Sunday 4 September 2011

measure 4L water

You have to measure 4L water with 2 measuring cups, one that can contain 3L water and other that can contain 5L water. Measuring cups obviously don't have per liter markings! :)
\via{Prashant}

My idea was as follows. It is not possible to directly have 4L in 1 measurement as 3 and 5 don't in any way make up 4. So, we have to somehow come up with method which will keep 4L in measuring cups themselves - either separately or combined - say 1+3, 2+2, 0+4 etc. But, it is not possible to have 4L divided up in 2 cups, because in say we want to achieve 1 in 3L and 3 in 5L, we don't have empty cups to measure anything at this point. This indicates that we can only have 0+4 or 4+0 in cups. Obviously, 3L cup cannot contain 4L, so we have to somehow have 4L kept in 5L cup in the end. Starting with this final step backwards, what keeps 4L in 5L cup? One way is to have 5L filled in completely and pour just 1L from it to 3L cup. This means to be able to do this, 3L cup should be already having 2L water in it, so that it can accommodate only 1L more. Getting 2L in 3L cup is fairly easy. So, overall following are the steps- (let A = 3L cup, B = 5L cup)
0. A = B = 0 \\ Both empty initially
1. A = 0, B = 5 \\ Fill in 5Lcup
2. A = 3, B = 2 \\ Pour 3L in A, 2L remains in B
3. A = 0, B = 2 \\ Empty 3L cup
4. A = 2, B = 0 \\ Pour 2L from B to A
5. A = 2, B = 5 \\ Fill B cup again
6. A = 3, B = 4 \\ Pour 1L from B to A, B has 4L remaining

2 comments:

  1. why so complicated??
    Fill 5L cup Two times with 3L(3+2) ..."1L remained in 3L cup"..empty 5L..Pour 1L from 3L cup to 5L..Fill 3L cup pour in 5L...(1L+3L=4L)..done!!

    ReplyDelete
  2. why so complicated??
    Fill 5L cup Two times with 3L(3+2) ..."1L remained in 3L cup"..empty 5L..Pour 1L from 3L cup to 5L..Fill 3L cup pour in 5L...(1L+3L=4L)..done!!

    ReplyDelete