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France Contests
French Mathematical Olympiad
1995 French Mathematical Olympiad
Problem 4
points in plane, AiBj=i+j
points in plane, AiBj=i+j
Source: French MO 1995 P4
April 22, 2021
geometry
Problem Statement
Suppose
A
1
,
A
2
,
A
3
,
B
1
,
B
2
,
B
3
A_1,A_2,A_3,B_1,B_2,B_3
A
1
,
A
2
,
A
3
,
B
1
,
B
2
,
B
3
are points in the plane such that for each
i
,
j
∈
{
1
,
2
,
3
}
i,j\in\{1,2,3\}
i
,
j
∈
{
1
,
2
,
3
}
it holds that
A
i
B
j
=
i
+
j
A_iB_j=i+j
A
i
B
j
=
i
+
j
. What can be said about these six points?
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