Difference between revisions of "Talk:2021 Fall AMC 12B Problems/Problem 17"
(→Solution 3) |
(→Solution 3) |
||
| Line 1: | Line 1: | ||
==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 | ||
| Line 17: | Line 19: | ||
% | % | ||
\\-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}
