900 cards numbered from 100 to 999
Source: Portugal OPM 1996 p3
May 18, 2024
number theory
Problem Statement
A box contains cards numbered from to . Paulo randomly takes a certain number of cards from the box and calculates, for each card, the sum of the digits written on it. How many cards does Paulo need to take out of the box to be sure of finding at least three cards whose digit sums are the same?