics