Hello,
Please excuse my bad English. My name is Ariyan and I live in Holland. I'm a great fan of your website and I visit it every day, just like your forum.
I have been having some problems with a problem that I saw in a magazine. I don't know if it has ever been put on this forum but I don't think so. Here goes.You have a big cake, you're going to receive 100 guests. The first guest gets 1% of the entire cake. The second guest gets 2% of what is left. The third guest gets 3% of what is left.
My question:
1) Which guest gets the biggest piece?
2) Is there a formula to calculate how big the piece is for the 'n-th' person?
I have been working on question 2 mostly but I'm just getting a very very long row. It is something like:
n) n/100(1-1/100-2/100(1-1/100)-3/100(1-1/100-2/100(1-1/100)-...-(n-1)/100(1-1/100-2/100(1-1/100)...(n-2)/100(1-1/100-2/100(1-1/100)-...(n-3)/100(1-1/100-2/100(1-1/100)-...and so on...
I came up with something, but I don't if it is correct. It goes as following:
Name every pre-calculation 'a' So the formule would get something like
n/100(1-1/100-2/100(a2)-3/100(a3)-...-(n-1)/100(a(n-1))-...and so on... and a2>a3>a4>a(n-1)
Well all of this is really work that hasn't got much to with the answer but still I like it
I appreciate all the help I get.
Thank you