Question

In one second a domino falls and knocks down two dominos. After another second, those two dominos fall and each knock down two other dominos. If this pattern continues, how many dominos are knocked down on the fifth second?

Answer 1

You might have noticed that the number of dominos being knocked down is increasing at an exponential rate, since each domino knocks down two others. You can say that after n second have passed, 2^n dominos have been knocked down. So after 1 second, 2^1 = 2 dominos have been knocked down, and after 2 seconds, 2^2 = 4 dominos have been knocked down.

After 5 seconds, 2^5 = 32 dominos have been knocked down!

Answer 2

so the answer is 32

Answer 3

shouldn't we count the first second as 1 domino falling? meaning the answer would be 16? @matt101

Answer 4

Actually I've just reread the question and there's one other thing to consider. They ask how many dominos were knocked down ON THE FIFTH SECOND, not the total number of dominos knocked down. We can find this simply by finding the difference between 2^5 and 2^4, or 32 - 16 = 16.

So your answer to this question would actually be 16 dominos. Also, @kennybm, 3 dominos fall during the first second technically, according to the question. We can ignore that very first one to keep the equations simple because the answer doesn't change.

Answer 5

ok

Answer 6

so it is 16

Answer 7

no its not 16

Answer 8

it has to be 32 i checked

Answer 9

Then I guess they do want the total knocked down. The question just makes it sound like they want to know just what's knocked down during the fifth second.

Answer 10

@matt101 I read the question again, haha yeah the first second has 2 dominos falling :)

Answer 11

At the first second 2 dominos
At the second second 4 dominos
At the third second 8 dominos
At the fourth second 16 dominos
At the fifth second 32 dominos