A Puzzle I Didn't Care for

Tue Oct 11, 2005

I began Not Just An Ordinary Ballerina while waiting on some comforters to wash and dry last night. Just so you know, “spoilers” are coming.

Early in the game, you find the following written on a blackboard:

 11426       34041
+ 6505        2431
------------------
 21234       42022

I thought–and immediately rejected–that this might be base-related. Why I rejected it, I don’t know, as, you may guess, that’s in fact what’s happening here. But anyway, you find another sheet of paper with “10612” written on it, indicating that it’s the code to the junction box which you can use to turn on power to the shopping mall you’re at after-hours on Christmas Eve in a desperate attempt to buy the aforementioned ballerina for your daughter. The control panel only has 0-4 buttons and a five-digit display.

Assuming that we were dealing with decimal here, I looked at the actual decimal sums for these figures and subtracted the ones listed from them. They turned out to be “3303” and “5550.” Sensing a pattern, I thought the difference between the four-digit sum and the actual code had to be “4044” with the imaginary sum being a five-digit number using only the digits 0-4. There are several solutions to that problem, which you can work out algebraically. And, using a spreadsheet, I did.

Of course they didn’t work because this is a stupid base problem. I wonder if the pattern I saw was a coincidence.