Well, I didn't win the contest. I guess the jokes were too obscure, and using Flash wasn't much of an advantage. Though I can't figure out, if I think Flash is better than Paint, why I keep returning to Paint. I mean, Paint pixelates everything, and redrawing a portion usually involves deleting the offending bit, meaning the... OK, I'll just get to the pictures.

The first is a lateral symbiotogram (to take John Langdon's terminology) of the words "true" and "false." ( First image )

The next one is an experimental 120-degree rotational ambigram. I actually worked on this in Flash, but put it into Paint for some reason. I really should have exported it, and then as a GIF, but it's a jpeg screenshot instead.( Second cut )

This next one is a rotational figure-ground relation set on a gray background. If you're not logged into LJ, try to guess the words in it before opening the lj-cut. ( CutforBandWidth )

All right. This fourth and last idea is something I actually lifted from ceruleanst. However, since today's Chinese New Year, and since he hasn't posted about it yet, I think I can safely post it here without being accused of theft. (Though maybe I shouldn't, since he's just gone through that thing with that other ambigrammist and it only got settled four days ago, but I'm hoping to start up a friendly competition. Hmm, maybe I should wait on this last one.)

UPDATE, FEBRUARY 10: ( Grand Finale below )

Spell-check watch: "pixelates" and "screenshot." But at least it caught "imbedded." FURTHER UPDATE: Which is an accepted variant.

I recently looked for a minimal greatest-cover of the alphabet using chemical symbols. More specifically, since J and Q are not part of any element's symbol (although Jl was proposed for element 105, dubnium, when it was called "joliotium"), I wanted to find a set of symbols that used each of the other 24 letters (hence "greatest-cover") with as few duplicates as possible (hence "minimal").

As it turns out, I found a cover that used exactly 24 letters rather easily by going through the alphabet in order, so I put a couple more constraints on the challenge. I've found several solutions with 13 symbols, for example. Solutions that minimize the sum or product of the corresponding atomic numbers are also preferable, but I've put this under "open" and not "math" because I think you don't need to optimize either of those unless you have both spare time and programming experience.

I have among my bookmarks some puzzle pages I don't visit frequently. One of those belongs to Bob Kraus, who has a taste for puzzles that involve long lists of numbers. I don't share this taste, since there is often very little to suggest that the solver is making progress in the right direction. However, since his site has not updated in a long time, I randomly felt like experimenting with lists and came up with these two puzzles.


1) I have separated the integers 1-8 into four ordered pairs, with the larger number coming first, and performed a different operation on each of those pairs: addition, subtraction, multiplication, and division. The result of each of those operations is called the "index." Each index happens to appear in one of those ordered pairs, but no two indices appear in the same pair, and none appears in the pair it was derived from.
Now, since each index appears in an ordered pair with an associated operation, each index can be said to point to that operation. When I perform the indicated operation on each ordered pair, the average of the results is an integer. What are the pairs, and what is the integer?

2) This puzzle is open. The method I'm using to calculate quartiles comes from Wikipedia, and runs as follows: "Use the median to divide the ordered data set into two halves. Do not include the median into the halves. The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data." (The second quartile is, of course, the median of the original list.)
Now, I've come up with a list of positive whole numbers, all distinct, and calculated the first, second, and third quartiles. These three numbers aren't necessarily in the list, or even integers, but the following six numbers (all different) relating to the terms on the list actually do appear on it:
a) The number of terms
b) The sum of the terms less than the first quartile
c) The product of the terms greater than the first quartile and less than the median
d) The difference of the terms greater than the median and less than the third quartile
e) The quotient of the terms greater than the third quartile
f) The average of all the terms
Your challenge: to find such a list while minimizing (with any priority) the number of terms, the sum of the terms, and the largest term. For example, my list has fewer than 10 terms, its sum is less than 100, and the largest term is under 25.

I may be getting a periodic aversion to writing. See, I'm currently taking a writing class in college, and that means I have to "set aside" a lot of time for essays I don't really enjoy.

