[IMO Shortlist 2009, C1] 

Consider 2009 cards, each having one gold side and one black side, lying on parallel on a long table. Initially all cards show their gold sides. Two players, standing by the same long side of the table, play a game with alternating moves. Each move consists of choosing a block of 50 consecutive cards, the leftmost of which is showing gold, and turning them all over, so those which showed gold now show black and vice versa. The last player who can make a legal move wins. 

a) Does the game necessarily end? 

b) Does there exist a winning strategy for the starting player? 

If the players start from left, their set of flipped cards don't overlap and they can take turns to reach 2000. During each turn 50 more cards are converted to black starting from the left. After that the player turning the remaining nine cards wins. Since 50 * 40 = 2000, the player starting first has a wining strategy and wins. This method and outcome assumes that none of the cards flipped once already are flipped again. Even if the non-starting player choose to play from the right or overlaps the cards he plays with the ones he played earlier, the starting player has pushed the leftmost possible card towards the right and reduced the window to play in and since he is left with turning the nine cards wherever they may occur, he can win. 

If the game is played from right to left, the player going first converts fifty cards from the right to black. The player going second can undo almost all of this except one by choosing just one more card to the left of this fifty and converting them back to gold again. The first card on the right is now black and left out as the game progresses towards the left.In a subsequent move, the second card from the right which is now gold is left out as the fifty cards to its left are flipped. Thus the game inches one by one to the left, leaving a trail of alternate black and gold. Since there are odd number of cards to begin with there are odd number of moves possible. After each odd number of moves, the player who doesn't start first always finds a gold card to make a move. Therefore this player always win and the starting player doesn't.
Note there is an official answer that there is no winning strategy for the starting player. This we have shown is not necessarily the case because it does not consider the starting player to play from the left.
The official answer however does prove that the game will end by saying that each card can have two states only and so they represent a binary notation of 2009 1s or 0s  and this number reduces on each move. If 0s represent black and leading 0s are allowed and because a black card is a final state in that it cannot be used to start a move, each move decreases the current number and therefore the game must end.
Since there are forty turns minimum, we can reduce the game to playing the forty cards without any consecutive cards to be flipped.
#codingexercise
Flip_gold_and_black_cards(ref Cards[] cards)
{
var index = get_first_gold_card_from_left(ref cards);
flip_next_fifty_cards_at(ref cards, index);
}
int get_first_gold_card_from_left(ref cards)
{
for (int I=0; I <cards.length; I++)
     if (cards[I].color == gold) return I;
return cards.length;
}
void flip_next_fifty_cards_at(ref cards, int start)
{
for (int I = start; I < cards.length; I++)
  cards[I]. color = cards[I].color == gold ? black:gold;
}
}
#BookReview
We review the book "The Responsible Entrepreneur" written by Carol Sanford.
She introduces us to the entrepreneur who is responsible - a special breed who challenge and refine cultural assumptions, laws and regulations and even the process of governance. As Kevin Jones, founder of SoCap said, this book is about being courageous and in fact he dares the readers to read and implement the bold useful advice.
Let us take a look at what Carol means by Responsible Entrepreneurs and what they achieve. She says these entrepreneurs are required to do and think far beyond what is usually required of business leaders. The Responsible Entrepreneurs offers us this 'blueprint'. By understanding the archetype  most aligned with their goals, entrepreneurs will learn how to grow their business and even change the game.
In this book she includes the following:
Some extraordinary people have changed the game for the better.
How modern archetypes are altering the future.
Why new measures of accomplishment are based on the success of the whole.

She says such entrepreneurs have the courage to take on what they don't yet know how to do and the dedication to build the capability to do it. These entrepreneurs are driven by the realization that the society and the planet need something big from them and that, if they don't rise to the challenge, the work may not get done.
Entrepreneuralism is about personal agency and the development of the will. While entrepreneurs are inventing new products, industries, sources of capital and models of enterprise, the responsible entrepreneurs are doing that and more because they want to create the right platform and support an ecosystem.  They run successful business while deeply caring about the innovation that can not only help them secure their business but also transform the world.
They enjoy developing the acumen needed to work on all parts of the business.
They maintain their own motivation, getting stimulus, training and innovation when they need it. They hold a positive attitude.
They are willing to take on big challenges that stretch them beyond what they currently know how to do and to ride the roller coaster of needing to continually rise to the occassion.
They tend to focus the game changing aspirations in one of four distinct domains
Industries - where the work is to disrupt and replace the automatic patterns
Social systems - where the work is to move upstream to the causes of social problems and address them at their source.
Cultural paradigms - where the enhance the belief systems into something more holistic and embracing
Foundational agreements - where the work is to renew and vitalize the deeper intention behind the governing documents, such as a corporate charter.

From these four domains she draws parallels to four archetypes
Warrior - The warrior protects the values of a community. In the business world, this work takes place within the industry.
Clown - The clown pokes fun at collective self-centeredness and unconsciousness, opening space for humility and heartfelt appreciation of others.
Hunter - The hunter perpetuates life by strengthening the mutual exchange between the tribe and the natural world.
Headman - The headman awakens the individuals to their potential and inspires them to work with others in order to contribute to something larger than themselves.

The four archetypes are all necessary to the healthy functioning of the society. In fact if any one of them is missing, the society becomes vulnerable.

To the entreprenueur, these archetypes translate into four unique roles as follows:
The warrior who changes an industry is the realization entrepreneur. He is driven by the vision of an improved reality.
The clown who changes social systems is the reconnection entrepreneur. She reveals the gap in our cognition regarding the impact of existing social systems
The hunter who changes cultural paradigms is the reciprocity entrepreneur. She tries to strike a balance between what is taken and what is given.
The headman or headwoman who changes the connection to foundation agreements is the regenerative entrepreneur.  She seeks to reveal and evolve the inherent potential of founding agreements that create the accepted structures within which the society operates.

The four roles do different work. For each of them the author takes examples and the principles or pillars that they operate on.