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Problems
Contests
National and Regional Contests
Iran Contests
Iran MO (2nd Round)
2020 Iran MO (2nd Round)
P2
P2
Part of
2020 Iran MO (2nd Round)
Problems
(1)
Mix the frog out of it
Source: Iranian second round 2020 day 1 P2
7/14/2020
let
x
,
y
,
z
x,y,z
x
,
y
,
z
be positive reals , such that
x
+
y
+
z
=
1399
x+y+z=1399
x
+
y
+
z
=
1399
find the
max
(
[
x
]
y
+
[
y
]
z
+
[
z
]
x
)
\max( [x]y + [y]z + [z]x )
max
([
x
]
y
+
[
y
]
z
+
[
z
]
x
)
(
[
a
]
[a]
[
a
]
is the biggest integer not exceeding
a
a
a
)
algebra
Inequality
floor function
inequalities