Anyway, here's another update to my webcomic crossover graph. I know, it's later than I said, but gimme a break. February and March were short this year. (Did you know that April used to be the next-shortest month after February? Stupid Bush, depriving us of a little bit of trivia.) Anyway, to make up for that, I've updated the graph through D. (That's like two letters, since D itself did not require alterations.) I've also moved the small unconnected parts of the graph out of the main section, so it looks nicer.

  HOSERS  Absurd Notions  Help Desk
   |  |         |          |
   | General Protection Fault--Kevin
   |          |                & Kell
   |    Joe   |  The Suburban
   |  Average |     Jungle
   |     |    |        |
Life at  |    |   The Class Menagerie
Bayside--+    |    |*        |
         |  Funny Farm---Newshounds
         |  |
Knights  CRfH!---Clan of---+---Alice
of the   ||     the Cats   |
Dinner--Fans!             Elf
Table    |                Life
         |
   It’s Walky!--Melonpool--Zortic

Magick  Beyond   Parallel  Sit &
   |    Reality  Dementia   Spin
Anarchy    |        |        |
         Emergency Exit   Avalon

The Wotch--The Accidental Centaurs

3rd Party--Charby the--Elijah
 Fantasy    Vampire    & Azuu

Adventurers--RPG World        

Guðrún--Alcydia    PvP--Dork Tower

A World like--The Devil’s
   My Own       Panties

 UC Rats   Bassetville  ConScrew
    |              ||   |
The Call           Fragile
of Whatever        Gravity

Goats--Bobbins--Waiting for Bob

Well, here I am.

About one month ago, I proposed and implemented the Reb Webcomic Crossover graph. Since then, I have been largely preoccupied with college and puzzles. However, with the help of this Webcomic Crossover & Cameo Archive, I managed to expand the graph to include all the crossovers through "A"... at the time. I wouldn't be surprised if a couple more occurred without my knowledge. Anyway, here's my revised graph, sans links:

  HOSERS  Absurd Notions  Help Desk
   |  |         |          |
   | General Protection Fault--Kevin
   |          |                & Kell
   |    Joe   |  The Suburban
   |  Average |     Jungle
   |     |    |        |
Life at  |    |   The Class Menagerie
Bayside--+    |    |*        |
         |  Funny Farm---Newshounds
A World  |  |
Like My  CRfH!---Clan of---+---Alice
  Own    ||     the Cats   |
   |    Fans!             Elf
  The   |  |              Life
Devil’s | Knights of the         Dork
Panties |  Dinner Table    PvP--Tower
        |
   It’s Walky!--Melonpool--Zortic

Magick  Beyond   Parallel  Sit &
   |    Reality  Dementia   Spin
Anarchy    |        |        |
         Emergency Exit   Avalon
 The                          
Wotch--The Accidental Centaurs

3rd Party--Charby the--Elijah
 Fantasy    Vampire    & Azuu
                              
Adventurers--RPG World        

Guðrún--Alcydia

I hope this will take much less than the obvious two-year estimate to "complete."

I just got my first comments! Yay!

Er, I should explain that title, huh? Well, take the following shape:

X
XX
XXX
XXXX
XXXXX

Obviously, it can be divided into five different-sized groups of 1 to 5 X's with four horizontal lines. However, one may save a line by using both horizontal and vertical lines, thus:

X
XX
XX|X
XX|XX
XX|XXX

The challenge is to cut a side-7 triangle of X's similarly with the minimum number of lines.

Open problems:
What about other size triangles?
What if the triangles can be divided with lines in three directions-- that is, lines parallel to any of the three sides?

This is a little thing I've cobbled together from memory and the Comixpedia comics wiki (which, by the way, is in desperate need of editing (which is why I relied on memory)). I had not seen such a graph of crossovers before, and I found this to be a terrible omission. To remedy that, here is the Reb Webcomic Crossover graph!

