Friable lacuna

friable (adj.): Easily crumbled, pulverized, or reduced to powder.

lacuna (n.): A blank space; a missing part; a gap.

Well, I'm back from Winter Camp. Unfortunately, seeing that I was more or less isolated from the rest of the world for the past few days, I guess there's not very many interesting things I can say, aside from how you shouldn't go to university at York unless you want to live in a closet and always eat fast food. It was fun though =). Camps with only around 14 people are much more awesome than huge camps, since it's much more informal and much more just like a get-together.

Back to the uninteresting stuff - seeing as I don't have too much to say, I'll just proceed in bashing Josh's third logic problem.

Third Logic Problem

This logic problem took me the longest to do, but not because it was hard to code. Au contraire, I had it coded in 10 minutes, give or take a few - much faster than the second problem. Yet of course, the program repeatedly discovered no solution.

Part of the reason for this were the several typoes in the problem that Josh corrected yesterday. The program still didn't work of course. The reason why? Apparently, colors are very, very strange.

If you actually decide to try this problem, you should notice that the five colors are:

pink
grey
red/brown (this 'contains' red)
red/green (this 'contains' green)
other

In particular, "red" itself, is not a color. Of course, after adjusting this, the program spits out:

2 3 0
0 0 0 0 0
3 2 4 1 0
1 2 3 0 4
4 1 3 0 2

Which is more easily understood as (highlight):

Cat in the Hat has 5 eyes, is other, and is hairy
Lorax has 4 eyes, is grey, and is lumpy
The Who has 6 eyes, is red/brown, and is greasy
Horton has 2 eyes, pink, and is fluffy
The Grinch has 1 eye, is red/green, and is smooth

The program itself, as always, can be downloaded on the sidebar.

Solution to Ghost

Randall Munroe posted his solution to Ghost using the Ubuntu wordlist on the xkcd blog. It is the simpler version, though, where you can add letters only to the end of words - still pretty cool though.

Piles of Stones

Here is a cool trick/problem shown to me at Winter Camp.

Take a bunch of piles of stones that add up to 21. Here we'll take 5 piles: 4 stones, 6 stones, 2 stones, 7 stones, 2 stones:

2 2 4 6 7

Each step, remove one stone from each pile, and put all those stones into a new pile:

1 1 3 5 6 5

Continuing (new piles in bold):

2 4 4 5 6
1 3 3 4 5 5
2 2 3 4 4 6
1 1 2 3 3 5 6
1 2 2 4 5 7
1 1 3 4 6 6
2 3 5 5 6
1 2 4 4 5 5
1 3 3 4 4 6
2 2 3 3 5 6
1 1 2 2 4 5 6
1 1 3 4 5 7
2 3 4 6 6
1 2 3 5 5 5
1 2 4 4 4 6
1 3 3 3 5 6
2 2 2 4 5 6
1 1 1 3 4 5 6
2 3 4 5 7
1 2 3 4 6 5

And here, at 1 2 3 4 5 6, the piles remain constant. Now, the cool thing is that it doesn't matter what piles you start with, as long as they, in total, contain 21 stones - you'll always end up with 1 2 3 4 5 6. In fact, if you take n(n+1)/2 stones, you'll always end up with 1 2 3 4 5 ... n.

This pretty cool fact is pretty hard to prove actually - there's a nice short proof though.

That's all for now. Maybe soon I'll talk about magic squares, since I've recently played with them again. Until then, ciao.

-squid out