Riddle?! 10 POINTS! the prize!?

Question

Three sailors land on an island where they find a pile of coconuts and a monkey. They agree to sleep overnight and divide up the pile in the morning. During the night, one sailor wakes up, gives one coconut to the monkey, takes exactly 1/3 of the rest, and falls back asleep. Then the second sailor wakes up and does the same. Later the third sailor wakes up and does the same. In the morning, there are fewer than 10 coconuts left. They each take 1/3. How many coconuts were there in the original pile?

please explain answer

thankyou
nice_libra_guy
dlim98
boba f
your answers are incredible, and detailed!
unfortunatly i dont know the exact answer... but i will find out
the answer 25 has made more sense & a # most agree on. so for now i'll go with that
thanks again for your time

Answer 1

25 coconuts. I did a guess and check doing it backwards from the end. I knew that the ending amount had to be a number that could be divisible by 3 because all the coconuts were divided by the three sailors at the end. So the three options under 10 is 3, 6, 9. I tried them until I found that 6 worked. 6/2 = 3+6 = 9 +1 = 10. this is how I figured that amount before the last person gave one away and took a third. I did this twice more to get 25. First sailor gives on (24) and takes a third (16). Second sailor gives one (15) and takes a third (10). Third sailor takes 1 (9) and takes a third (6) . All three sailors take 2 each.

Answer 2

Well, fewer than 10 makes the answer to thsi question a bit open....
I used Mathematics to solve this... Here is how i did it -

Let X be the number of coconuts in the original pile
Let A be the Amount of Coconuts taken by 1st Person
---- B -------------------------------------------------- 2nd---------
-----C----------------------------------------------------3rd----------

Using this we can say -
X - (A+B+C) = 10

And;

A = 1/3(X-1) Since he gives 1 to monkey and takes 1/3rd of rest

And;

B = 1/3(X-A-1) As the amount now is Original minus A's Share minus 1 to the monkey, and B takes 1/3rd of what is left.

Similarly;

C = 1/3(X-A-B-1)

Now;

A = 1/3(X-1) = (X-1)/3

B = 1/3(X - (X-1)/3 - 1) Putting the value of A in terms of X

= (2X-2)/9

Similarly C = (12X+34)/81

Now, Putting these values in the equation -

X - (A+B+C) = 10

We Get -

X - [ (X-1)/3 + (2X-2)/9 + (12X+34)/81 ] = 10

Solving this we get X = 34...
So....
A = 34 -1 / 3 = 11
B = 22 - 1 / 3 = 7
C = 14 - 1/3 = 4 (13 is not divisible by 3, this is where the "Fewer than 10 comes into play", if i had the exact number remaining, i could have solved correctly)

And 9 Coconuts remain.................

11+7+4+3+9 = 34

The one above has gussed correctly! But i tried to calculate the whole thing, and the maths part of it was enjoyable, so i dont mind!!

Answer 3

working from the bottom to the top, there are fewer than 10 coconuts left. lets call that (end). (end) must be divisible by 3 as they each take a third. therefore (end) could equal 3, 6 or 9.

so the 3rd sailor must have woken up to see a number of coconuts such that when he gave away one, there was a number divsible by 3 remaining, allowing him to take exactly one third. lets cal his share (sailor3) cos he's the third sailor.

then the number he saw must have been (sailor3) + (end) + 1.
and we know that (end) is twice as much as (sailor3) for sailor 3 to have taken exactly one third of the coconuts. for (end) to be twice as much as (sailor3) and our options are 3,6 and 9 from the above point, then (end) has to equal 6

the same applies for sailor 2. (sailor2) = [(sailor3) + (end) + 1] divided by 2. and the number of coconuts sailor 2 must have seen when he woke up is (sailor2) + 1 + [(sailor3) + (end) + 1].

then you have sailor 1 who woke up first. (sailor1) = (sailor2) + 1 + [(sailor3) + (end) + 1] divided by 2. and the total number of coconuts is (sailor1) + 1 + {(sailor2) + 1 + [(sailor3) + (end) + 1}, lets call this (start).

lets see what the total is.

(start) = (sailor1) + 1 + {(sailor2) + 1 + [(sailor3) + (end) + 1]}
(start) = (sailor1) + 1 + {(sailor2) + 1 + [(sailor3) + 6 + 1]}
(start) = (sailor1) + 1 + {(sailor2) + 1 + [3 + 6 + 1]}
(start) = (sailor1) + 1 + {(sailor2) + 1 + 10}
(start) = (sailor1) + 1 + {5 + 1 + 10}
(start) = (sailor1) + 1 + 16
(start) = 8 + 1 + 16
(start) = 25

so there were originally 25 coconuts.

Answer 4

40 coconuts because if there is only 10 coconuts left and the sailors took 1/3 then there should have been 40 in the beginning.

Answer 5

25

Answer 6

40

Answer 7

13 coconuts

Answer 8

46 coconuts?