Can you solve it? Is “yes” the answer to this question? | Mathematics

For readers who answered “yes”, you are right.

For readers who answered “no”, you are also right.

(I hope no one answered “maybe”.)

A similar logic applies to today’s puzzles. Am I the kind of person who would make you such a challenge? Absolutely!

A dubious planet

A certain planet is inhabited by two types of foreigners, cricks and goops. The two types of foreigners – which 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 living in this planet who asks you “am I a goop?”

2. You meet two friends, Katja and Anja. Katja asked Anja once “is at least one of us a goop?” What are Katja and Anja?

3. You hear a conversation between two people. One of them asks “Am I the genre that might ask you if there is a sorcerer on this planet?”. What are the chances that there is a sorcerer on the planet?

4. You later learn that there is exactly a magician on this planet of Cricks and Goops. You would like to know who it is. You meet an extraterrestrial called Andrew. He asks you “Am I the type that might ask you if I’m not the wizard?” Do you have enough information to say with certainty who is the assistant now?

5. A strange extraterrestrial asks you “Am I the genre that could ask you the question I ask now?” What can we say about her?

I will be back at 5 p.m. from the United Kingdom with the solutions. Please don’t spoilers. Rather, ask questions in the comments that are true, whether or not the answers are.

Update: The answers can be read here.

Today’s puzzles have been designed by We Solve Problems, a fantastic charitable organization that is described as a “social club for children who love mathematics”. The WSP directs free mathematical circles for high school students (United Kingdom 7 to 11 years) in nine cities of the United Kingdom. If you want to register for the next academic year, you can apply here.

We solve problems also organizes “mathematical battles”, which I spoke in 2022

I have been putting a puzzle here on alternative Mondays since 2015. I am still looking for big puzzles. If you want to suggest one, send me an email.