Question 5
A $5\times5$ square board has one identical-looking coin on each cell. Exactly two coins are counterfeit, of equal weight; all genuine coins have the same weight and are heavier than the counterfeit coins. The counterfeit coins occupy two cells sharing exactly one vertex. Can one guarantee identifying (a) 13 genuine coins; (b) 15 genuine coins; (c) 17 genuine coins, using only one weighing on a balance without weights? Original weights: (a) 2 points, (b) 3 points, (c) 2 points.
