2023 AMC 8 Problems/Problem 16

The letters P, Q, and R are entered into a table according to the pattern shown below. How many Ps, Qs, and Rs will appear in the completed table?

\[ \begin{array}[b]{|c|c|c|c|c|c} \vdots &\vdots&\vdots&\vdots&\vdots&\iddots\\\hline Q&R&P&Q&R&\cdots\\\hline P&Q&R&P&Q&\cdots\\\hline R&P&Q&R&P&\cdots\\\hline Q&R&P&Q&R&\cdots\\\hline P&Q&R&P&Q&\cdots\\\hline \end{array} \]

Ps, Qs, Rs Ps, Qs, Rs Ps, Qs, Rs Ps, Qs, Rs Ps, Qs, Rs

Solution 1

In our grid we can see there are , and of the letters P, Q and R’s respectively. We can see our pattern between each is , , for the P, Q and R’s respectively. This such pattern will follow in our bigger example, so we can see that the only answer choice which satisfies this condition is

(Note: you could also "cheese" this problem by listing out all of the letters horizontally in a single line and looking at the repeating pattern.)

~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat

Animated Video Solution

https://youtu.be/1tnMR0lNEFY

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