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?
![$\begin{array}[b]{|c|c|c|c|c|c} \vdots &\vdots&\vdots&\vdots&\vdots&\iddots\\\hline Q&R&P&Q&R&\cdots\\\hline P&Q&R&P&Q&\cdots\\\hline R&P&Q&R&P&\cdots\\\hline Q&R&P&Q&R&\cdots\\\hline P&Q&R&P&Q&\cdots\\\hline \end{array} 'Table made by Technodoggo'$](http://latex.artofproblemsolving.com/2/4/9/2494420738cada1d73972f39ff0f2ce3ee2afd11.png)
\boxed{\text{A}}~132\text{ Ps, }134\text{ Qs, }134\text{ Rs}$$ (Error compiling LaTeX. Unknown error_msg)\boxed{\text{B}}~133\text{ Ps, }133\text{ Qs, }134\text{ Rs}$$ (Error compiling LaTeX. Unknown error_msg)\boxed{\text{C}}~133\text{ Ps, }134\text{ Qs, }133\text{ Rs}$$ (Error compiling LaTeX. Unknown error_msg)\boxed{\text{D}}~134\text{ Ps, }132\text{ Qs, }134\text{ Rs}$$ (Error compiling LaTeX. Unknown error_msg)\boxed{\text{E}}~134\text{ Ps, }133\text{ Qs, }133\text{ Rs}$== Solution 1 ==
In our$ (Error compiling LaTeX. Unknown error_msg)5 \times 5
8
9
8
xx+1x
\boxed{\text{(C)}\hspace{0.1 in} 133, 134, 133}$
(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
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