Library / /211 of 428

, 2025

Combinatorics Difficulty 1.2 Junior Find the answer Canada

A figure is made by placing a triangle on top of a square, as
shown.

The triangle is coloured either red or yellow. The square is coloured
either blue or purple or green. How many different ways can the figure
be coloured?

Pick one

Solution

There are 2 ways to colour the triangle and $3$ ways to colour the square, and so there are $2\times3=6$ ways to colour the figure. We can write the $6$ colourings of
the figure as ordered pairs in which the first colour listed in the pair
is the colour of the triangle and the second is the colour of the
square. These are: (red, blue), (red, purple), (red, green), (yellow,
blue), (yellow, purple), and (yellow, green).

Figure for this problem

Want a route through all this instead of an archive? The track puts 2,604 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.