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Problem 79

Combinatorics Difficulty 1.2 Multiple choice CEMC Gauss (Grade 8) · Canada · 2025

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

Official 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).

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