There are 3 boxes. 1 has apples, 1 has oranges and the other has apples and oranges. The boxes are labeled wrong so that no label is correct. Sue opens just one box, and without looking in the box, takes out 1 piece of fruit. She looks at the fruit and immediately labels all the boxes correctly. Which box did she open and how did she know?
2007-10-12 02:25:51 · 14 answers · asked by DicK 2 in Science & Mathematics ➔ Mathematics
thank you, ms. lexi!!!
2007-10-12 04:04:07 · update #1
She takes an orange out of the box with apples and oranges in it. The label on the front says 'oranges'. This way she knows it is the box with apples and oranges, as it cannot be only oranges because the label is wrong. And because the labels are all wrong, the box that says 'apples' on it must have oranges in it, as the first already has oranges and apples and therefore the box that says 'apples and oranges' must have apples in it.
2007-10-12 02:31:03 · answer #1 · answered by Anonymous · 2⤊ 4⤋
First box to be opened is the box labelled "both oranges and apples".
Since it is not labelled correctly-it should be either apples or oranges.
If she finds apples the other boxes should have actually either oranges or mixture. But the labels will be either apples or oranges. The orange labelled box can not have oranges label, it should be having mixture of fruits and the box labelled apples will have mixed fruits.
I f she finds oranges, then the the apples labelled box should have mixed fruits and oranges labelled box will have
apples
2007-10-12 03:02:56 · answer #2 · answered by mohanrao d 7 · 0⤊ 0⤋
She opened the box labeled "Apple and Oranges". Because all of the boxes are labeled incorrectly, this must either be the box with only apples or the box with only oranges, and the fruit that she sees will allow her to correctly label this box.
She can label the other boxes this way. If she saw an apple, the remaining labels will be "Apples" and "Oranges", and the remaining boxes will contain oranges and apples + oranges. Because both of these must be also labeled incorrectly, the box labeled "Oranges" must contain both apples and oranges, and the box labeled "Apples and Oranges" must contain just oranges.
2007-10-12 02:36:49 · answer #3 · answered by Kristian D 3 · 0⤊ 0⤋
She opened the box containing oranges and apples. She knew because the box was marked 'apples' and the the piece of fruit she picked up was also an apple. Since all boxes are marked incorrectly, it cannot be the box with apples only. It also cannot be the box containing oranges only as in that case, she would not have picked up an apple. So she concluded that it was the box containing both apples and oranges. Now, the rest two boxes are marked 'oranges' and 'apples and oranges'. So obviously the one marked oranges must be apples and the one marked oranges and apples is apples.
2007-10-12 02:37:04 · answer #4 · answered by Madhukar 7 · 0⤊ 0⤋
She opened the box with apples, but the label said oranges. Then she knew that the box with the label of both was oranges, and the box with the label apples was both.
2007-10-12 02:37:41 · answer #5 · answered by hunted1820 2 · 0⤊ 1⤋
She openned the apple and orange box. She knew that the label was wrong, so that whatever fruit she drew out was the fruit of the correct label.
The other two boxes can be figured out by deduction knowing that they have the wrong label.
2007-10-12 02:31:42 · answer #6 · answered by Frst Grade Rocks! Ω 7 · 1⤊ 1⤋
Let's call the boxes AA (all apples), AO (apples and oranges) and OO (all oranges).
She takes a piece of fruit from the box labeled Apples and Oranges (AO).
If she has an Apple, then this box contains All Apples (AA), since it can't be the all oranges (OO) box, nor the Mixed box (AO), since then the label would be correct.
If she has an Orange, then this box contains All Oranges (OO), since it can't be the all apples (AA) box, nor the Mixed box (AO), since then the label would be correct .
Label this box correctly, (either AA or OO based on the fruit you hold), and swap the labels on the other 2 boxes, since they are incorrectly labeled.
2007-10-12 02:57:55 · answer #7 · answered by Don E Knows 6 · 1⤊ 0⤋
she opened the box labeled "apples and oranges". whatever she pulled out, that's what that box was (either "apples" or "oranges"). so the box labeled "apples" if she got an orange or the box labeled "oranges" if she got an apple, must be "apples and oranges". the last box is whatever is left.
2007-10-12 02:36:02 · answer #8 · answered by ? 4 · 0⤊ 0⤋
she opened the one falsely labelled applange (mix of A and O). if she took apple out, the box was "apple" originally, and vice versa. the one labelled apple is actually "orange" and the last is the mix.
2007-10-12 04:37:27 · answer #9 · answered by Mugen is Strong 7 · 0⤊ 0⤋
I think she opened the box which had apples and oranges.
2007-10-12 02:36:11 · answer #10 · answered by dimplesoft 3 · 0⤊ 0⤋