# Math Corner - September 21, 2023 Edition

9-21-2023

## Question

To decipher a four-digit binary code (consisting of only 0’s and 1’s) in a video game, gamer Alpha can get help from four strangers: Beta, Gamma, Delta, and Omega. All Alpha knows about these four strangers is that one is a soothsayer (who never lies), two are liars (who always lie), and the other is the sibling of one of the liars (who would never lie if they answer a question before their sibling answers but would always lie if they answer after their sibling answers).

Alpha asks: “What is the first digit in the code?”

Gamma says “0” followed by Delta who says “0” then Beta says “1” and finally Omega says “1”.

Alpha then asks: “What is the second digit in the code?”

Gamma says “1” followed by Beta who says “0” then Omega says “0”, and finally Delta says “1”.

Alpha then asks: “What is the third digit in the code?”

Beta says “0” followed by Delta who says “1” then Gamma says “1”, and finally Omega says “0”.

Alpha then asks: “What is the fourth digit in the code?”

Gamma says “0” followed by Beta who says “1” then Delta says “0”, and finally Omega says: “1”.

Based on this information, Alpha knows the code. What is the code?

0110 (Delta is the soothsayer, Beta and Omega are the liars, and Gamma is Omega’s sibling.)

COinS