Warren Buffet and Bill Gates
There is a round table conference. Warren Buffet is the richest person while Bill Gates sitting on his right has one dollar less then him. And the person on Bill’s right has two dollars less than Warren. And so on. Warren feels game and gives 1 dollar to Bill. He in turn gives 2 dollars to the person on his right. And so on.
But at one stage some one says, "Now I don’t have 1 dollar extra to give to the person on my right." However, he also says that he has 101 dollar more than him. How many dollars did Warren have initially and how many people were there?
But at one stage some one says, "Now I don’t have 1 dollar extra to give to the person on my right." However, he also says that he has 101 dollar more than him. How many dollars did Warren have initially and how many people were there?
Labels: logic, mathemagic
posted by Rajesh Lal at
8:53 AM
9 Comments:
What does "And so on mean", is it 1,2,4,8... or 1,2,3,4...?
Chris it means 1,2,3,4.
Thanks ToM, I had just come to the conclusion that was possible and that there might be about 100 people, but my brain has just fried on a silly counting issue.
I think I've got the hang of it now. If it is about a 100, that's pure luck. Back soon:)
It's interesting. Suppose there were n Waren' dollars initially and there are k+1 persons. The poorest (call him last) one has n-k dollars. After the last resieves his first cash from his left person, he has n dollars, and Waren has n-1, his right n-2 and so on. Now you can guess that when the m circle of money transmission goes to the end, the last has n+mk-k dollars, Waren has n-m, his right n-m-1 and so on. Sum these dollars: there number is constant. Also to the end of m circle last gets mk+m-1 dollars.
There are two main variants. First is when last has a money giving problem. He should give mk+m, thus
n+mk-k+1=mk+m , hence n=m+k-1.
101 dollars difference with Waren gives
mk+m-k=101. There are various solutions of this two equations, e.g.
(n,m,k)=(51,3,49),(28,5,24),(24,6,19).
Another possibility is when money problem has not the last. Threfore this one has just resieved 100 dollars which gives total difference 101 with his right. If his number after Waren is s, he now has n-m-s+100, his right has n-m-s-1 dollars. s should give him 101 dollars, therefore
n-m-s+100+1=101, hence n=m+s. The other equation is the expression of cash value 100 he gets:
mk+m+s=100.Still lots of solutions.
This post has been removed by the author.
What a liar I am. I've given up, If found it too much like hard work making up the tables and trying to extract an equation. Byeee.
I dont get it.. does the poorest guy (left of buffet) have 0$ or 1$, tht will change the whole answer,
Also another thing is, the poorest guy may have muc more than 1$, and multiple circles my hae been done, to get his money to 0.
So, unless u tell me the number of circles, or the money the poorest guy had originally, or the amt. of eople, i find it impossible..
Too many variables are there which cannot be tken out.
Hi A. I share your doubts after spending ages trying to get a method. But, it would be really out of order if the problem didn't have a nominally unique solution with the information given.
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