Comments on: Math is congruent with fun!

Math is congruent with fun!

cortex — Thu, 12 Apr 2007 11:51:31 -0800

You have spacial skills. Apply them in Building Houses 2, on mathsnet.net. Or freestyle in Building Houses 1. Or at night! Oh and also there's like a hundred more puzzles over there too. Some java required.

By: cortex

cortex — Thu, 12 Apr 2007 11:52:06 -0800

Via #mefi.

By: DU

DU — Thu, 12 Apr 2007 12:00:57 -0800

spacial = spatial + special?

By: cortex

cortex — Thu, 12 Apr 2007 12:03:20 -0800

Dammit, I knew that didn't look right.

By: Wolfdog

Wolfdog — Thu, 12 Apr 2007 12:07:18 -0800

I like the exercise, but is there no acknowledgment when you produce a solution? Perhaps I missed something. Also, it's not obvious (it wasn't to me, anyway) that unsupported, "floating" blocks are allowed.

By: Mister_A

Mister_A — Thu, 12 Apr 2007 12:10:14 -0800

Awesome post cortex! See you next week, productivity!

By: cortex

cortex — Thu, 12 Apr 2007 12:10:25 -0800

The puzzle (on 2, at least) will show a dot next to the name of the level when you have a solution—a green dot denotes a visually-correct solution, a yellow dot denotes a perfect (minimal blocks) solution.

By: cortex

cortex — Thu, 12 Apr 2007 12:13:29 -0800

Note also that level 8 can be done in 12, but they ask for 16—an error, as far as I can tell.

By: kittens for breakfast

kittens for breakfast — Thu, 12 Apr 2007 12:30:37 -0800

You have spacial skills. Ohhhhh, but I really, really don't. Brain = ow.

By: quonsar

quonsar — Thu, 12 Apr 2007 12:43:07 -0800

MAMA! AH HAVE FINALLY FOUND MAH SPACIAL PURPOSE!

By: French Fry

French Fry — Thu, 12 Apr 2007 12:48:55 -0800

Man. I'm still not done being addicted to Desktop Tower Defense. How will I ever pretend to be productive again? Sigh I guess it's another 24 straight hours of clicking for me.

By: nasreddin

nasreddin — Thu, 12 Apr 2007 12:53:45 -0800

note also that level 8 can be done in 12, but they ask for 16—an error, as far as I can tell. No, it's deliberate, I think. Look at problem 9--you can do it in 15 or less, but they ask for 24. I am pretty sure this is impossible, though.... Otherwise, I can do all of them except 1.

By: Mister_A

Mister_A — Thu, 12 Apr 2007 12:59:53 -0800

ahh so 1 really is hard then. I can't get it in less than 14.

By: hydrophonic

hydrophonic — Thu, 12 Apr 2007 13:06:20 -0800

Whew. I was ready to give up after about half an hour on #1, but that one turned out to be the hardest.

By: hydrophonic

hydrophonic — Thu, 12 Apr 2007 13:12:11 -0800

Look at problem 9--you can do it in 15 or less, but they ask for 24. It asked me for 15.

By: solid-one-love

solid-one-love — Thu, 12 Apr 2007 13:14:36 -0800

It's pretty trivial to find a non-optimal solution for most of these puzzles: in the top view, make a stack of four blocks for each appropriate cell. Switch to the front view and remove ny blocks in that view that don't belong. Repeat for the right-side view. This will also get you yellow dots for some puzzles. Puzzle #10, however, can't be done this way. The optimal solution is ingenious, and took a couple minutes.

By: googly

googly — Thu, 12 Apr 2007 13:20:41 -0800

This is a wonderful application of the old joke about the sculptor who, when asked how he turns a block of marble into a beautiful sculpture of an elephant, says that he simply looks at the block of marble and trims away everything that doesn't look like like an elephant.

By: cortex

cortex — Thu, 12 Apr 2007 13:21:05 -0800

The reverse of solid-one-love's procedure works well, too: fill the space, then carve against each view to produce needed openings. It works a bit too well, in some cases: this method leaves you with a perfect solution to figure 5 without an extra work.

By: googly

googly — Thu, 12 Apr 2007 13:21:06 -0800

Or, of course, what s-o-l said.

