Label the Box correctly


There are three boxes which are labeled as Rs100, Rs150, and Rs200. One box contains two notes of Rs. 50. The second box contains one note of Rs50 and one note of Rs100 The third box contains two Rs. 100 notes. All boxes are labeled incorrectly.

What is the minimum number of boxes you must check in order to label all boxes correctly?

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    If I already know that all three labels are wrong (before proceeding to check), checking only ONE box should suffice.

    There are only TWO possible combinations of labels such that they are all wrong, as shown in the picture below.

    Actual Status => Box 1 Box 2 Box 3
    100 150 200
    Label Set 1 150 200 100
    Label Set 2 200 100 150

    In either case, once I open one box, say, Box 1, I can know on which box each label should go.

    e.g. Suppose the scenario is Case 1 (150/200/100). I open box 1 (Labelled ‘150’) and sees that it contains Rs. 100 (2 x 50) ,  I know for sure that the box labelled ‘200’ actually contains Rs. 150 and hence the label should go to that box (Box 2). Moreover, since I have already seen that Box 1 contains Rs. 100, I know that I should remove the label that says ‘100’ (which is Box 3) and place it on the Box 1.  Hence solved. Likewise in the second case as well.

    Viji_Pinarayi Expert Answered on 25th July 2021.
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