Difficult math, Diophantine equations.
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Mickey
May 10, 2010, 6:05:36 AM5/10/10
to nextgen_engg
Five men and a monkey were shipwrecked on a desert island, and they
spent the first day gathering coconuts for food. Piled them all up
together and then went to sleep for the night. But when they were all
asleep one man woke up, and he thought there might be a row about
dividing the coconuts in the morning, so he decided to take his share.
So he divided the coconuts into five piles. He had one coconut left
over, and he gave that to the monkey, and he hid his pile and put the
rest all back together. By and by the next man woke up and did the
same thing. And he had one left over, and he gave i t to the monkey.
And all five of the men did the same thing, one after the other; each
one taking a fifth of the coconuts in the pile when he woke up, and
each one having one left over for the monkey. And in the morning they
divided what coconuts were left, and they came out in five equal
shares. Of course each one must have known there were coconuts
missing; but each one was guilty as the others, so they didn't say
anything. How many coconuts were there in the beginning?
Regards,
Jyoti
spent the first day gathering coconuts for food. Piled them all up
together and then went to sleep for the night. But when they were all
asleep one man woke up, and he thought there might be a row about
dividing the coconuts in the morning, so he decided to take his share.
So he divided the coconuts into five piles. He had one coconut left
over, and he gave that to the monkey, and he hid his pile and put the
rest all back together. By and by the next man woke up and did the
same thing. And he had one left over, and he gave i t to the monkey.
And all five of the men did the same thing, one after the other; each
one taking a fifth of the coconuts in the pile when he woke up, and
each one having one left over for the monkey. And in the morning they
divided what coconuts were left, and they came out in five equal
shares. Of course each one must have known there were coconuts
missing; but each one was guilty as the others, so they didn't say
anything. How many coconuts were there in the beginning?
Regards,
Jyoti
sabitha reddy
May 10, 2010, 11:50:42 AM5/10/10
to nextge...@googlegroups.com
answer: 3121
Explanation: let say there are x coconuts after fifth person took his share. Next day these 'x' were equally distributed by all five. if there are 'x' left at the end, it means there were 5x/4 + 1 when 5th woke up. similarly,5(5x/4 + 1)/4 + 1=(25x+36)/16 when 4th woke up. If you proceed with this backward approach, you get (3125x+8404)/1024 when 1st person woke up.
by solving this I got x=1020. So, there were 3121 coconuts at the beginning.
Explanation: let say there are x coconuts after fifth person took his share. Next day these 'x' were equally distributed by all five. if there are 'x' left at the end, it means there were 5x/4 + 1 when 5th woke up. similarly,5(5x/4 + 1)/4 + 1=(25x+36)/16 when 4th woke up. If you proceed with this backward approach, you get (3125x+8404)/1024 when 1st person woke up.
by solving this I got x=1020. So, there were 3121 coconuts at the beginning.
Mickey
May 11, 2010, 2:35:35 AM5/11/10
to nextgen_engg
You must have done a lot of mathematics to get this. :)
On May 10, 8:50 pm, sabitha reddy <sabitha.re...@gmail.com> wrote:
> answer: 3121
>
> Explanation: let say there are x coconuts after fifth person took his share.
> Next day these 'x' were equally distributed by all five. if there are 'x'
> left at the end, it means there were 5x/4 + 1 when 5th woke up.
> similarly,5(5x/4 + 1)/4 + 1=(25x+36)/16 when 4th woke up. If you proceed
> with this backward approach, you get (3125x+8404)/1024 when 1st person woke
> up.
> by solving this I got x=1020. So, there were 3121 coconuts at the beginning.
>
On May 10, 8:50 pm, sabitha reddy <sabitha.re...@gmail.com> wrote:
> answer: 3121
>
> Explanation: let say there are x coconuts after fifth person took his share.
> Next day these 'x' were equally distributed by all five. if there are 'x'
> left at the end, it means there were 5x/4 + 1 when 5th woke up.
> similarly,5(5x/4 + 1)/4 + 1=(25x+36)/16 when 4th woke up. If you proceed
> with this backward approach, you get (3125x+8404)/1024 when 1st person woke
> up.
> by solving this I got x=1020. So, there were 3121 coconuts at the beginning.
>
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