World Quiz Question

[Woodstock]

Any ideas on this one?

Assume that you have just heard a scandal and that you are the first to know.  You pass it on to four people in a matter of 30 minutes.  Each of these four people in turn passes it to another four people in the nexr 30 minutes and so on.  Assume that no one hears it more than once and that the world population is 5.6 billion.  How long will it take for everyone in the world to get to know the scandal?

[crofter]

Assuming that the "billion" in the question is a UK billion (that is, one million million) I reckon that it should take 13hrs 21mins and 34 secs!

Solution on request!

[ck1]

I make it about 8 hours, crofter how did you work it out?

[crofter]

After 8 hours there will have been 16 "pass ons". At the last pass 4^16 (4 to the power 16) extra people will know.

At that point, the total number who are in the know is given by 1 + 4 + 4^2 + 4^3 + ... +4^16

This is a geometric progression, whose sum is given by (4^17 - 1)/(4 - 1) = 5.7266 US billions

Do you want me to go on? ck1 you have assumed an american billion (that is a thousand million)

[thikasabrik]

Tell the scandal to my ex mother in law and I reckon it would take about 30 mins total

[Woodstock]

Wow, Crofter, that's heady stuff, too complicated for me to work out - I'll take your word for it.  Many thanks.

ck1 - thanks for your time and effort - but I think I've got to go with the English version.

I don't get the answer until after 16th June, so I'll post it here as soon as I hear.

thickasabrik - love your answer - I think we've all known a few mother-in-laws like that!

[THECORBYLOON]

The term "billion" is assumed to be 1,000 million when speaking about the world's population so in the question posed it would be 5,600,000,000. In that case it would be 8 hours to the nearest 1/2 hour which is what ck1 made it.

[Woodstock]

Thanks, THECORBYLOON. perhaps I should bow to your greater knowledge.

[THECORBYLOON]

Woodstock what was said about billions is correct. Strictly speaking, a British billion is a million million and an American and Continental billion is a thousand million. When folk speak about the Earth's population being 6.5 billion they mean 6,500,000,000. 

The British Government started using the "smaller" American billion in 1974 even though the word "milliard" means 1,000,000,000. Sorry for going off the subject

[Woodstock]

THECORBYLOON - you never cease to amaze me!  Keep it up.

[crofter]

Picking up on the correspondence with everyone, the "accurate" answer is then 7 hrs 59 mins and 31 secs!

This is only 29 seconds below the "approximate" answer of 8 hours (which I am sure is the answer they are looking for)!