Difference between revisions of "Talk:2021 Fall AMC 12B Problems/Problem 17"
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==Solution 3== | ==Solution 3== | ||
+ | <math></math> | ||
Use generating function, define <math>c_{n}\cdot x^{n}</math> be <math>c_{n}</math> ways for the end point be <math>{n}</math> unit away from the origins. | Use generating function, define <math>c_{n}\cdot x^{n}</math> be <math>c_{n}</math> ways for the end point be <math>{n}</math> unit away from the origins. | ||
+ | <math></math> | ||
Therefore, | Therefore, | ||
− | + | if the current point is origin, need to <math>\cdot6{x}</math> | |
\\if the current point on vertex of the unit hexagon, need to <math>\cdot(x^{-1}+2)</math>, where there is one way to return to the origin and there are two ways to keep distance = 1 | \\if the current point on vertex of the unit hexagon, need to <math>\cdot(x^{-1}+2)</math>, where there is one way to return to the origin and there are two ways to keep distance = 1 | ||
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% | % | ||
\\-wwei.yu | \\-wwei.yu | ||
+ | \end{left} |
Revision as of 14:31, 28 November 2021
Solution 3
$$ (Error compiling LaTeX. Unknown error_msg)
Use generating function, define be
ways for the end point be
unit away from the origins.
$$ (Error compiling LaTeX. Unknown error_msg)
Therefore,
if the current point is origin, need to
\\if the current point on vertex of the unit hexagon, need to
, where there is one way to return to the origin and there are two ways to keep distance = 1
\\Now let's start
\\init ;
\\1st step:
\r\n
\\2nd step:
\\3rd step:
\\4th step:
\\5th step:
\\So there are ways for the bug never moves more than 1 unit away from orign, and
% \\-wwei.yu \end{left}