23 August 2007


You have three boxes of fruit. First box contains just Apples, second contain just Oranges and the third box contains a mixture of both. Each box is labeled -- one says "Apples", one says "Oranges", and one says "Apples and Oranges." However, it is known that none of the boxes are labeled correctly. How can you label the boxes correctly if you are only allowed to take and look at just one piece of fruit from just one of the boxes?

For Solution SCROLL DOWN...

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Take a piece of fruit from the box marked "apples and oranges." Suppose the fruit you take is an apple. Then that box must be the box containing just apples. Therefore, the box marked "oranges" can't be the box containing just apples, and it can't be the box containing just oranges either -- so it must be the box containing apples and oranges. The remaining box is therefore the box containing just oranges.

If the fruit you take out is an orange, the solution is derived in a similar fashion: the box marked "apples and oranges" is the box containing just oranges; the box marked "apples" is the box containing both apples and oranges; and the box marked "oranges" is the one containing just apples.

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rahul said...

a-> apple box, o->orange box
a&o->apple and oranges box
take out a fruit from a&o box
if apple comes out
a&o -> a
if orange comes out

Harishankar Naganathan said...

Apples Box labeled with ORANGE,
Orange Box labeled with APPLE&ORANGE,
Apple/Orange Box labeled with APPLE.

We should take a fruit from the box labeled APPLE&ORANGE.

when the Result is Orange:
Interchange ORANGE label with APPLE/ORANGE and then interchange APPLE/ORANGE label with APPLE label.

when the Result is APPLE:
Interchange APPLE label with APPLE/ORANGE and then interchange APPLE/ORANGE label with ORANGE label.

This is because, we are known that all the boxes are labeled wrongly.

Anonymous said...

as the question says none of them is correct

then take out a fruit frm Apple nd orange labelled box

if it is apple then Label it as Appple if it is Orange lablel it as Orange Bcoz as The Labels are not true the fruit will give u the correct ANS

then Label the another one as Orange or apple respectively

which one was previously labeled from which we exchnd the label

then finally label the last one as apple nd orange

it is similar 2 rahul.........

prashant said...

take out a fruit from 'apples n oranges' box. if apple comes out, then it is apples' box, if orange comes out, it is oranges' box.

suppose an apple comes out. then the box previously called 'orange' cannot have only oranges in it(bcoz the question says that none r labelled corrctly).
it cannot have only apples in it coz we have already found out the box which has only apples. so that box has both apples and oranges. the third box- apples now has to have only oranges in it!!

a similar analysis can be done if an orange comes out of the 'apples n orange' box initially.

chaitu said...

let apples=a,
let oranges=o,
let oranges and apples=o&a,
there are only two possibilities that the alla the three lables are wrong.
1.(o, a, o&a)=(a, o&a, 0).
(right) (wrong)
2.(o, a, o&a)=(o&a ,o, a).
(right) (wrong)
now 1st take a fruit from o&a labble box(wich is said to be wrongly labled).if the fruit is apple then make that box labble as "apple".and box containin orange lable is achnged to "apple and oranges"
and the box containig apple lable is changed to"oranges".this can be done ussing 1st possibility from above.
similarly 2nd possibility is done if the fruit taken from box(which is wrongly labled)is orange.

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