Recently, Rajesh visited the local casino where he came across a new card game. Two players, using a normal deck of $52$ playing cards, play this game. One player is called the 'dealer‘ and the other is called the 'player‘. First, the player picks a card at random from the deck. This is called the base card. The amount in rupees equal to the face value of the base card is called the base amount. The face values of ace, king, queen and jack are ten. For other cards the face value is the number on the card. Once the 'player‘ picks a card from the deck, the 'dealer‘ pays him the base amount. Then the 'dealer‘ picks a card from the deck and this card is called the top card. If the top card is of the same suit as the base card, the 'player‘ pays twice the base amount to the 'dealer‘. If the top card is of the same colour as the base card (but not the same suit), then the 'player‘ pays the base amount to the 'dealer‘. If the top card happens to be of a different colour than the base card, the 'dealer‘ pays the base amount to the 'player‘. Rajesh played the game four times. First time he picked eight of clubs and the 'dealer‘ picked queen of clubs. Second time, he picked ten of hearts and the 'dealer‘ picked two of spades. Next time, Rajesh picked six of diamonds and the 'dealer‘ picked ace of hearts. Lastly, he picked eight of spades and the 'dealer‘ picked jack of spades. Answer the following questions based on these four games.
The initial money Rajesh had (before the beginning of the game sessions) was Rs. X. At no point did he have to borrow any money. What is the minimum possible value of X?
- $16$
- $8$
- $100$
- $24$