Difference between revisions of "2023 AMC 8 Problems/Problem 16"
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P&Q&R&P&Q&\cdots\\\hline | P&Q&R&P&Q&\cdots\\\hline | ||
\end{array}</math> | \end{array}</math> | ||
| − | + | Table made by Technodoggo | |
| + | |||
<math>\boxed{\text{A}}~132\text{ Ps, }134\text{ Qs, }134\text{ Rs}</math> | <math>\boxed{\text{A}}~132\text{ Ps, }134\text{ Qs, }134\text{ Rs}</math> | ||
<math>\boxed{\text{B}}~133\text{ Ps, }133\text{ Qs, }134\text{ Rs}</math> | <math>\boxed{\text{B}}~133\text{ Ps, }133\text{ Qs, }134\text{ Rs}</math> | ||
Revision as of 21:36, 24 January 2023
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?
![$\begin{array}[b]{|c|c|c|c|c|c} \vdots &\vdots&\vdots&\vdots&\vdots&\iddots\\\hline Q&R&P&Q&R&\cdots\\\hline P&Q&R&P&Q&\cdots\\\hline R&P&Q&R&P&\cdots\\\hline Q&R&P&Q&R&\cdots\\\hline P&Q&R&P&Q&\cdots\\\hline \end{array}$](http://latex.artofproblemsolving.com/4/3/5/435420b40a00c0721a0b744419b425ea9264fdd0.png)
Table made by Technodoggo
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
~Star League (https://starleague.us)
