This year I wrote one of the problems on the Univ of MD High School Programming Contest. The following conversation did not take place but could have.
BILL: Here is my problem. Imagine that you have a remote control
for a TV set but that only a few of the numbers work.
Also the UP-ONE and DOWN-ONE buttons work. Write a program
that, given which numbers are available, and given
x and y, return the sequence of botton pushes that
get you from x to y in the least number of pushes.
(NOTE- this description is incomplete- see
problem 7 for a formal description.)
PROGRAM COORDINATOR: Is this some sort of Ramsey Thing in disguise?
PROGRAM COORDINATOR: Then how did you think of it?
BILL: The remote at my in-laws only had 4 and 5 and UP and DOWN working.
The Broken Remote problem is not hard in that it does
not need cleverness. But there alot of details to get right.
Only 2 schools got the problem; however, the reason might be
because problem 3 was harder than anticipated, hence some
did not get to problem 7.
The point of all this?- similar to
this post- everyday situations can inspire a math or comps sci
Is the problem original? Hard to define what ``original'' means;
however, I would not be surprised if it a similar
problem appeared in some other contest.