# Problem Solving

## Christopher Small's Problem Archive

The Mathematics Problem Archive.

## The Grey Labyrinth

(Dic. 15, 1997) Se dice que una función de dos variables f(m,n) , con m,n números enteros, es armónica , si su valor en cada punto (m,n) es el promedio de sus valores en los 4 vecinos más cercanos: f(m,n)=[f(m+1,n)+ f(m-1,n)+ f(m,n+1)+ f(m,n-1)]/4, para todos enteros m,n . Se dice que una función f es acotada si existe un número positivo M tal que el valor absoluto de f(m,n) es menor que M , para todos enteros m,n . Demuestra que una función armónica acotada es constante. Solución: PDF | PS . (Ene. 30, 1998)

## Ravi Vakil

Office: 383-Q Winter and spring 2013: on sabbatical, partly at the American Institute of Mathematics I am a Professor of Mathematics and the Robert K.

## RMC General Information

General Information The Virginia Tech Regional Mathematics Contest is sponsored each fall by the Mathematics Department at Virginia Tech. More than 130 colleges and universities throughout VA, DC, GA, IL, MD, NJ, NY, OH, NC, PA, SC, TN, WV and other states are invited to participate each year. Even if you do not receive an invitation, you are still welcome to take part; you will need to fill out and sign the registration form, as indicated in the Invitation Letter Now approaching its 34th year, the contest began in 1979 and has grown to the point where over 50 schools with over 300 contestants participate in a typical year. Contestants at each participating school take the two and one-half hour exam on their own campus under the supervision of one of their own faculty members.

## Putnam Directory

<p> Your browser does not appear to support JavaScript, or you have turned JavaScript off. You may use unl.edu without enabling JavaScript, but certain functions may not be available. </p> The William Lowell Putnam Mathematics Competition is a North American math contest for college students.