This looks significantly better on screen, after scanning it in, I think. It’s like one of those images which has too much detail: you have to blur your vision or back away for the bigger picture to form, and I’d had my face up close to the paper for far too long.

!/gfx/world-small.jpg!

Here the bigger picture is of course abstract, but the same effect is present. Also, being able to crop the edges (I’m not going to do that to the original) helped center the design and make it more pleasing to the eye. Realize that a great deal isn’t captured in the scan, such as that I mistakenly used a different shade of black ink for part of the design… That nonetheless worked out well in the end, though.

!/gfx/world-inset.jpg!

The above is a close-up of the top right corner.

As long as we’re on the topic of solutions, here’s the answer to the Prisoners & Hats brain teaser of a few days ago. Or, I’ll start with a hint, rather, and if you want to stop after reading the hint and not read the solution until you’ve had some time to think about it, then you can. Or if you want to stop now and read the brain teaser again, do that.

Anyway, here’s the hint. I’ll tell you first that all of the prisoners in line will give the correct answer and live, except for the one at the back of the line (who is asked the question first). Obviously he can’t know the color of his own hat and so has a 50% chance of getting it right.

Given that the rest of the prisoners live, each MUST state the color of his own hat and nothing else. So you know what each prisoner says, the only thing you don’t know is what the first-asked one says to start off the chain.

Here’s the answer:

The last in line (asked first) prisoner counts the number of, say, white hats on all the 99 prisoners in front of him. It’s either even or odd, and he says black or white, respectively. He has a 50% chance of dying because he has no info about his own hat. The next in line counts the number of white hats on the 98 prisoners in front of him to determine his own color. For example, if it’s even and the guy behind him said white, he knows he must have a white hat.

Now each prisoner, when asked, has counted the number of known white hats in front of him visually and behind him auditorially. He gets an even (->black) or odd (->white) total from those 98 others. The first-asked person could see 99 others. So for each prisoner N, if he gets a different answer from that of the first guy, he says “white”, and if he gets the same answer he says “black”.

Solution to the “Remote Desktop keeps popping to the foreground every five minutes when I leave it running and just minimize it” problem:

Before minimizing the Remote Desktop session, restore the window (double click on the trapezoid-shaped title) so it’s not in full-screen mode anymore. Then the session will politely stay minimized and not periodically pop up to ask for attention. I’ve left sessions minimized like this for days, and they still stay active.

I still think Remote Desktop is the best thing since sliced bread (and whatever else it was that I said is better-than or close-to sliced bread in greatness) and it’s nice that Microsoft has integrated it into Windows XP Pro. There’s still VNC, but that’s very slow by comparison, doesn’t support the notion of the multiple simultaneous user sessions (through the “fast user switching” capability that XP Pro has), and doesn’t have “easy to use” encryption built in. One can tunnel VNC over SSH, but that’s an extra connection step to make.

Today’s word of the day is troglodyte. Why? Because it popped into my head for some reason. Interesting how the word is ambiguous as to its connotation, positive or negative.

That “prisoners” brain teaser of my prior post actually works for any arbitrary number of colors. For example, the hats could be chosen at random from red, green and blue, or ROYGBV. (I refuse to put Indigo in there because it’s almost the same thing as Blue. It’s basically just dark blue, and they have it there just to make the mnemonic more pronounceable. I learned the spectrum as “red, orange, yellow, green, blue, purple” and I don’t need some silly mnemonic with silly colors like “indigo” and “violet”. It’s just purple, everyone!)

(There should be something that tells you when you’re typing and you forget to close a parenthetical remark. That should be a simple enough feature for a spellchecker, you know, but I don’t think they check that.

Forget the story or why this situation occurred, you can make that up yourself. Or not.

Anyway, the situation is that there are 100 prisoners in a line, and each one has on either a black hat or a white hat. Each prisoner doesn’t know the color of his own hat, but he can see the colors of the hats of everyone in front of him.

The prison wardens have arranged this situation, and they now plan to start at the back of the line and move up towards the front, asking each prisoner in turn what color his (that prisoner’s own) hat is. If he’s wrong, that prisoner will be shot on the spot.

The prisoners knew about this situation beforehand, so they devised a plan to minimize the number which could be killed. What’s the plan?

And… to head off another potential solution which I thought of (and liked, and I still think it’s the most elegant one, sorry!): the prisoners, when asked, can only say “black” or “white”. One can’t inflect his voice upwards or cough or breathe in a certain way or anything like that to communicate to the person in front of him what color his hat is.

Thanks again, Vicky, for sharing this one, too!

And John, I already thought of the answer (figured it out myself, thank you very much), so don’t worry about spoiling it for me, at least. But if you thought of it, please don’t post it on the board for a few days. You can email me directly if you want. :)

Note to self: don’t share a brain teaser with others until you’ve fully figured it out yourself! (Unless you’re stuck, that is.) Otherwise they’re going to try and solve it and might just give you the answer.

I’m tired!

Man! I mean… HRMMMMMMM!! Not speak like Yoda you must, hmmmmm? Criticize Yoda intelligence of, hmmmm? THINK CORRECT GRAMMAR CAPABLE SPEAK NOT I AM OF, HMMMMMM? *Pant* *pant*… calm down I must… anger Dark Side path to is. Calm I am now. *Cough* *hack* There is… another… Sky… Walk… LIGHT SABER UP YOU WITH CUT I WILL! GRRRRRHHHMMMMMMM!!! *COUGH* *COUGH*

Frank Oz: drink…need…I…a…
Lucas: Here, have some of this brandy.

I’m getting ready for an all-nighter. Have to finish up a PHP project I’ve been working on for some time.

Vicky says: “You have two ropes. Each takes exactly 60 minutes to burn. They are made of different material so even though they take the same amount of time to burn, they burn at separate rates. In addition, each rope burns inconsistently. How do you measure out exactly 45 minutes?”

Now that’s a HARD brain teaser and I’m still thinking about it. I came up with one answer that works but it involves an infinite number of something (to get arbitrarily close to 45 minutes), so there has to be a more elegant solution to get “exactly” 45 minutes. Something to think about when you’re bored… Thanks Vicky!

Oh well, it’s technically “Tuesday morning” now. I could adjust the date of this post, but that would be horribly dishonest and I’m not that sneaky.

Remember Megaman 2 for Gameboy? It had completely different music from the original game for NES. One of the limitations was that they only had two or three sound channels to work with. Anyway, the Gameboy music used the “noise” function a lot, and FL Studio has a “3X Osc” instrument that allows us to add a noise channel which resulted in something reminiscent of that old Gameboy game. So I started putting in some notes and ended up with this (mp3) little bit. Shows how easy it is to write music in that style? There could actually be a “Bat Man” level, but still the subject’s a bit misleading. Anyway, more when I have more time to kill. …Which I didn’t, really. Just taking a break, you know? I would have loved to compose music for those old NES and Gameboy games, by the way.