Difference between revisions of "1977 Canadian MO Problems/Problem 7"
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twice. Show that the number <math>f(m,n)</math> of different paths she can take to work satisfies <math>f(m,n)\le 2^{mn}</math>. | twice. Show that the number <math>f(m,n)</math> of different paths she can take to work satisfies <math>f(m,n)\le 2^{mn}</math>. | ||
| − | <math>\underbrace{ \left \begin{ | + | <math>\underbrace{ \left. \begin{array}{|c|c|c|c|c|c|c|c|c|c|c| } |
\hline | \hline | ||
&&&&&&&&&& \\ \hline | &&&&&&&&&& \\ \hline | ||
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&&&&&&&&&& \\ \hline | &&&&&&&&&& \\ \hline | ||
&&&&&&&&&& \\ \hline | &&&&&&&&&& \\ \hline | ||
| − | \end{ | + | \end{array} |
| − | \right \}n}_m</math> | + | \right\}n}_m</math> |
== Solution == | == Solution == | ||
Latest revision as of 19:14, 10 March 2015
Problem
A rectangular city is exactly 
blocks long and 
blocks wide (see diagram).
A woman lives on the southwest corner of the city and works in the northeast corner. She walks
to work each day but, on any given trip, she makes sure that her path does not include any intersection
twice. Show that the number 
of different paths she can take to work satisfies 
.
