For readers who answered “yes”, you are correct.
For readers who answered “no”, you are also correct.
(I hope no one answered “maybe”.)
A similar logic applies to today’s puzzles. Am I the kind of person who would set you such a challenge? Absolutely!
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?”
2. You meet two friends, Katja and Anja. Katja once asked Anja “Is at least one of us a Goop?” What are Katja and Anja?
3. 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?
4. 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?
5. 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?
I’ll be back at 5pm UK with the solutions. PLEASE NO SPOILERS. Instead ask questions in the comments that are true whether or not the answers are yes or no.
UPDATE: Answers can be read here.
Today’s puzzles were devised by We Solve Problems, a fantastic charity that describes itself as a “social club for maths-loving kids.” 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 year you can apply here.
We Solve Problems also organises “maths battles”, which I wrote about in 2022
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.