# Candy jars with mixed lids [duplicate]

One day Nasrudin went to a candy store where the owner had mistakenly mixed the lids of three candy jars, leaving each one wrongly labeled. One contained peppermint candies, another contained chocolate candies, and the remaining contained peppermint candies and chocolate candies mixed. All the candies had the same packaging, so without tasting them it was impossible to tell which kind of candy it was.

The owner told Nasrudin that he would give him a bunch of candies if he could determine the least amount of candies that he should try in order to tell the correct label for each candy jar.

That day Nasrudín left the candy store with great joy with his gift.

How many candies did Nasrudin taste in order to get the prize? And how did he get the correct answer?

• This is a very old classic.
– Jens
Apr 9 '20 at 8:25
• Indeed. Searched it here but couldn't find it. So I posted it for some that may not know it ;) However the story telling is a bit of my own. Apr 9 '20 at 8:26
• This is essentially A modified version of apples and oranges logic + a few other linked questions there. Apr 9 '20 at 8:32
• Well, it appears to be similar @Glorfindel. With the difference that in that question you have the hint about the minimum number of items you have to take. Apr 9 '20 at 8:35

You'll need

only one candy from the mixed jar. Since it's wrongly labeled, if it's a chocolate, you know it's entirely made of chocolates; in that case, the one with the mint label can only be the mixed one and the one labelled chocolate must be the mixed one.
If it's a mint, it's entirely made of mints, the one with the chocolate label can only be the mixed one and the one labelled mint must be the mixed one.

The minimum amount requested is

1, from the mixed candy jar

Because

Due to being mislabeled and label having both candy types, we know that one will contain only one candy type, the one you drew.

This, then, means

The jar labeled as the candy you did NOT draw will have mixed candy. It cannot have what it says because it's labeled wrong, and it cannot have what you drew 'cause that's what is contained in the previous jar. Thus, it has mixed.

Which leaves

The jar labeled as the candy you drew will have the other type of candy.