By: papakwanz

papakwanz — Thu, 12 Apr 2007 13:21:24 -0800

I can get 2-8, but I'm stuck at 14 on 1, 18 on 9, and a pathetic 24 on 10

By: nasreddin

nasreddin — Thu, 12 Apr 2007 13:29:21 -0800

10 is actually quite beautiful when you get the solution.

By: Skorgu

Skorgu — Thu, 12 Apr 2007 13:33:06 -0800

Is it just me or is it entirely non-intuitive that yellow is "better" than green? Shouldn't it be the reverse? All yellows isn't hard once you get past the complete lack of instructions.(and bad Java implementation that makes the "number of blocks you're allowed" completely invisible on Linux).

By: solid-one-love

solid-one-love — Thu, 12 Apr 2007 13:38:26 -0800

I think we're thinking of the same thing, cortex, except that I'm not filling the entire field; I'm just filling the appropriate columns in the top view.

By: freebird

freebird — Thu, 12 Apr 2007 13:39:07 -0800

I finally got to 12 on 1 (which is a neat shape) and spent a few moments in agonizing confusion when the little indicator didn't flip. I was *sure* it worked! Rotating faster and faster, I was wild eyed with trying to see what was wrong... until noticing it doesn't update until you click another figuur. Do we need new words for emotions involved with interface design?

By: Mach5

Mach5 — Thu, 12 Apr 2007 13:40:04 -0800

w00, all perfects! That was fun.

By: pokermonk

pokermonk — Thu, 12 Apr 2007 13:44:31 -0800

1 and 10 are the tricky ones; the rest seem to fall in place very quickly. Felt good to finish them all after being stumped on the first for a while. I think the best way to solve 10 may be to start as a 2x2 cube and work your way out w/o wasting any pieces. Then it's just a matter of a clip here and there. I'm still not done being addicted to Desktop Tower Defense I work so hard at breaking 7000 and just can't do it.

By: maxwelton

maxwelton — Thu, 12 Apr 2007 13:45:11 -0800

Yeah, very nice. Got them all. Am I CEO of something now?

By: Falconetti

Falconetti — Thu, 12 Apr 2007 13:49:06 -0800

It took me hours to figure out figuur1 and then I had my epiphany and it fell into place. I was convinced it was impossible for awhile.

By: solid-one-love

solid-one-love — Thu, 12 Apr 2007 14:00:58 -0800

I think the best way to solve 10 may be to start as a 2x2 cube and work your way out w/o wasting any pieces. My solving method was to determine which top view, when rotated three additional times through 90 degrees each time, had no overlaps.

By: anotherpanacea

anotherpanacea — Thu, 12 Apr 2007 14:30:31 -0800

For Building Houses 2, what's the answer to figuur 1? I can't do it in less than 14 blocks, and I can see how removing any of them would work. All the others are pretty easy, though, so I'm tempted to call it a typo. :-)

By: anotherpanacea

anotherpanacea — Thu, 12 Apr 2007 14:31:33 -0800

can != can't

By: Ambrosia Voyeur

Ambrosia Voyeur — Thu, 12 Apr 2007 14:41:34 -0800

Wow, after spending an hour on 1, 5 seems like a joke.

By: lucasks

lucasks — Thu, 12 Apr 2007 14:42:42 -0800

The trick to #1 is to realize that each view sees the max number of blocks. Thus, to solve it one must position all 12 blocks in such a way that none obscures the other in all three views.

By: H-Bar

H-Bar — Thu, 12 Apr 2007 14:44:34 -0800

anotherpanacea: You probably ran into a dead end trying to modify something that looks nothing like the actual solution. I was stuck until I erased everything and tried to build it up one block at a time.

By: muddgirl

muddgirl — Thu, 12 Apr 2007 14:46:47 -0800

My method of solving all of these, except #10, was to fill the whole space, delete blocks until each view looked right, then delete any blocks that overlapped in two or more views. 2 or 3 of them were solved after step 2! For # 10...I won't reveal how I finally solved # 10, because there's really only one Aha! moment, then it's pretty trivial. #1 was pretty hard the first few times - the hardest one to say, "Ah, this block is redundant!"

By: hydrophonic

hydrophonic — Thu, 12 Apr 2007 14:53:16 -0800

SPOILER: Here are four views of the answer to figuur 1. But don't look! You can figure it out!

By: lastobelus

lastobelus — Thu, 12 Apr 2007 15:03:04 -0800

it did seem like only the first one was slightly tricky and all the rest were very easy. But the by night one looks trickier. When I have time...

