If the first click STARTS the timer, Buzzy is the fastest clicker with 19 clicks in 20 seconds (19/20), followed by Emily with 9/10 then by Anthony with 4/5.
To better illustrate we need to consider the time between clicks and not the number of clicks in a period of time.
C = Click (no time)
T = Time period
For Anthony, he's clicking by following the series below
C T C T C T C T C in 5 seconds
4T = 5 seconds => T = 1.25
Anthony will then complete 40 clicks in 39xT => 39x1.25 = 48.75 seconds
C T C T C T C T C T C T C T C T C T C in 10 seconds
9T = 10 seconds => T = 1.11 seconds
Emily will then complete 40 clicks in 39xT => 39x1.11 = 43.33 seconds
C T C T C T C T C T C T C T C T C T C T C T C T C T C T C T C T C T C T C T C in 20 seconds
19T = 20 seconds => T = 1.05 seconds
Buzzy will then complete 40 clicks in 39xT => 39x1.05 = 41.05 seconds (THE FIRST TO GET TO 40 CLICKS)
What a long (and complicated) thread to read... So here's my contribution to this subject.
Going back to the original OP, the 2 players are masters of logic (and both love beer). They want to maximize the number of beers, they don't look to get more than each other. The word "sucker" will not affect their judgements either (emotional triggers do not affect masters of logic). In that case defecting would be stupid, illogical and an EMOTIONAL decision.
That being said, Masters of logic would always cooperate. Defecting even once is an emotional decision
Now I realize that, since this thread is taking so long, people are considering these masters of logic as regular people with feelings, who may seek EGO results and even vengeance.
Well, in that case, NOTHING BIG really changes either. The only chance of defecting would be at the last round (unless these masters of logic are plain stupid). If that round is defined before hand, they may both defect or both cooperate that round and the total number of beers they accumulated will change by a maximum of 1 beer.
Now if we don't take the "masters of logic" part literally, we will end up in what the humanity has been through since early history. And one of the 2 brothers will kill the second to maximize its winnings and wealth. We may even find a World War I or II scenario. In real life, this game will never end. People will end (being mortal), but the game won't, it will continue with our children and grand-children playing it.
That is why now we know that our decisions are much more emotional than rational, and some people (egoistic, short-term people), may at some point choose to defect.
I assume that this puzzle may have something to do with the situation the world is right now. And if you don't know what I'm talking about, just watch the news.
I don't intend to discuss politics, I hate this subject (everybody assumes they are on the "right" side of the conflict). But in my opinion, the intention behind the United Nations was to provide an arena for this game to be played rationally. (My opinion about the UN set aside).
Remember this: "We decide emotionally, then justify it rationally!"
In 2 words, No one wil be sober after that game ends
Never be the first to go for the average in your counter offer!!!!
In the previous solutions, it was assumed that the seller would start by asking for $75
In my opinion, the seller being more professional and experienced would have waited untill Sean agreed on paying $75, then he would ask for the new average.
superprismatic was right on both accounts I think.
Since there is no information about my rowing speed in the OP (usually much less then my running speed), the proposed solutions may leave me running in circles, never getting to shore!! A very tight giant spiral will be my final trajectory.
In fact, there must be some minimum rowing speed where I can reach the shore with the ogre at least a feet away from me, so that I can outrun it. This would make a nice puzzle!
I'm forgetting something. It seems there's something I'm not counting, or more precisely, removing more than once! See, my final formula in post#7 was: d^n/n. Very close to yours, but where did I go wrong?
Eureka! I simply multiplied by "d" instead of "n"... This would've got me the same results.
I am now sure that your formula stands... Great job...