Determine what the correct labels [duplicate]

The father bought gifts for each of his three daughters, whose names were Black, White, and Gray. Thinking it would be amusing, he bought two black scarves for Black, two white scarves for White, and a white scarf and a black scarf for Gray. He had the store clerk wrap the three presents and label them with the names of his daughters.

But, there was a momentary distraction. The scarves did not get mixed up, but all three labels were wrong. By lifting a corner of the wrapping on any one of the gifts, it is possible to see the colour of one of the two scarves in that package.

How many corners does the father have to lift to determine what the correct labels should be?

marked as duplicate by ffao, Wen1now, JonMark Perry, Sid, Rubio♦Sep 13 '17 at 9:12

• If the scarves didn't get mixed up, they should be in the right places, so the answer is 0 – boboquack Sep 13 '17 at 7:29
• I did changes.. – Smart Sep 13 '17 at 7:31

1

How:

Look in the box marked grey. WLOG it is black; then since the label is wrong the black things must be there and the white scarves must be in the box marked black (since they can't be in the box marked white). Thus we know all three boxes' colours.

How: All of three labels are wrong, so I will lift a corner in the Grey box.
If the corner is Black, this Grey box is Black, the Black box is White, and the White box is Grey.
If the corner is white, The Grey Box is White, the White box is Black and the Black box is Grey.

1

You can do this by:

looking in the GREY package.
GREY: You see white (say), then GREY->WHITE as the other scarf cannot be black (all labels are wrong remember), then BLACK->GREY because it can't go to black, and finally WHITE->BLACK. If you see a black scarf, GREY->BLACK, etc...

With either other package, say BLACK: say you see black, then BLACK->GREY, white can't be white so WHITE->BLACK, GREY->WHITE. The reverse holds for the WHITE package if you see white.
But if you see white after you open the package labeled BLACK, the other package contents are determined by the missing BLACK scarf. Say the missing scarf is W, then W->G, G->B, say B, then W->B and G->W. So this requires at least 2 corners to be peeked at.

It is

2 corners at the minimum

As,

By randmomly selecting a box, lifting a corner and looking at the color results in the information of only one color, which is insufficient to decide what type of box it is.