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8
HMMT Team 2019/8: Variant on old USA TST
HMMT Team 2019/8: Variant on old USA TST
Source:
February 17, 2019
HMMT
combinatorics
graph theory
Problem Statement
Can the set of lattice points
{
(
x
,
y
)
∣
x
,
y
∈
Z
,
1
≤
x
,
y
≤
252
,
x
≠
y
}
\{(x, y) \mid x, y \in \mathbb{Z}, 1 \le x, y \le 252, x \neq y\}
{(
x
,
y
)
∣
x
,
y
∈
Z
,
1
≤
x
,
y
≤
252
,
x
=
y
}
be colored using 10 distinct colors such that for all
a
≠
b
a \neq b
a
=
b
,
b
≠
c
b \neq c
b
=
c
, the colors of
(
a
,
b
)
(a, b)
(
a
,
b
)
and
(
b
,
c
)
(b, c)
(
b
,
c
)
are distinct?
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