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Problem 134

Number theory Difficulty 1.4 Multiple choice CEMC Gauss (Grade 8) · Canada · 2025

An integer from $3$ to $20$ , inclusive, is randomly selected. What
is the probability that the integer selected is a perfect square?

Pick one

Official solution

The perfect squares are $1^2=1$ , $2^2=4$ , $3^2=9$ , and so on.

There are $18$ integers between $3$ and $20$ inclusive.

Of these $18$ integers, only $2^2=4$ , $3^2=9$ and $4^2=16$ are perfect squares.

(We note that $1^2=1$ and $5^2=25$ are not among the integers
given.)

The probability of randomly selecting a perfect square from the integers
given is $\dfrac{3}{18}=\dfrac{1}{6}$ .

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