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NMTC
2019 NMTC Junior
3
Chain of inequalities
Chain of inequalities
Source: NMTC 2019 Junior P3
November 2, 2019
algebra
inequalities
Problem Statement
Find the number of permutations
x
1
,
x
2
,
x
3
,
x
4
,
x
5
,
x
6
,
x
7
,
x
8
x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8
x
1
,
x
2
,
x
3
,
x
4
,
x
5
,
x
6
,
x
7
,
x
8
of the integers
−
3
,
−
2
,
−
1
,
0
,
1
,
2
,
3
,
4
-3, -2, -1, 0,1,2,3,4
−
3
,
−
2
,
−
1
,
0
,
1
,
2
,
3
,
4
that satisfy the chain of inequalities
x
1
x
2
≤
x
2
x
3
≤
x
3
x
4
≤
x
4
x
5
≤
x
5
x
6
≤
x
6
x
7
≤
x
7
x
8
.
x_1x_2\le x_2x_3\le x_3x_4\le x_4x_5\le x_5x_6\le x_6x_7\le x_7x_8.
x
1
x
2
≤
x
2
x
3
≤
x
3
x
4
≤
x
4
x
5
≤
x
5
x
6
≤
x
6
x
7
≤
x
7
x
8
.
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