Puzzles and logic › Processes, invariants and strategy › Board operations and invariants
Guaranteed score erasing blackboard numbers
University · ●●●●● 200 pts
There are 68 pairs of non-zero integers on a blackboard. Some pairs may be identical. For each positive integer , at most one of the pairs and appears on the blackboard. A student erases some of the 136 numbers so that the sum of any two erased numbers is not . For each of the 68 pairs, if at least one number from that pair is erased, the student scores one point. Find the largest score that the student can guarantee, whatever the 68 pairs on the blackboard are.