Difference between revisions of "2023 AMC 8 Problems/Problem 16"
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The letters P, Q, and R are entered into a <math>20\times20</math> table according to the pattern shown below. How many Ps, Qs, and Rs will appear in the completed table? | The letters P, Q, and R are entered into a <math>20\times20</math> 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 | \vdots &\vdots&\vdots&\vdots&\vdots&\iddots\\hline | ||
Q&R&P&Q&R&\cdots\\hline | Q&R&P&Q&R&\cdots\\hline | ||
Line 8: | Line 8: | ||
Q&R&P&Q&R&\cdots\\hline | Q&R&P&Q&R&\cdots\\hline | ||
P&Q&R&P&Q&\cdots\\hline | P&Q&R&P&Q&\cdots\\hline | ||
− | \end{array} | + | \end{array} |
− | + | 'Table made by Technodoggo' | |
<math>\boxed{\text{A}}~132</math> Ps, <math>134</math> Qs, <math>134</math> Rs | <math>\boxed{\text{A}}~132</math> Ps, <math>134</math> Qs, <math>134</math> Rs | ||
<math>\boxed{\text{B}}~133</math> Ps, <math>133</math> Qs, <math>134</math> Rs | <math>\boxed{\text{B}}~133</math> Ps, <math>133</math> Qs, <math>134</math> Rs |
Revision as of 20:24, 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?
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
~Star League (https://starleague.us)