By: Ambrosia Voyeur

Ambrosia Voyeur — Thu, 12 Apr 2007 15:05:55 -0800

WOW, #1 got pwndz! Here's a spoiler shot for you weaklings. RESIST! It's very rewarding to unlock the pattern.

By: Ambrosia Voyeur

Ambrosia Voyeur — Thu, 12 Apr 2007 15:06:09 -0800

WOW, #1 got pwndz! Here's a spoiler shot for you weaklings. RESIST! It's very rewarding to unlock the pattern.

By: peep

peep — Thu, 12 Apr 2007 15:06:13 -0800

SPOILER: Here are four views of the answer to figuur 1. But don't look! You can figure it out! Are you kidding me? Is there something wrong with my brain? I think I scored like in the 12th percentile of the spatial portion of the ASVAB in high school. I got down to 14 cubes but wasn't even close to that solution. Oh well.

By: Ambrosia Voyeur

Ambrosia Voyeur — Thu, 12 Apr 2007 15:06:27 -0800

awwww, hydro!!! pfft.

By: Rock Steady

Rock Steady — Thu, 12 Apr 2007 15:23:32 -0800

Yeah, neat post. It was truly satisfying to grok the pattern necessary to get number 1. That was so much geeky fun I'm a little embarrassed to admit how much I enjoyed it. Anyone want to do some word problems for extra credit?

By: cortex

cortex — Thu, 12 Apr 2007 16:39:28 -0800

I think I scored like in the 12th percentile of the spatial portion of the ASVAB in high school. 'Spacial', natch. #1 was very much the gatepost; once you get that one down conceptually, the rest goes pretty easily. And SPOILER #10 is just #1 with some blocks in the middle. So it's reducible to figuring what do do with four blocks in eight total possible places, and super obvious if you treat it as its own 2*2*2 puzzle.

By: cortex

cortex — Thu, 12 Apr 2007 16:40:06 -0800

And I'd love to see someone take this idea and dress it up in a good UI.

By: sappidus

sappidus — Thu, 12 Apr 2007 16:45:39 -0800

For what it's worth, I think there is a much more "natural" solution to #1 than the admittedly very neat one exhibited by hydrophonic.

By: cortex

cortex — Thu, 12 Apr 2007 17:04:40 -0800

Screenshot us! (My solution differs slightly from hydro's, but only because of a symmetry function inherent in that particular level.)

By: Eideteker

Eideteker — Thu, 12 Apr 2007 17:10:04 -0800

Because I am a geek, I made the triple G-E-B from the cover of Godel Escher Bach in a 5x5x5 grid on v. 1. A screenshot is left as an exercise to the reader.

By: sappidus

sappidus — Thu, 12 Apr 2007 17:24:04 -0800

You may just be thinking of mine, cortex. Here's one-quarter of the solution I was thinking of. It leads to a solution that is, of course, in a sense just trivially different from hydrophobic's, but his partitions less easily in my head. See, because of the complete symmetry of figure #1, and the knowledge that only 12 cubes are necessary, I thought it would be easy to find a 3-cube structure that would cover 1/4 of the required figure. In fact, because of the symmetry and all, one such structure suggests itself immediately. That's the picture I linked to; you just have to repeat it in the proper 4 corners of the (big) cube.

By: freebird

freebird — Thu, 12 Apr 2007 17:26:04 -0800

Sappidus beat me to it.

By: freebird

freebird — Thu, 12 Apr 2007 17:31:28 -0800

Eideteker gets the prize - though do you know how many blocks you are supposed to use? Well, start with a list of numbers. if you take the leftmost number and simply add 1 on to it, then take the second left number from the next number in the sequence, and so on . . . you are left with a number, which, because it has been operated on by every number in the sequence,is not itself be part of the sequence. That number is the number of blocks you need represent the G-E-B.

By: cortex

cortex — Thu, 12 Apr 2007 17:36:38 -0800

Two can play at that game, Eideteker.

By: freebird

freebird — Thu, 12 Apr 2007 17:40:39 -0800

/clap /whistle /train

By: sappidus

sappidus — Thu, 12 Apr 2007 17:50:31 -0800

freebird reminds me of a thought I'd had: is there some generalized way of going about proving that, say, figure #2 can't be done in less than 14 cubes? I'm thinking that it probably pretty much boils down to something like proving pentomino figures in the plane are inpossible, i.e., specialized techniques for every individual instance. But maybe someone else has some thoughts on it.

