MathDB
Logic AND Bashing

Source:

April 26, 2022

Problem Statement

Find the number of 8-tuples of binary inputs {A,B,C,D,E,F,G,H}\{A, B, C, D, E, F, G, H\} such that {(A AND B) OR (C AND D)} AND {(E AND F) OR (G AND H)} \{ (A \text{ AND } B)\text{ OR } (C \text{ AND } D)\} \text{ AND } \{ (E \text{ AND } F)\text{ OR } (G \text{ AND } H)\}={(A OR B) AND (C OR D)} OR {(E OR F) AND (G OR H)} = \{ (A \text{ OR } B)\text{ AND } (C \text{ OR } D)\} \text{ OR } \{ (E \text{ OR } F)\text{ AND } (G \text{ OR } H)\} The AND gates produce an output that is ON only if both the inputs are ON, and the OR gates produce an output that is OFF only if both inputs are OFF.
2022 CCA Math Bonanza Individual Round #12