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Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1990 Swedish Mathematical Competition
2
2
Part of
1990 Swedish Mathematical Competition
Problems
(1)
min of \sum PA_i, when A_i are collinear
Source: 1990 Swedish Mathematical Competition p2
4/2/2021
The points
A
1
,
A
2
,
.
.
,
A
2
n
A_1, A_2,.. , A_{2n}
A
1
,
A
2
,
..
,
A
2
n
are equally spaced in that order along a straight line with
A
1
A
2
=
k
A_1A_2 = k
A
1
A
2
=
k
.
P
P
P
is chosen to minimise
∑
P
A
i
\sum PA_i
∑
P
A
i
. Find the minimum.
Sum
Geometric Inequalities
geometry
collinear