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2023 LMT Fall
22
22
Part of
2023 LMT Fall
Problems
(1)
2023 Fall LMT Speed p22 pairs of points in 3D
Source:
3/2/2024
Consider all pairs of points
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
and
(
d
,
e
,
f
)
(d,e, f )
(
d
,
e
,
f
)
in the
3
3
3
-D coordinate system with
a
d
+
b
e
+
c
f
=
ā
2023
ad +be +c f = -2023
a
d
+
b
e
+
c
f
=
ā
2023
. What is the least positive integer that can be the distance between such a pair of points?Proposed by William Hua
geometry
3D geometry
algebra