Absurd Notions     HOSERS
        |            |
General Protection Fault--Help
         |    |           Desk
Clan of  | Kevin & Kell
the Cats |
   |     | The Class Menagerie
   |     |  |*        |      |
   | Funny Farm---Newshounds |
   | |                       |
  CRfH!--- --Life at Bayside |
  ||      |                  |
 Fans!   Joe      The Suburban
 |  |  Average       Jungle
 |  |
 | Knights of the Dinner Table
 |
It’s Walky!--Melonpool--Zortic

Dork Tower   Beyond   Parallel
     |       Reality  Dementia
    PvP         |        |
              Emergency Exit
 The
Wotch--The Accidental Centaurs

Of course, I ignored cameos, one-ways, spinoffs, and anything else I may have forgotten (which made ignoring them easier). Here are explanations for some of the symbols, plus a running commentary.

|
Starting slow. This is just a vertical connector.
I started the graph by going from A (Absurd Notions) to Z (Zortic).

-
A hyphen, though it's not used like that in the graph (yet). In groups of two or more, it's a horizontal connector.
I've included links to those webcomics I read on a regular basis. (Dropped GPF a while after Eric Burns did, right before the main cast jumped to the evil twin universe.)

|*
This is an unorthodox crossover; while characters from "Funny Farm" appeared in "The Class Menagerie" at about the same time, in about the same place, as characters from the latter appeared in the former, this is much more like two one-way crossovers. (So is that more like half-duplex or full-duplex?) Good thing it's not on the main line!
The GPF/Funny Farm crossover was one of the stranger attempts IMO, since the main characters of the latter look like furries. (Actually, R. Smith has said that's only to differentiate the main characters. I wonder how that works with the "Newshounds" crossover. Ah well, I guess it's flexible.) I was fully expecting another comparison between Mr. Westone (FF) and Sean Connery (GPF).


This is the only instance I have seen of more than two comics (three, obviously) in the same crossover. Form follows function.
This is where I toss up my hands and say, "What's the deal?" Comixpedia has bios for nearly all the "CRfH!" characters, but nothing about the crossovers. It's not as if it hasn't reached a threshold; the "GPF" article lists five crossovers with five webcomics, and "CRfH!" has had that many, in a configuration that should be considered much more interesting but is instead ignored! By the way, the current "This Week!" article on the front page is no less than six months old! There's just no excuse for that! (pant pant wheeze)

||
These two vertical connectors simply represent two crossovers between the same two comics. This counts for two crossovers and the fifth webcomic for "CRfH!"
In my opinion, the most underappreciated (read: I enjoy them, but Eric Burns doesn't read them) comics on this graph are "Absurd Notions" and "The Wotch."


Empty space (I know, I know. I'm running out of symbols.) means there is no crossover.
I have made a little effort to alphabetize the titles in small areas, subverted by my efforts to keep the lines straight and the graph compact. Final size: 25 lines x 30 characters, about 600 total characters. The top connected portion's only 18 lines.

EDIT, 12-23-07: Nuts. The helpful Snap Shots are interfering with the three-way and the Class Menagerie/Suburban Jungle connectors. Rather than edit the graph (since the icon is like 2 2/3 characters wide), here's a link to the latest version as of this date. Alternatively, click the "comics" tag above.

Occasionally, such as now, I will pose problems to which I don't have answers. Depending on my resources, I might give out prizes for the first or best answer. Anyway here we go!

Is it possible to arrange the names of the musical notes into a word square?

The names I'm talking about, of course, are DO, RE, MI, FA, SO, LA, TI, and DO again. The word square I'm looking for is 4x4, no larger and no smaller, with four-letter words reading down the four columns and left to right along the four rows. An appropriate arrangement will include DO twice and each other name once, and the letters of the respective names will be orthogonally adjacent- you know, like dominoes.

To be sure you understand, here's an example that has words reading across, but not down. The "dominoes" here are all horizontal, but I fully expect some to be vertical in a full solution.

ALIT
SOFA
MIRE
DODO

With minimal effort, too!