Difference between revisions of "2021 AMC 12A Problems/Problem 8"
| Line 5: | Line 5: | ||
==Solution== | ==Solution== | ||
| − | {{ | + | Making a small chart, we have |
| + | <math></math>\begin{center}\begin{tabular}{c|c|c|c|c|c|c|c|c|c} | ||
| + | <math>D_0</math>&<math>D_1</math>&<math>D_2</math>&<math>D_3</math>&<math>D_4</math>&<math>D_5</math>&<math>D_6</math>&<math>D_7</math>&<math>D_8</math>&<math>D_9</math>\\\hline | ||
| + | 0&0&1&1&1&2&3&4&6&9\\\hline | ||
| + | E&E&O&O&O&E&O&E&E&O | ||
| + | \end{tabular}\end{center}<math></math> | ||
| + | This starts repeating every 7 terms, so <math>D_{2021}=D_5=</math> E, <math>D_{2022}=D_6=</math> O, and <math>D_{2023}=D_7=</math> E. Thus, the answer is \boxed{C) \text{(E, O, E)}} | ||
| + | ~JHawk0224 | ||
==See also== | ==See also== | ||
{{AMC12 box|year=2021|ab=A|num-b=7|num-a=9}} | {{AMC12 box|year=2021|ab=A|num-b=7|num-a=9}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 16:30, 11 February 2021
Problem
A sequence of numbers is defined by 
and 
for 
. What are the parities (evenness or oddness) of the triple of numbers 
, where 
denotes even and 
denotes odd?
Solution
Making a small chart, we have
$$ (Error compiling LaTeX. Unknown error_msg)\begin{center}\begin{tabular}{c|c|c|c|c|c|c|c|c|c}
&
&
&
&
&
&
&
&
&
\\\hline
0&0&1&1&1&2&3&4&6&9\\\hline
E&E&O&O&O&E&O&E&E&O
\end{tabular}\end{center}$$ (Error compiling LaTeX. Unknown error_msg)
This starts repeating every 7 terms, so 
E, 
O, and 
E. Thus, the answer is \boxed{C) \text{(E, O, E)}}
~JHawk0224
See also
| 2021 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 7 |
Followed by Problem 9 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
