Three boxes with Wrong Labels

Three boxes are labelled, "Apples", "Oranges", and "Apples and Oranges". Each label is incorrect. You may select only one fruit from any one box. (No peeking permitted.) How can you label each box correctly?

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Comments

Select a fruit from the "Apples and Oranges" box. Since you know that each label is incorrect and therefore the said box cannot have both fruits, you know that the box contains only whatever fruit you picked . Then, you know that the fruit that wasn't picked cannot be in the box first labelled "Apples and Oranges", and it also cannot be in the box first labelled the fruit name, so this fruit must be in the third box. The last box remaining must have both apples and oranges.

My explanation is probably extremely poorly written and unclear, so hopefully this example will make things a bit more clear.

Example:

Pick from "Apples and Oranges" box. Let's assume that the fruit picked is an orange. This box must only have oranges.
Apples cannot be in the box labelled "Apples and Oranges" (since you know it only has oranges), and it cannot be in the box labelled "Apples", so they must be in the box labelled "Oranges".
The box with apples and oranges must be the last remaining box, "Apples".

Vincent Yao - 8 years, 2 months ago

this is right , my calculation shows the same result

Ahmed Rashique - 8 years, 2 months ago

not at all hard

Shourya Pandey - 8 years, 2 months ago

the labels are all wrong .. which means the box labelled" apples and oranges " is either all oranges or all apples . so we pick randomly from it and if it's an apple so that's all apples .. the oranges box does not contain oranges so its either apples or " apples and oranges " .. but since the apples box doesnot contain apples that means the oranges box contains apples .. which leads us to the apples box having apples and oranges

Muhammad Atef - 6 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$