John is at a table with other people. He has $1 more than the person to his right & that person has $1 more than the person to his right and so on around the table. Then, John gives one dollar to the person to his right and he in turn gives $2 to the person to his right and that person gives $3 to the person to his right and so on. This process continues around the table as many times as is necessary until someone has no money left. At that time, John has 9 times the money as the person to his right. How many men are there along with John, how much money did he start with, and how much money does he have at the end?
Can you prove the uniqueness of the solution?
2006-12-23 11:07:03 · 19 answers · asked by oscarD 3 in Science & Mathematics ➔ Mathematics
yes, actually I can 'god knows and sees else Yahoo'. will you bet otherwise?
2006-12-23 11:15:09 · update #1
Including John, there are 17 ppl at the table. John starts with $23, and when the person to his immediate left is knocked out, he has $135.
Steve
Note that if the 9 in the problem is replaced by a prime number, interesting things happen. For example, if John ends up with 11 times as much money as the person to his right, there are 3 solutions:
3 ppl, John starts with $5 and ends with $11
7 ppl, John starts with $13 and ends with $55
21 ppl, John starts with $29 and ends with $209
Note also that 17 = 2*9-1. No matter what 9 is replaced with, 2*m-1 is always a possible solution.
2006-12-23 12:22:50 · answer #1 · answered by Anonymous · 1⤊ 0⤋
17 people. John had $23 to start with. Process goes on for 7 rounds. John is left with $135 when the person to his left is down to $0. The solution is unique because the equation for the number of people around the table = 17 / ( 8 - i ), where "i" is the number of rounds. The only integral solution for this equation is when the denominator is 1. Which gives a value of 7 for "i". Everything else follows with their own unique values.
2006-12-23 12:55:03 · answer #2 · answered by ramshi 4 · 1⤊ 0⤋
i've got seen a shaggy dog tale like this yet what i heard grew to become into: you're trapped in a cement room without residing house windows or doors. you have a chew of paper. How do you get out? You rip the piece of paper in 0.5, positioned it decrease back at the same time to make an entire and climb out of 'hollow'
2016-11-23 13:52:20 · answer #3 · answered by Anonymous · 0⤊ 0⤋
9 men, including John.
John had 1 dollar, so had the 8 other men.
John has 9 dollars - and every one else had 0 dollars left.
It's to late to think anymore about this question.
***So, I was wrong - but here is the link to Scott R. - Question # 11
click on it and you find the answer.
http://answers.yahoo.com/my/profile;_ylt=AsG6jTwdOCYxTMaSEBdbscnsy6IX?show=c511575866d062562bfb645d4ee5d618aa&link=answer&more=y
2006-12-23 11:29:46 · answer #4 · answered by ? 6 · 0⤊ 2⤋
Steve's solution is the correct one. There are multiple solutions. In fact, I think there are infinite solutions, and I believe, but have not proved, it is alephnull (countable infinity) of which I believe is a unique solution. It is unproven, to me, how many infinities there are, but only a single countable infinity.
2006-12-23 13:53:39 · answer #5 · answered by joe blow u still dont know 2 · 1⤊ 1⤋
* ATTENTION *
This was asked by Scott R Member since: 13 June 2006
2006-12-23 11:19:12 · answer #6 · answered by ou812 2 · 1⤊ 0⤋
$5 + 9% tip
2006-12-23 14:14:09 · answer #7 · answered by Jared L 4 · 1⤊ 1⤋
All I know is that there are three ppl including John, he started with $9.00 and I'm to lazy to finish the equation someone else can do it for me but that's what it is.....
2006-12-23 11:50:45 · answer #8 · answered by dominicandyme22 2 · 1⤊ 2⤋
How many people were at the table?
2006-12-23 11:09:27 · answer #9 · answered by Butterfly 1 · 1⤊ 2⤋
u know im not very smart put that is one heck og a question did u make it yourself if so bravo i bet my brother could figure it out but hes in collage nice job
2006-12-23 11:11:54 · answer #10 · answered by loserlover 1 · 1⤊ 2⤋