MathDB

3

Part of 1996 Portugal MO

Problems(1)

900 cards numbered from 100 to 999

Source: Portugal OPM 1996 p3

5/18/2024
A box contains 900900 cards numbered from 100100 to 999999. 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?
number theory