Mathematics Problem Of the Week
Fall 2004
POW 1: Safecracker
You are trying to
break into a safe with a keypad lock.
There is no clear key, but if the last n keys match the n keys of the
password, it will open. For example, if the password is “ab”
and you key in “acadab” it will open since “ab” is at the end.
1.
If
you only have 4 keys (a, b, c, d) and the password is 2 characters long, what is
the fewest number of button presses you would need to type in to guarantee the
safe will open?
2.
If
you have 4 keys (a, b, c, d)
and the password is 3 characters long, what is the fewest number
of button presses you would need to type in to guarantee the safe will open?
3.
(Bonus)
If you have 4 keys (a, b, c, d) and the password is n characters long,
what is the fewest number of button presses you would need to type in to
guarantee the safe will open?
Solutions
should be submitted to Dr. Maegan Bos’ mailbox in the Math office or sent via
e-mail to mbos@stlawu.edu
Presentation counts! The prize-winning entry will
be selected from all correct submissions, based on the clarity, creativity and
elegance of the solution.
Look
for the SLU POW on the Web at http://it.stlawu.edu/~math/activities/