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1997 Nordic
1
1
Part of
1997 Nordic
Problems
(1)
maximal number (x, y, z) of 7 elements with x < y & x + y=z
Source: Nordic Mathematical Contest 1997 #1
10/4/2017
Let
A
A
A
be a set of seven positive numbers. Determine the maximal number of triples
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
of elements of
A
A
A
satisfying
x
<
y
x < y
x
<
y
and
x
+
y
=
z
x + y = z
x
+
y
=
z
.
combinatorics
maximization
triplets
Extremal combinatorics