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I'm having trouble solving a puzzle in Swedish. I've translated it below:

  1. How many earrings do you have to pick up to be sure to get a pair of the same in a mix of earrings where "favorable outcomes" represent 4/20 from the start. This was not a probability calculation to be performed because logical thinking gives that you have to pick up all the remaining sixteen to know that no error possibilities remain. So you have to pick up 18 to be sure to get the pair in your hand.

I'm not sure where to begin with this puzzle. How do I calculate the number of earrings that need to be picked up to ensure that I get a pair of the same type?

Here is the origin of the puzzle: https://cdn.discordapp.com/attachments/869145673197580298/1083855309942030346/PIL_-_sammanfattning_av_fragor_oscar_bakhouch.doc

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  • $\begingroup$ As is the case with many of your recent posts, the question you've asked here may be puzzling to you, but that does not make it a puzzle. This is a fairly basic math/probability problem one might find in a textbook; such questions are off-topic here, as there is no real puzzling element to be solved. Please take some time to look around and familiarize yourself with the kinds of questions that are well-received here, ideally before you post any more questions. $\endgroup$
    – Rubio
    Mar 12, 2023 at 15:44

1 Answer 1

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I am going to assume that the desired earrings are equal for both ears, i.e. the earring in the left ear is identical to the earring in the right ear and you can exchange them between ears indistinctively.

This means that there are 4 single and identical earrings out of 20, and other 16 earrings different to those 4.

Picking up 2 out of those 4 identical earrings would give you a correct pair of earrings to wear.

Now, imagine the worst case scenario, where you keep picking earrings and you are so unlucky that in your first 16 tries, you pick up all the wrong ones. This means that they remain only 4 to be picked up, but any of the remaining 4 are valid because they only remain the 4 identical earrings that you are looking for. For this reason, you only need to pick 2 more, that will necessarily be the right choices. If you add this 2 tries to the first 16 attempts at picking up the right earrings, this makes 18 attempts.

As this is the worst case scenario, you only need to pick up 18 earrings at most to be sure that you got the right pair of earrings, not needing to pick up all 20 (you can always leave 2 inside the box).

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