six degrees of separation?

6**N > 100,000 (6**N means 6 raised to the Nth power)

log (6**N) > log( 100,000)

N log 6 > log 100000

N > log 100000 / log 6

N > 6.43 or 7 degrees of seperation

If they all diligently send out their six you would still have to consider how long it wiould take for each one to do so. Some people might not get around to doing it for a whiole year, So time is the main factor in such considerations. It is therefore virtually impossible to give an answer to this question. It would also depend upon the relative importance of the petition in the perception of the individuals involved. Some may consider the petition not worth the effort so these [people would not be involved in your exercise.

If you are interested in this from a purely mathematical viewpoint then you would simply square the six and keep squaring the result until you reach a number close to 100,000. In this event however there would be no consideration of time.

That's not what 6 degrees of separation means. 6 degrees of separation says that if you had a sheet of paper, sent it to everyone you know and told them to do the same, that would only have to happen 6 times to get one to everyone on the planet. Roughly. There are some socially secluded communities that either won't get covered, or only get covered partially.

If you do that in practice, it will depend on how diverse your group is. They may just start sending it to each other, even if they are not allowed to send it to the person who directly gave it to them.

6^6 =46,656...

6^7 = 279,936...