Maths Olympiad Prep

Library / /46 of 310

, 2023

Combinatorics Difficulty 1.2 Junior Find the answer Canada

Vivek is painting three doors. The doors are numbered 1, 2 and 3.
Each door is to be painted one colour: either black or gold. One
possibility is that door 1 is painted black, door 2 is painted gold, and
door 3 is painted gold. In total, how many different ways can the three
doors be painted?

Pick one

Solution

Since there are 3 doors and 2 colour choices for each door, there
are 23=82^3 = 8 ways of painting the
three doors.

Using “B” to represent black and “G” to represent gold, these ways are
BBB, BBG, BGB, BGG, GBB, GBG, GGB, and GGG.

Want a route through all this instead of an archive? The track puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.