Could you please check my answer?
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?
ANSWER: 72
Sorry, 72 is not correct.
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?
So the answer should be 48?
Correct!
To check your answer, let's work through the problem together step by step:
Given:
- Daniel lost four times consecutively and had 3 cards left.
Let's assume for this problem that Daniel started with X number of cards. Now let's solve:
Loss 1: After the first loss, Daniel gives half of his cards to the other player. So, he is left with X/2 cards.
Loss 2: After the second loss, Daniel gives half of his remaining cards (X/2) to the other player. So, he is left with (X/2)/2 = X/4 cards.
Loss 3: After the third loss, Daniel gives half of his remaining cards (X/4) to the other player. So, he is left with (X/4)/2 = X/8 cards.
Loss 4: After the fourth loss, Daniel gives half of his remaining cards (X/8) to the other player. So, he is left with (X/8)/2 = X/16 cards.
Since Daniel had 3 cards left at the end, we can equate X/16 = 3 and solve for X:
X/16 = 3
Multiplying both sides by 16:
X = 3 * 16
X = 48
Therefore, Daniel must have started with 48 cards, not 72. It seems like your answer was incorrect.