If you pinched 10 people, telling each one to pinch 10 others, how long would it take to cause a global pinch?

Answer 1

Dr D made me think about this again so here goes....

assuming no one is pinched twice (otherwise the pinching could go on forever without everyone being pinched)

one iteration = 10 people pinched = 10^1 (keep in mind the pincher is not pinched...)
second iteration = 100 new people pinched + 10 previous pinches= 10^2 + 10^1
third iteration = 1000 = 10^3 + 10^2 + 10^1

in general, the number of people pinched = sum 10^n from n = 1 to n = i where i is the iteration.

since there are 6.6 billion people living on earth right now (from here http://en.wikipedia.org/wiki/World_population)

so find i for

Σ 10^n (from n=1 to n=i) = 6.6 x 10^9

but Σ 10^n (from n=1 to n=i) is a geometric series who's sum would be

Σ 10^n (from n=1 to n=i) = {[10^(i+1) - 1] / [10 - 1] } -1
= 6.6 x 10^9
or
[10^(i+1) - 1] / = (6.6 x 10^9 +1) x 9 = 5.9 x 10^10
which gives
10^(i+1) = 5.9 x 10^10
take log of both sides gives
i+1 = log (5.9 x 10^10) = log 5.9 + 10 x log 10 = .77 + 10 = 10.77

which gives i = 10.77-1 = 9.77 iterations...

now, you asked how long it would take. it's up to you to decide how long an iteration is. if you're standing in a room with 10 people it would take you a lot less time to pinch them then it would take 660 million people to travel around the world and find the other 6 billion people and pinch them.

Atif Karbelkar, you wrote 6 x 10^6 people in the world. that's 6 million. I think you meant 10^9. ie 6 billion.....

Answer 2

It depends on how long a "round" of pinching takes, assuming that the rounds have a constant time and that nobody is pinched twice. (None of these assumptions could actually happen; this whole thing is just for fun).

After one round, 10 people are pinched.
After two rounds, 10 + 100 people are pinched.
After three rounds, 10 + 100 + 1000 people are pinched.

We need to pinch, what, 7 billion people?
Each round ends in a number of the form 1111....10, so we'll actually have to pass 7 billion and land on 11.11....1 billion.
So that's 11,111,111,110. There are ten 1's, so it took 10 rounds.

Thus, if t is the amount of time it takes one person to pinch ten people, then the entire world is pinched in less than 10t units of time, probably about 9.5t units.

Answer 3

This game could stop at 11 people. Then there will always be 10 others to pinch. You didn't say that you have to pinch an unpinched person.

Anyway, if you only allow pinching of previously unpinched people, then you have a geometric series:
1 + 10 + 100 + ...
whose sum = (1 - 10^n) / (1 - 10)
We want this to equal six billion = 6 x 10^9
10^n = 54 x 10^9 + 1
n = log (RHS) = 10.73

This would turn into a global pinch after 11 rounds.

Answer 4

Here is a trick you might find useful since you conveniently picked powers of ten. population of the earth = 7 billion +. Count the zeros. Decide how long a round of pinching takes, multiply, and there is your answer with assumptions.
But someone of the first 10 will charge you with assault. And someone else will try the pinching and be charged with assault. Now you can have a cellmate. Are there lessons in both solutions?

Answer 5

It would never happen.

The most that will be pinched is 110 people (because you never said that it had to be continuous, telling each pinched person to pinch ten others and telling them to do the same, over and over forever. All we have are two generations of pinched, the first ten and each of their ten)

And the fewest would be 11 (since you never said that the same people couldnt be pinched more than once)

Answer 6

The time it would take to find people that haven't been pinched is not linear. Anyways, I'm sure the 10 people would probably decide to pinch you back instead :P

Answer 7

how long is a difficult question. there are 6 * 10 ^ 6 people in the world approx. if u consider all people in the world are standing in a que so that as soon as a person pinches one that person can pinch ten other, and each person is pinched only once, in say ten seconds. thus, it would take six stages in all to reach the figure of six million and a total of SIXTY SECONDS.

Answer 8

assuming people travel instantaneously, and are able to pinch once per minute... a bit under ten minutes.

clearly those assumptions are wrong. it's going to take a while to pinch those last few people in antarctica or on the international space station. in fact you could probably just figure out how long it would take to get to those places and you'd have your answer.

Answer 9

Yeah you would have to account for the ***-kickings that would likely be involved after the pinching, and those would certainly delay the process.

Answer 10

None because I bet you the first person you pinch its going to punch you on the face.