I’d like to share an interesting, intermediate level puzzle I created for my book Mental Mosaics.
Ficticious Fast Food
You’ve arrived at a fast-food restaurant. Upon entering the building, you see an interesting note on the wall that reads, “There are three cashiers, two of whom are truth tellers and one of whom is a liar. If you can correctly identify the liar by asking up to two yes–no questions to exactly one cashier, you’ll get your meal for free.” What can you do to guarantee yourself a free meal?
Is there a way to determine if any given cashier is a liar in one question?
Answer: There are multiple solutions, one of which is given below.
Pick any two cashiers and ask the following questions:
- Ask the first cashier, “If I were to ask you if you are the liar, would you answer yes?”
- If they answer no, ask them if the second cashier is the liar.
Explanation: If the first cashier is the liar, they will say yes to your first question because they would answer no to the question “Are you the liar?” and must lie about that response. If they answer no, then you know they are a truth teller, at which point you can ask them if the second cashier is the liar.
If you enjoyed this puzzle, you’ll also enjoy my puzzles book with 200 puzzles. This puzzle was taken from the chapter “Liar Liar” that includes fourteen liar-based puzzles.
is a collection of 200 unique puzzles and challenges on an eclectic range of subjects, including clocks and calendars, liars, demons, chess boards, rotatable words, and hidden infinities. Each chapter is a self-contained unit that focuses on its own unique subject, starts with one or two simple puzzles to set the tone, progresses to a number of moderately difficult puzzles, and concludes with a small number of highly difficult puzzles to test your mastery. This book includes 184 novel puzzles created by the author, Brandon Quinn, and ends with 16 puzzles that are famous across the world, concluding with The Hardest Logic Puzzle Ever.