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Math Prize For Girls Problems
2019 Math Prize for Girls Problems
2
2
Part of
2019 Math Prize for Girls Problems
Problems
(1)
Math Prize 2019 Problem 2
Source:
10/15/2019
Let
a
1
a_1
a
1
,
a
2
a_2
a
2
,
…
\ldots\,
…
,
a
2019
a_{2019}
a
2019
be a sequence of real numbers. For every five indices
i
i
i
,
j
j
j
,
k
k
k
,
ℓ
\ell
ℓ
, and
m
m
m
from 1 through 2019, at least two of the numbers
a
i
a_i
a
i
,
a
j
a_j
a
j
,
a
k
a_k
a
k
,
a
ℓ
a_\ell
a
ℓ
, and
a
m
a_m
a
m
have the same absolute value. What is the greatest possible number of distinct real numbers in the given sequence?
Math Prize for Girls