Question 5
Alice has eight coins. She knows that seven are genuine and have equal weight; one is counterfeit and is either heavier or lighter. Bob has a balance which shows which pan is heavier, not the weight difference. Before each weighing Alice pays Bob one of her remaining coins. If it is genuine, he reports the true outcome; if it is counterfeit, he reports an arbitrary outcome. Can Alice guarantee identifying five genuine coins without giving any of those five to Bob?
