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# Logic puzzle?

Three red hats and three blue hats are placed in three boxes, with to hats to a box. The boxes are all labeled incorectly. To determine what each box actually contains, you may select one hat from one box; without looking at the contents of the box. Explain how this will allow you to determine the contents of each box?

this question is from a geometry book prentice hall geometry and with the problem it has a picture of three boxes: one has 2 red hats, one has 2 blue hats, and one has 1 red and one blue hat.

### 8 Answers

- Ooh, Ooh pick meLv 51 decade agoFavorite Answer
Assuming that the labels must equal the total of the hats (3 red & 3 blue), then the three boxes are labeled:

Box 1 = 1 Blue/1 Red

Box 2 = 2 Blue

Box 3 = 2 Red

Select a hat from box 1. If it is Red then box 1 contains 2 Red hats, if it's Blue the box contains two Blue Hats.

Knowing this you solve for the other boxes.

If Box 1 = 2 Red hats then the two remaining boxes must contain 2 Blue and 1 Blue/1 Red. Therefore,

Box 2 = 1 Blue/1 Red (since it can't be 2 Blue)

Box 3 = 2 Blue (because that's what's left)

If Box 1 = 2 Blue hats then the two remaining boxes must contain 2 Red and 1 Blue/1 Red. Therefore,

Box 3 = 1 Blue/1 Red (since it can't be 2 Red)

Box 2 = 2 Red (because that's what's left)

- 1 decade ago
you can use probabilty.. so that if one hat in a box is red and then the other box and the other box has a red one you can tell that the boxes each has one red and one blue or compare what you get with the labels

- Anonymous1 decade ago
If all the boxes are labelled incorrectly, then all the ones with 'Blue hat' written on would have red hats, and vice versa.

---Addition---

I'm sure there were 6 boxes originally...

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- Anonymous1 decade ago
I'm gonna go with what JC said.