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1992 Swedish Mathematical Competition
3
25x25 inequality system 2x_{25} - 5x_1 + 3x_2 >= 0
25x25 inequality system 2x_{25} - 5x_1 + 3x_2 >= 0
Source: 1992 Swedish Mathematical Competition p3
April 2, 2021
inequalities
System
algebra
Problem Statement
Solve:
{
2
x
1
−
5
x
2
+
3
x
3
≥
0
2
x
2
−
5
x
3
+
3
x
4
≥
0
.
.
.
2
x
23
−
5
x
24
+
3
x
25
≥
0
2
x
24
−
5
x
25
+
3
x
1
≥
0
2
x
25
−
5
x
1
+
3
x
2
≥
0
\begin{cases} 2x_1 - 5x_2 + 3x_3 \ge 0 \\ 2x_2 - 5x_3 + 3x4 \ge 0 \\ ...\\ 2x_{23} - 5x_{24} + 3x_{25} \ge 0\\ 2x_{24} - 5x_{25} + 3x_1 \ge 0\\ 2x_{25} - 5x_1 + 3x_2 \ge 0 \end{cases}
⎩
⎨
⎧
2
x
1
−
5
x
2
+
3
x
3
≥
0
2
x
2
−
5
x
3
+
3
x
4
≥
0
...
2
x
23
−
5
x
24
+
3
x
25
≥
0
2
x
24
−
5
x
25
+
3
x
1
≥
0
2
x
25
−
5
x
1
+
3
x
2
≥
0
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