Problem

Source: IV Caucasus Mathematic Olympiad

Tags: algebra



Vasya has a numeric expression $$ \Box \cdot \Box +\Box \cdot \Box $$and 4 cards with numbers that can be put on 4 free places in the expression. Vasya tried to put cards in all possible ways and all the time obtained the same value as a result. Prove that equal numbers are written on three of his cards.