Difference between revisions of "2021 AMC 12A Problems/Problem 8"
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==Solution== | ==Solution== | ||
Making a small chart, we have | Making a small chart, we have | ||
− | < | + | |
+ | <math>\begin{tabular}{c|c|c|c|c|c|c|c|c|c} | ||
D_0&D_1&D_2&D_3&D_4&D_5&D_6&D_7&D_8&D_9\\hline | D_0&D_1&D_2&D_3&D_4&D_5&D_6&D_7&D_8&D_9\\hline | ||
0&0&1&1&1&2&3&4&6&9\\hline | 0&0&1&1&1&2&3&4&6&9\\hline | ||
E&E&O&O&O&E&O&E&E&O | E&E&O&O&O&E&O&E&E&O | ||
− | \end{tabular}</ | + | \end{tabular}</math> |
+ | |||
This starts repeating every 7 terms, so <math>D_{2021}=D_5=E</math>, <math>D_{2022}=D_6=O</math>, and <math>D_{2023}=D_7=E</math>. Thus, the answer is <math>\boxed{\textbf{(C) }(E, O, E)}</math> | This starts repeating every 7 terms, so <math>D_{2021}=D_5=E</math>, <math>D_{2022}=D_6=O</math>, and <math>D_{2023}=D_7=E</math>. Thus, the answer is <math>\boxed{\textbf{(C) }(E, O, E)}</math> | ||
~JHawk0224 | ~JHawk0224 |
Revision as of 15:58, 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
$
This starts repeating every 7 terms, so , , and . Thus, the answer is ~JHawk0224
Video Solution by Hawk Math
https://www.youtube.com/watch?v=P5al76DxyHY
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.