Maths Olympiad Prep

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, 2025

Combinatorics Difficulty 1.5 Junior Find the answer Canada

Yesterday, 200200 people bought
ice cream at the Cayley Creamery.

A total of 8585 people ordered fudge
with their ice cream.

A total of 6060 people ordered
sprinkles with their ice cream.

A total of 3232 people ordered both
fudge and sprinkles.

How many of the 200200 people ordered
neither fudge nor sprinkles?

Pick one

Solution

Of the 8585 people who ordered fudge, 3232 also ordered sprinkles, and so 8532=5385-32=53 people ordered fudge without
sprinkles.

Of the 6060 people who ordered
sprinkles, 3232 also ordered fudge,
and so 6032=2860-32=28 people ordered
sprinkles without fudge.

Therefore, 5353 people ordered fudge
only, 2828 ordered sprinkles only,
and 3232 ordered both fudge and
sprinkles.

Of the 200200 people who bought ice
cream, the number of people who ordered neither fudge nor sprinkles was
200532832=87200-53-28-32=87.

We can represent the given information in a Venn diagram, as shown
below.

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