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Problem 206

Number theory Difficulty 1.5 Find the answer CEMC Fermat · Canada · 2024

Anila’s grandmother wakes up at the same time every day and
follows this same routine:

She gets her coffee $1$ hour
after she wakes up. This takes $10$
minutes.
She has a shower $2$ hours
after she wakes up. This takes $10$
minutes.
She goes for a walk $3$ hours
after she wakes up. This takes $40$
minutes.
She calls her granddaughter $4$ hours after she wakes up. This takes
$15$ minutes.
She does some yoga $5$ hours
after she wakes up. This takes $30$
minutes.

If Anila’s grandmother woke up $5$
minutes ago, what will she be doing in $197$ hours?

Getting her coffee
Having a shower
Doing some yoga
Going for a walk
Calling her granddaughter

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

We first note that $197 = 8 $\cdot$ 24 +
5$.

This tells us that the time that is $197$ hours from now is $8$ days and $5$ hours.

Since Anila’s grandmother’s activities are the same every day, then in
$197$ hours and $5$ minutes she will be doing the same
thing as she is doing in $5$ hours
and $5$ minutes, at which point she
is doing yoga.

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