956-4 = 15621
is it right ????
Five pirates and a monkey are shipwrecked on an island. The pirates have collected a pile of coconuts which they plan to divide equally among themselves the next morning. Not trusting the others, one pirate wakes up during the night and divides the coconuts into five equal parts with one left over, which he gives to the monkey. The pirate then hides his portion of the pile. During the night, each of the other pirates does exactly the same thing by dividing the pile he finds into five equal parts leaving one coconut for the monkey and hiding his portion. In the morning, the pirates gather and split the remaining pile of coconuts into five equal parts and again one is left over for the monkey. What is the smallest number of coconuts the pirates could have collected for their original pile?
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9 Answers
9consider
f(x) = 4/5(x-1)
now acc to given conditions
f5(x) = 5λ = 45(x+4)/55 -5
now x +4 is multiple of 56
now least possible x = 56-4 satisfies all criteria with ( f,f2,f3...f5) all natural
9i dont know about those mod thingies ( will try learning in holidays)
wat ive derived seems correct confirm if u know official ans
(method is right means ans is right !! )
btw uve gone an xtra step in morning 5116 coconuts
9vivek starting with 15621
after
1 12496
2 9916
3 7996
4 6396
5 5116 ....(this is wat is present in morning )
now 5116 -1 is multiple of 5
1i don't know much either,its just like u write in java/C++
5%2 = 1
(replace % with mod)
4092%5=2
what i meant here is that after dividing into 5 parts there will be 2 coconuts left
anyway doesn't matter i went a step further
are u sure this is the smallest possible?
1http://www.math.okstate.edu/~wrightd/crypt/lecnotes/node24.html
well i just stumbled upon it (using the stumbleupon extension in firefox ) and found this