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Mango apples and bag labels

You have three bags and three labels. One bag has only Mangoes, one has only Apples and one has both Mangoes and Apples. Three labels are M, A and MA. M label was meant for the bag with only Mangoes, A label was meant for the bag with only Apples and MA for the bag with both Mangoes and Apples. Victor by mistake labelled the bags wrongly such that all the labels are wrong, how many minimum number of Fruits he should pick and from what bags to correct the labels? It is given that each bag has unlimited number of Fruits to be picked.

Solution :


The minimum number of Fruits Victor should pick to identify correct labels is 1 from the bag with label MA

How just 1 ball ?

As the label of all the bags are wrong, bag with label MA can either have all Mangoes or all Apples.

Now Victor will either get Mango or the Apple.

Case 1: Lets assume Victor gets Mango
Bag with label MA is the bag with all the Mangoes.
So now MA is M.
Bag with label A can either be MA or M(as all the labels are wrong) but as we already know M bag so it can only be MA.
We know 2 bags correctly so third bag with label M should be A.

Case 2: Victor gets Apple
Bag with label MA is the bag with all the Apples(A).
Now MA is A
Bag with label M can either be MA or A(as all the labels are wrong) but as we already know A bag so it can only be MA.
we know 2 bags correctly so third bag with label A should be M.
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