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2021 AIME Problems
3
Permutation Sum
Permutation Sum
Source: 2021 AIME II #3
March 19, 2021
AMC
AIME
AIME II
Problem Statement
Find the number of permutations
x
1
,
x
2
,
x
3
,
x
4
,
x
5
x_1, x_2, x_3, x_4, x_5
x
1
,
x
2
,
x
3
,
x
4
,
x
5
of numbers
1
,
2
,
3
,
4
,
5
1, 2, 3, 4, 5
1
,
2
,
3
,
4
,
5
such that the sum of five products
x
1
x
2
x
3
+
x
2
x
3
x
4
+
x
3
x
4
x
5
+
x
4
x
5
x
1
+
x
5
x
1
x
2
x_1x_2x_3 + x_2x_3x_4 + x_3x_4x_5 + x_4x_5x_1 + x_5x_1x_2
x
1
x
2
x
3
+
x
2
x
3
x
4
+
x
3
x
4
x
5
+
x
4
x
5
x
1
+
x
5
x
1
x
2
is divisible by
3
3
3
.
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