Did you solve it? Is “yes” the answer to this question?

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"Logic Puzzles Challenge Understanding of Alien Communication"

Did you solve it? Is “yes” the answer to this question? analysis cover image The Guardian 9.3
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Original Article Source: https://www.theguardian.com/science/2025/jun/23/did-you-solve-it-is-yes-the-answer-to-this-question
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TruthLens AI Summary

In a recent puzzle challenge, five logic problems were posed, each involving a fictional planet inhabited by two types of aliens known as Cricks and Goops. The Cricks can only ask questions that have 'yes' as the answer, while the Goops can only ask questions that have 'no' as the answer. The first problem involved determining if a person could ask the question, 'Am I a Goop?' The solution revealed that this scenario is impossible because it leads to contradictory outcomes, demonstrating the inherent logical constraints of the aliens' communication styles. The second problem featured two friends, Katja and Anja, where analyzing Katja's question about their identities led to the conclusion that Katja is a Crick and Anja is a Goop due to the logical implications of their answers.

The subsequent problems continued to explore the nuances of logic in the context of these alien beings. One question asked whether there was a wizard on the planet, leading to the answer that there indeed was one. The reasoning hinged on the type of question asked by the aliens and their respective capabilities. Another problem posed by an alien named Andrew, who questioned if he could ask whether he was not the wizard, highlighted that while it was known he was not the wizard, it did not provide enough information to identify who the actual wizard was. Finally, the last puzzle involved a strange alien asking if she could pose her current question, and through logical deduction, it was concluded that she must be a Crick. These puzzles not only entertain but also encourage critical thinking and logical reasoning skills, showcasing the importance of understanding the structure of questions and answers in problem-solving scenarios.

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Source URL: https://www.theguardian.com/science/2025/jun/23/did-you-solve-it-is-yes-the-answer-to-this-question

Earlier todayI set five logic problems. Here they are again with solutions.

A questionable planet

A certain planet is inhabited by two kinds of alien, Cricks and Goops. Both types of alien – who are physically identical – have a strange way of speaking. They only ask questions. Cricks can only ask questions whose answer is yes, while Goops can only ask questions whose answer is no.

  1. Could you meet a person inhabiting this planet who asks you “Am I a Goop?”

SolutionNo

If the answer is ‘no’, then the person must be a Goop because only Goops ask such questions. But if the answer is ‘no’, they are stating they are not a Goop. There’s a contradiction so this situation is impossible.

If the answer is ‘yes’, they are a Crick. But if the answer is ‘yes’, they are a Goop! This situation is also impossible.

  1. You meet two friends, Katja and Anja. Katja once asked Anja “Is at least one of us a Goop?” What are Katja and Anja?

SolutionKatja is a Crick and Anja a Goop.

Say the answer is ‘no’, then Katja is a Goop. But if it is not the case that at least one is a Goop, none are Goops, and there is a contradiction. So this is impossible.

So the answer is ‘yes’, which means Katja is a Crick. And if one of them is a Goop, it must be Katja.

  1. You overhear a conversation between two people. One of them asks “Am I the kind that could ask you whether there is a wizard on this planet?”. What are the chances that there is a wizard on the planet?

SolutionThere is a wizard on the planet

If the answer to this question is yes, then the questioner is a Crick and if they can ask whether there is a wizard on the planet, that means there is a wizard on the planet, as Cricks can only ask questions to which the answer is yes.

If the answer to this question is no, then the questioner is a Goop. If they couldn’t ask you whether there is a wizard on the planet, this means there must be a wizard on the planet, as Goops can ask questions only if their answer would be no. As they can’t ask this one, the answer must be yes.

Note: the question is of the form ‘Am I the kind that can ask you whether X’, and X is true whichever alien type asks it. This insight will be used in the next question.

  1. You later learn that there is exactly one wizard on this planet of Cricks and Goops. You would like to find out who that is. You meet an alien called Andrew. He asks you “Am I the kind that could ask whether I am not the wizard?” Do you have enough information to tell for sure who the wizard is by now?

SolutionNo

The quertion is of the form ‘Am I the kind that can ask you whether X’. So we know X is true, that is, we know that Andrew isnotthe wizard. But we still dont know whoisthe wizard.

  1. A strange alien asks you “Am I the kind who could ask you the question I am now asking?” What can be said about her?

SolutionShe is a Crick

Suppose the answer is no. This would mean that the strange alien is a Goop. But it also means she can’t ask the question she is asking. Not only does this not make sense (as she is asking it...) but also this implies the answer to the question is yes, as she can’t ask it and she is a Goop, which is a direct contradiction.Now suppose the answer to the question is yes. Therefore she is a Crick and she can ask the question she is asking, so the answer to the question is yes. Everything checks out.

Thanks toWe Solve Problemswho devised these puzzles. WSP runs free maths circles for secondary school students (UK years 7 to 11) in nine cities in the UK. If you want to sign up for the next academic yearyou can apply here.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one,email me.

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Source: The Guardian