SEAMO 2027 - Paper F - SET 10 - Self-study Question 2

Andrew and Bob play a game with five cards numbered 1, 2, 3, 4 and 5. Andrew shuffles them and places them face-down on a table. Each round Bob chooses any three cards and Andrew states the value of one of those three. Bob may repeat this as often as he likes. How many cards at most does Bob need to choose to ensure that he knows the positions of all the cards?

“Ensure” means a guarantee for every permitted truthful choice of reply by Andrew; no cooperative or random reply rule is assumed.