Flipping cardsDiscrete Mathematics Level 5
A game is played with 16 cards laid out in a row. Each card has a black side and a red side, and initially the face-up sides of the cards alternate black and red with the leftmost card black-side-up. A move consists of taking a consecutive sequence of cards (possibly only containing 1 card) with the leftmost card black-side-up and the rest of the cards red-side-up, and flipping all those cards over. The game ends when a move can no longer be made. What is the maximum possible number of moves that can be made before the game ends?
This problem is from the OMO.