# The 3 closed boxes [duplicate]

We have 3 closed boxes. One contains apples and the second contains oranges and the third contains apples and oranges . They have labels Apples, Oranges, Apple & Oranges but all the labels are put on the wrong boxes. How do you put the labels on boxes correctly if you can only open one box to see what is inside ?

• This is not really a duplicate as you have to choose which box to draw from. In First day of school you didn't choose. Sep 13 '15 at 21:48
• guys calm down I didn't take from any previous post Sep 13 '15 at 21:52
• @RossMillikan They are logically equivalent. I was wrong to say that they were not dupes. Sep 13 '15 at 21:56
• I can't read all the old posts before posting and i just signed up an hour ago Sep 13 '15 at 21:57
• aha I didn't know the system here Sep 13 '15 at 22:07

If picking from Apples is right, by symmetry so is picking from Oranges. Also if you pick from Apples and get an orange, you don't know if the box is Oranges or mixed. You have to pick from Apples & Oranges. Whatever you get, you know what box it is. Then the fact that both the remaining labels are wrong will let you sort out the other two.

Rereading the question, you can open any box you like. If you open Apples and see Oranges, the Apples label goes on the box that currently says Apples and Oranges. When I heard this the first time, you were only allowed to draw one fruit from the box you picked. In that case it must be the Apples and Oranges box.

• BAAAAAANG RIGHT Sep 13 '15 at 21:51
• You can also upvote this answer if you like. Sep 13 '15 at 22:07
• It says i should have at least 14 reputation to do that Sep 13 '15 at 22:13

Look at the box labelled "Apples". If there are only oranges in it, then the one labelled as mixed has only non-oranges (apples) and the remaining one both. If there are both in the first box, the one labelled with the non-apple (orange) is actually the apple box and the remaining one the orange box. By a similar logic you can also choose the one labelled as an orange box thanks to the symmetry.

• you are right two many ways to solve it Sep 13 '15 at 22:09
• The answer you accepted mentions that too. Sep 13 '15 at 22:59