MathDB

A Magician and a Detective play a game. The Magician lays down cards numbered from

1

52

face-down on a table. On each move, the Detective can point to two cards and inquire if the numbers on them are consecutive. The Magician replies truthfully. After a finite number of moves, the Detective points to two cards. She wins if the numbers on these two cards are consecutive, and loses otherwise.
Prove that the Detective can guarantee a win if and only if she is allowed to ask at least

50

questions.
Proposed by Anant Mudgal

Problem Statement