Daniel played a cards game in which each
loss meant that he had to give the other player half the cards he had left. He lost four times, one after the other, and then had 3 cards left.
How many cards did he have when he started?

Look at it this way:
He now has 3 cards left.
Before he lost the fourth time, he had 2*3=6 cards.
Before he lost the third time, he had 2*6=12 cards.
Before....
Can you finish it?