By: cortex

cortex — Thu, 12 Apr 2007 17:59:11 -0800

sappidus: yeah, one of the things that appeals to me about this puzzle is the sense that there must be some completely non-visual way to describe the solution sets. I don't know what the math would be, but it is certainly there to be wrangled. There's probably a few good papers out there that treat the subject, and I bet at least one of them has Paul Erdos' name on it. And as long as we're being geeky and mathy, I made a level 3 Menger Sponge.

By: hydrophonic

hydrophonic — Thu, 12 Apr 2007 18:01:16 -0800

Wow, sappidus, that's a really neat solution. I don't think I would have ever thought to break down the puzzle into smaller parts.

By: sappidus

sappidus — Thu, 12 Apr 2007 18:14:31 -0800

hydrophobic: Wow, sappidus, that's a really neat solution. I don't think I would have ever thought to break down the puzzle into smaller parts. Thanks! But I fell into the "fill it up, clear empty spaces, putter around taking away unnecessary blocks" for almost all of the rest of the figures. :-) cortex: yeah, one of the things that appeals to me about this puzzle is the sense that there must be some completely non-visual way to describe the solution sets. Agreed. Oh, I neglected to thank you for the excellent find -- it really is a great little puzzle. Second the idea of someone gussying it up and making more examples.

By: sappidus

sappidus — Thu, 12 Apr 2007 18:16:34 -0800

(whoops, too much protein folding on the brain! hydrophoNic)

By: kyleg

kyleg — Thu, 12 Apr 2007 20:35:09 -0800

That was a lot of fun. When I hit on the solution sappidus and freebird did, it was a total Aha! moment. But like others said, most of the other puzzles were a matter of filling the space and chipping away everything in the way. I would like to see more non-symmetrical puzzles, it got pretty easy when whipping through 2-9.

By: BrotherCaine

BrotherCaine — Thu, 12 Apr 2007 21:37:42 -0800

That was an hour I didn't have in the middle of tax season cortex, damn you. My obsessive nature compelled me to finish it though.

By: whatnotever

whatnotever — Thu, 12 Apr 2007 21:39:18 -0800

Hm... I did #6 using 10 blocks. It gave me a green dot, and it wants me to add another block for 11 total. I'd guess it's an error, like cortex said about #8, which can be done in 12 blocks when it asks for 16.

By: BrotherCaine

BrotherCaine — Thu, 12 Apr 2007 21:45:06 -0800

There are two solutions to #10

By: [expletive deleted]

[expletive deleted] — Fri, 13 Apr 2007 00:17:06 -0800

The best part about this game is getting that flash of inspiration where in an instant, a perfectly elegant solution appears fully formed in your head. For me, this happened with numbers 1 and 10. *spoiler* For 1, it was the opposing corners solution, and for 10 it was, for the lack of a better term, the parallel surfaces solution.

By: tula

tula — Fri, 13 Apr 2007 00:27:14 -0800

Thanks, that absorbed me completely for a while. They seemed to get easier after #1, but I'll probably still dream about yellow cubes and negative space tonight.

By: muddgirl

muddgirl — Fri, 13 Apr 2007 05:17:27 -0800

I don't think there's necessarily a unique solution for every single puzzle, even if you don't count rotations and mirror images. This is best seen w/ #1, but I think it's true for #10 too. Of course, I'm too lazy to test that.

By: hydrophonic

hydrophonic — Fri, 13 Apr 2007 09:42:23 -0800

SPOILER: Here are three ways to do figuur 10. Plus, you can take any solution and "shuffle' it by moving the layers around it to get who knows how many combinations. Here's an example of taking the bottom layer and moving it to the top.

By: [expletive deleted]

[expletive deleted] — Fri, 13 Apr 2007 09:48:21 -0800

Figuur 6 is not optimal. It asks you to use 11 cubes, but it can be constructed with 10 As for Figuur 10, there are a great many possible solutions. I've already constructed 4 different ones that are not mirror images or rotations.

By: Ambrosia Voyeur

Ambrosia Voyeur — Fri, 13 Apr 2007 11:25:22 -0800

The use of excess blocks is not, in the total scheme of the game in its several forms, unusual enough to be classified as a design flaw. I agree that it's not "optmal" for this form of gameplay, but it's part of the challenge in the other versions.