In: Advanced Math
4. Suppose there are 99 lockers numbered 1 through 99,
and 99 students numbered
1 through 99. Initially, all lockers are closed. Now each
odd-numbered student
1, 3, 5, 7, · · · , 99, in numerical order from 1 through 99, will
open/close all the lockers
that are numbered to be a multiple of the number of the student.
For example, student
1 will open/close all the lockers, and student 3 will open/close
all the lockers numbered
by 3, 6, 9, 12, · · · , 99, etc. Now find all the lockers that will
be open when all students
are done.
Note: An answer containing a computer search only is worth 10
marks. But you can
start a computer search first and see if the results inspire
you.