fragmentary ideas ䷿ intellectual what-nots ䷷ and haskell programming ䷴

I’ve fixed a bug related to upgrading GHC to version 6.12 (thanks to Cale and the folks on haskell-cafe who helped me with the issue) and got my Befunge-93 interpreter up on hackage. The program is written in haskell (as usual). You should be able to get it soon with a:

$> cabal install Befunge93

If you want to read about how I designed it you can check out the source above, or take a look at my previous blog post.

Please report any bugs to me, and I’m also very interested in patches or suggestions for performance improvements if anyone ends up being interested in this program.

EDIT: Here is the package page: http://hackage.haskell.org/package/Befunge93

The Problem

Problem A in the qualifying round of this year’s Google CodeJam contest was really clever. The problem used a classic made-for-TV gadget from the 80s: The Clapper™ (“snapper” in google’s version) and went like this:

The Snapper is a clever little device that, on one side, plugs its input plug into an output socket, and, on the other side, exposes an output socket for plugging in a light or other device.

When a Snapper is in the ON state and is receiving power from its input plug, then the device connected to its output socket is receiving power as well. When you snap your fingers — making a clicking sound — any Snapper receiving power at the time of the snap toggles between the ON and OFF states.

In hopes of destroying the universe by means of a singularity, I have purchased N Snapper devices and chained them together by plugging the first one into a power socket, the second one into the first one, and so on. The light is plugged into the Nth Snapper.

Initially, all the Snappers are in the OFF state, so only the first one is receiving power from the socket, and the light is off. I snap my fingers once, which toggles the first Snapper into the ON state and gives power to the second one. I snap my fingers again, which toggles both Snappers and then promptly cuts power off from the second one, leaving it in the ON state, but with no power. I snap my fingers the third time, which toggles the first Snapper again and gives power to the second one. Now both Snappers are in the ON state, and if my light is plugged into the second Snapper it will be on.

I keep doing this for hours. Will the light be on or off after I have snapped my fingers K times? The light is on if and only if it’s receiving power from the Snapper it’s plugged into.

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Note: this is part of a series of posts is related to the “17×17 Challenge” posted by Bill Gasarch. The goal is to color cells of a 17 by 17 grid, using only four colors, such that no rectangle is formed from four cells of the same color.

In a previous post I presented rotations of some single-color rectangle-free grids which were symmetrical along a diagonal axis. I also noticed that, of the single-colorings of optimal size which I could generate, all with an odd number side-length could be made symmetrical along both diagonals (the evens could not):

Perhaps all odd-sided optimal single-colorings are doubly-symmetrical in one of their rotations! That would be a cool thing to learn, and it would also mean that if we wanted to generate an optimal coloring, then our search space would be roughly 1/4 of the grid.

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