The Locker Problem POW

The Locker Problem POW
THE LOCKER PROBLEM
Imagine you are at a school that has 100 lockers, all shut and unlocked
The first student goes along the row and opens every locker.
The second student then goes along and shuts every other locker beginning with locker
number 2.
The third student changes the state of every third locker beginning with number 3. (If the
locker is open the student shuts it, and if the locker is closed the student opens it.)
The fourth student changes the state of every fourth locker beginning with number 4.
Imagine that this continues until 100 students have followed the same pattern.
In the end, which lockers will be open and which will be closed?
Problema de la Semana: El Problema de los
Casilleros
EL PROBLEMA DE LOS CASILLEROS
Imagínate que estás en una escuela que tenga 100 casilleros, todos cerrados pero sin
seguro.
El primer alumno pasa por la fila y abre todos los casilleros.
Entonces, el segundo alumno pasa por la fila y cierra un casillero sí otro no a partir del
casillero número 2.
El tercer alumno cambia el estado de cada tercer casillero empezando con el número 3.
(Si el casillero está abierto, el alumno lo cierra; y si el casillero está cerrado, el alumno lo
abre.)
El cuarto alumno cambia el estado de cada cuarto casillero empezando con el número 4.
Imagínate que esto continúa hasta que 100 alumnos hayan seguido el mismo modelo.
Al final, ¿cuáles de los casilleros estarán abiertos y cuáles estarán
cerrados?
20618rgk_Translated by the LAUSD Translations Unit
Locker Problem
Teacher Notes
There are many ways for students to solve this problem.
It may be helpful to give students graph paper if they are struggling with this POW which
will help them organize their ideas and perhaps draw pictures to represent the situation.
For other information and resources on this problem, see:
http://mathforum.org/alejandre/frisbie/student.locker.html