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Contests
National and Regional Contests
Bosnia Herzegovina Contests
JBMO TST - Bosnia and Herzegovina
2020 Bosnia and Herzegovina Junior BMO TST
4
4
Part of
2020 Bosnia and Herzegovina Junior BMO TST
Problems
(1)
JBMO TST Bosnia and Herzegovina P4
Source:
8/10/2020
Determine the largest positive integer
n
n
n
such that the following statement holds: If
a
1
,
a
2
,
a
3
,
a
4
,
a
5
,
a
6
a_1,a_2,a_3,a_4,a_5,a_6
a
1
,
a
2
,
a
3
,
a
4
,
a
5
,
a
6
are six distinct positive integers less than or equal to
n
n
n
, then there exist
3
3
3
distinct positive integers ,from these six, say
a
,
b
,
c
a,b,c
a
,
b
,
c
s.t.
a
b
>
c
,
b
c
>
a
,
c
a
>
b
ab>c,bc>a,ca>b
ab
>
c
,
b
c
>
a
,
c
a
>
b
.
algebra