Opt for the pennies
BillyFalcon wrote:The rumor puzzle reminds me of the man who was hiring a man for thirty days.
The new 30 day employee could get $1,000,000 one milllion cash for the thirty days. He was offered the option of a penny for his first day, two cents for his second day, four cents for his third day, eight cents for his fourth day, the amount to be doubled each day.
Thee boss wanted a snap decision. Which way should he have opted for?
He should take the pennies. By the end of the 30 days he will have earned app. $21,474,836.47. It's more than just doubling the pennies each day, you still have to add them together. On day one he gets 1 penny, day two he gets 2 pennies, on day three he gets 4 pennies, on day four he gets 8 pennies. In four days he already has 15 pennies. So first you double the amounts 1x2=2x2=4x2=8x2=16x2=32.....and so on and then go back and add all of the amounts together. I wish someone would offer me that deal. That would be SWEET to earn over 21.4 million dollars in 30 days.
Kraven
Forgive me for saying you are wrong, but you are. The question, IMHO, has not yet been answered correctly, though satt_focusable pointed to the flaw (though not particularly clearly)
Let me put it this way. If I tell four people in 30 minutes, unless I tell all four at exactly the same time and everyone else tells every 'next four' at exactly the same time, I - and the subsequent tellers - will only AVERAGE four every 30 mins.
Let 't' be the units of time (7.5 mins each but it looks prettier with a bit of algebraic looking stuff!) At t = 0, only one knows. At t=1 I tell one person so now two know. At t=3, both he and I tell someone and now four know. At t=4, all four tell one other person, so now eight know and not the five that the 'simple' answer provides. The number that know will always be "two to the power of t-1")
But 't' = 7.5 mins, so the total time to inform the world will be whatever the population of the world is expressed as a power of two, the index minus one times 7.5 mins will give the answer. It does not take quite as long as Ronrocks says.
I do not claim that this answer is any more a definitive answer than any other. The question does not specify how that 30 minutes is divided up, so given that one' two, four, or whatever can be told at one time, there are a range of answers that are all consistent with the question.
