Question 6
There are $68$ ordered pairs (not necessarily distinct)
of nonzero integers on a blackboard.
It's known that for no integer $k$ does both $(k,k)$ and $(-k,-k)$ appear.
A student erases some of the $136$ integers such that
no two erased integers have sum zero, and scores one point
for each ordered pair with at least one erased integer.
What is the maximum possible score the student can guarantee?
Proposed by Gerhard Woeginger (credit in the supplied third-party notes).
of nonzero integers on a blackboard.
It's known that for no integer $k$ does both $(k,k)$ and $(-k,-k)$ appear.
A student erases some of the $136$ integers such that
no two erased integers have sum zero, and scores one point
for each ordered pair with at least one erased integer.
What is the maximum possible score the student can guarantee?
Proposed by Gerhard Woeginger (credit in the supplied third-party notes).