# Flipping cards

**Discrete 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.

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