Math Corner: Binary Figures

By Jason Gershman •

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?