Impossible Math Problem! Help!?

Question

Each of 3 pails, A, B, and C, contian some water. The Following steps are taken
1] 1/4 of the water from pail A is poured into pail B
2] 1/4 of the water from pail B is poured into pail C
3] 1/4 of the water from pail C is poured into pail A

In the End, all pails contain 18 liters of water each.
Find the amount of water that was origionally in each pail.

if you pour a fourth of water into a then pour a fourth from a to b a will have a different fouth than that poured into it.

Answer 1

a = amount in A at the beginning
b = amount in B at the beginning
c = amount in C at the beginning


After step 1, pail B has b + a/4 liters of water, A has 3/4a liters.
After step 2, pail C has c + 1/4(b+a/4) liters of water, B has 3/4(b + a/4) liters of water which is 18.
After step 3, pail A has 3/4a + 1/4(c + 1/4(b + a/4))) liters, which is 18. And C has 3/4(c + 1/4(b + a/4)) liters, which is 18.

The 3 equations are:
Pail A: 3/4a + 1/4(c + 1/4(b + a/4))) = 18
Pail B: 3/4(b + a/4) = 18
Pail C: 3/4(c + 1/4(b + a/4)) = 18

Let's start with B because that looks the easiest.
3/4(b + a/4) = 18
b + a/4 = 18 * 4/3
b + a/4 = 24

Now we can substitute that into C:
3/4(c + 1/4(b + a/4)) = 18
3/4(c + 1/4(24)) = 18
3/4(c + 6) = 18
3/4c + 18/4 = 18
3c + 18 = 72
3c = 54
c = 18

And for pail A:
3/4a + 1/4(c + 1/4(b + a/4))) = 18
3/4a + 1/4(c + 1/4(24)) = 18
3/4a + 1/4(24) = 18
3/4a + 6 = 18
3/4a = 12
a = 4/3 * 12
a = 16

Finally b must be 20 (a + b + c = 3 * 18)

A started with 16 liters
B started with 20 liters
C started with 18 liters

You can double-check this:
Step 0: [ 16 ] [ 20 ] [ 18 ]
Step 1: [ 12 ] [ 24 ] [ 18 ] (16 / 4 = 4 liters transferred to B)
Step 2: [ 12 ] [ 18 ] [ 24 ] (24 / 4 = 6 liters transferred to C)
Step 3: [ 18 ] [ 18 ] [ 18 ] (24 / 4 = 6 liters transferred to A)

So as non-intuitive as it may seem, the answer is *NOT* 18 liters in each one. The answer is 16, 20 and 18 respectively.

Answer 2

Pail A in step 3 has 6 litres added to the original total to have 18 there. So, pail A had 12 in it before the 6 was added in step 3, but 16 when it started (b/c 3/4 of 16 leaves 12 in the pail after step 1).

Step 2 takes 1/4 of pail A's total out, leaving 18. That means that it has 24 in it (3/4 of 24=18)...but you have to remember that you also added 4 from pail A. So, pail B started out with 20 litres.

Finally, pail C is left with 18...But if it gives 1/4 of its water to pail a, it must have had 24 in it after step 2. 24-6 from pail B = 18

pail a=16 (12 left after 1, then 6 added in 6 to =18)
pail b=20 (4 added from 1, then 6 subtracted to =18)
pailc=18 (6 added from 2, then 6 subtracted and added to the 12 in a to =18)

Am I making any sense?

Answer 3

after step 3, C has 18 liters , which is 3/4 of what it had before step 3, so before step 3, C had 24 liters, and A had 12 liters. These 12 liters are 3/4 of what it had before step 1, so A had 16 liters at the beginning

after step 2 B has 18 liters, so before step 2 B had 24 liters and C had 18 liters. If after step 1 B has 24 liters which included 4 it got from A, then it had 20 liters at the beginning

so we started with A= 16, B= 20, C = 18

1) take 4 from A to B, so now A=12 and B=24
2) take 6 from B to C, so now B=18 and C= 24
3) take 6 from C to A, so now A= 18 and C=18

Answer 4

it all depends on whether or not the 1/4 of water from B into C is the original pail, or the new amount that is in there now. If its the original amount in B and in C, then each pail would originally contain 18 litres.

Answer 5

the original amount of water from A, B and C is 16(A), 20(B), and 18(C)...

see the work out:

A (16) 1/4 is 4 litre --> B (20) 20+4 = 24litre

B(24) 1/4 is 6 litre( 24 - 6 = 18) --->C (18) 18+6 = 24litre

C(24) 1/4 litre is 6 litre ( 24 - 6 = 18)--> A(12) 12+6 = 18 litre

and you can get the answer..

Answer 6

so you get 18 and divide it by 3 since theres 3 pails. its baiscally a trick question. cuz A was poured in to B and B was poured into C and C was poured into A. so in da end they all have da same amount of water they started with in da beginnig. so the answer would be 6 LITERS

Answer 7

listed right here are some opportunities: Goldbach conjecture: each and every even huge type larger than 2 is the sum of two primes. all and sundry believes it fairly is genuine even though it has never been shown. See first link. Squaring the circle: build a sq., utilising ruler and compass, that has a similar section as a given circle. This has been shown to be impossible, however the data isn't straightforward and a great form of crackpots stated as "circle squarers" shop attempting to do it. See 2d link. The impossible 15 puzzle. If the products are set up awesome on the beginning up it relatively is provably impossible to unravel, yet relaxing to purpose. See third link.

Answer 8

18 l .

Answer 9

it is so easy, if they poured the same amount each time, the original amount was 18 liters

Answer 10

i dont know if this is right cuz im like totaly guessing.... 18 liters?? hahha