Math CentralQuandaries & Queries


Question from Liaqath, a parent:

You have squares and triangles.
Altogether there are 33 sides.
How many squares do you have?
How many triangles do you have?

Hi Liaqath,

Suppose there are $s$ squares and $t$ triangles, then the number of sides is $4 \times s + 3 \times t.$ Hence

\[$4 \times s + 3 \times t = 33\]


\[$4 \times s = 33 - 3 \times t.\]

Notice that the right side is divisible by 3 and hence the left side is divisible by 3. But 4 is not divisible by 3 so $s$ is divisible by 3. Thus $s = 3, 6, 9,\mbox{ or }, \cdot\cdot\cdot.$ What is $s?$


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