Difference between revisions of "2021 AMC 12A Problems/Problem 8"
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~JHawk0224 ~MRENTHUSIASM | ~JHawk0224 ~MRENTHUSIASM | ||
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+ | ==Video Solution (Quick and Easy)== | ||
+ | https://youtu.be/ecLkESGj-pY | ||
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+ | ~Education, the Study of Everything | ||
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==Video Solution by Aaron He (Finding Cycles)== | ==Video Solution by Aaron He (Finding Cycles)== |
Latest revision as of 23:25, 22 October 2022
Contents
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
We construct the following table:
Note that
and
have the same parities, so the parity is periodic with period
Since the remainders of
are
we conclude that
and
have the same parities, namely
~JHawk0224 ~MRENTHUSIASM
Video Solution (Quick and Easy)
~Education, the Study of Everything
Video Solution by Aaron He (Finding Cycles)
https://www.youtube.com/watch?v=xTGDKBthWsw&t=7m43s
Video Solution by Hawk Math
https://www.youtube.com/watch?v=P5al76DxyHY
Video Solution by OmegaLearn (Using Parity and Pattern Finding)
~ pi_is_3.14
Video Solution by TheBeautyofMath
https://youtu.be/cckGBU2x1zg?t=227
~IceMatrix
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 |
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