MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AIME Problems
2024 AIME
11
Nerfed 2023 JMO 1
Nerfed 2023 JMO 1
Source: 2024 AIME II P11
February 8, 2024
AIME
AIME I
AIME II
Hi
Problem Statement
Find the number of triples of nonnegative integers
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
satisfying
a
+
b
+
c
=
300
a + b + c = 300
a
+
b
+
c
=
300
and
a
2
b
+
a
2
c
+
b
2
a
+
b
2
c
+
c
2
a
+
c
2
b
=
6
,
000
,
000.
a^2b + a^2c + b^2a + b^2c + c^2a + c^2b = 6{,}000{,}000.
a
2
b
+
a
2
c
+
b
2
a
+
b
2
c
+
c
2
a
+
c
2
b
=
6
,
000
,
000.
Back to Problems
View on AoPS