Building Cities

[Michael Wallace]

So I recently acquired a mobile phone from Libya, and it features a game called Tower Bloxx (which, if you want, you can play here). Its rules, when simplified slightly, pose what might be an interesting puzzle.

You have a grid of 5x5 squares, and you can build 4 different types of building, Blue, Red, Green and Yellow (they have some name in the game, but I can't be bothered to check, and they're not really important). You build a building by placing it in one of your squares. The following rules apply:

1) You can build a Blue building anywhere.
2) A Red building can only be built next to (adjacent, not diagonal) a Blue one.
3) A Green building can only be built next to a Red and a Blue one.
4) A Yellow building can only be built next to a Red, Green and Blue one.
5) You can replace any building on your map as you go along, as long as the new building is placed according to the above rules.

For the purposes of this puzzle:

1) A Blue building is worth 1 point
2) A Red building is worth 2 points
3) A Green building is worth 3 points
4) A Yellow building is worth 4 points.

What I'm interested in doing is maximising the score, bearing in mind you have to obey the above construction rules. In particular, note that because you can replace buildings, it is possible to have, say, a Red building that was originally built next to a Blue one, but is no longer.

I haven't thought about this particularly hard, and my first attempt got me a score of 75, so the puzzle is in two parts. Find a way to construct your city so that it has a value of 75, and, hopefully more interestingly, try and beat it. To begin with people should probably just post their scores, if they beat 75 (which I expect people will quite quickly), and then the challenge is for other people to work out how they did it. I quite enjoy discussing strategy, but I know plenty of people will just want to try it for themselves, so if you also want to discuss strategy, put it in a funky colour so it's hard to read by mistake.

If anything isn't clear, let me know. This was a bit rushed because I need to go and shoot some zombies.

[Kieran Child]

Edit: don't read below. It's rubbish, still working on it though.
Edit: you can read below now, but I'm still not sure of myself.

First step:
Place a blue anywhere, and reds around it. Now put a blue on one of those reds, and turn the old blue red, and turn red all the new adjacent blocks. By doing this you can end up with all squares red but for one square blue.
Second step:
By slinking around the blue, you can get the corners green, and the edges (apart from the middle egdes) green, and so on until everything is green apart from a central cross.
Third step:
Put the blue one diagonal away from a corner and turn the two adjacent edge pieces yellow. Do this for all corners, and then you can also turn the squares one diagonal in from the corner yellow.
Fourth step:
Turn everything one space from the centre green
This leaves us with this patternhttp://img21.imageshack.us/img21/3813/69319649.jpg
Only with those four squares around the centre green.
Which scores 81. Can anyone improve?

[Michael Wallace]

To begin with people should probably just post their scores, if they beat 75 (which I expect people will quite quickly), and then the challenge is for other people to work out how they did it. I quite enjoy discussing strategy, but I know plenty of people will just want to try it for themselves, so if you also want to discuss strategy, put it in a funky colour so it's hard to read by mistake.

I suppose I should have been more precise about what I meant by 'strategy'. The basic principle being to try and avoid giving away the/an answer to people who don't want to see one.
Edit: Thanks Kieran.

[Kieran Child]

No you were fine, I just didn't read all of your post. Sorry. Changed accordingly.

[Richard Brittain]

Well, I came up with this:



But it doesn't seem right, because I didn't use any green or yellow.

[Michael Wallace]

Kieran, I've had a chance to think about your method, and I think I'm missing something, in particular in this step:

Third step:
Put the blue one diagonal away from a corner and turn the two adjacent edge pieces yellow. Do this for all corners, and then you can also turn the squares one diagonal in from the corner yellow.

How can you turn the squares one diagonal in from the centre yellow, when you've already turned two of the four adjacent squares yellow? (as in, if the squares are labelled A1 from top left to E5 to bottom right, your method suggests to me that you've turned A1 green, A2 and B1 yellow (the two adjacent edge pieces", and then somehow you've turned B2 yellow. What am I missing?

[Charlie Reams]

Well, I came up with this:

This does suggest a sensible approach to the problem, by solving the cases where there are only two types of building, then 3, and build up to 4.

[Kieran Child]

Terribly sorry Michael. Though my post did come with a semi-warning of being rubbish XD
The final pattern I end up with is the following:
http://img193.imageshack.us/img193/1754/71609302.png

[Michael Wallace]

Terribly sorry Michael. Though my post did come with a semi-warning of being rubbish XD
The final pattern I end up with is the following:
http://img193.imageshack.us/img193/1754/71609302.png

Ah excellent, yes, now it makes sense. My 75 has the same pattern of yellows, just with more blues and fewer greens. I suppose unless someone can better 81, the next challenge is proving it's optimal.

[Matt Morrison]

TOWER BLOXX! Fucking awesome. I used to enjoy playing this on my last phone.

After reading the start of someone else's ideas on the Internet, and spending quite a while thinking about it, I made the following picture guide:
here it is. (I will just link to it rather than post the picture here in case it pisses anyone off.)

It's not perfect but it was certainly close enough for me to not bother coming back to it, though I did also change phones shortly afterwards.

Fairly obvious colour coding:
- grey for ones which haven't changed since the last stage.
- black for ones you need to change on the current stage.
- strong coloured backgrounds for those you are adding that will be permanent.
- lighter coloured backgrounds for permanent ones you've added in previous stages.

[Charlie Reams]

TOWER BLOXX! Fucking awesome. I used to enjoy playing this on my last phone.

For the lazy amongst us, what was your score?

[Matt Morrison]

Do you mean the Proper Score, or using Michael's 1-2-3-4 points system?
I think using the simplified system the grid is worth 81 points.

I make it 80 (13 yellows, 5 greens, 6 reds and 1 blue = 52 + 15 + 12 + 1), but I might have miscounted.

[Matt Morrison]

Ballsacks, just noticed Kieran's already got an 81. However, knowing Kieran, he probably just found it on the Internet, did his own drawing and claimed it as his own logic puzzle.
Whereas I spent a load of time thinking about mine and gave it visual step-by-step instructions. Win.

[Kieran Child]

Hey hey hey wooah. What are all these accusations flying about?
Speaking about flying, there are 10 birds in a tree and I shoot one, how many are left in the tree?

[Matt Morrison]

Do you mean the Proper Score, or using Michael's 1-2-3-4 points system?
I think using the simplified system the grid is worth 81 points.

I make it 80 (13 yellows, 5 greens, 6 reds and 1 blue = 52 + 15 + 12 + 1), but I might have miscounted.

What the fuck? Is that you signing in to the forum as me Charlie? Ah well, explains where those unfunny posts Kirk mentioned must have come from.

[Matt Morrison]

Seriously, what's going on? More than a little confused, someone else has edited my whole long post (from which the "Do you mean the Proper Score" quote was just a portion) and replaced it with the "I make it 80" message. Not happy.

[Charlie Reams]

...Not me.

[Matt Morrison]

I'm going to call you Michael Wallace forever, never will you deserve the jovial nickname Raccoon. I spent a good ten minutes writing that post, trying to contribute to your thread!

(No worries, correct it if you can though please)

[Charlie Reams]

Raccoon is sacked as moderator. Zef assumes the position immediately.

[Derek Hazell]

Hey hey hey wooah. What are all these accusations flying about?
Speaking about flying, there are 10 birds in a tree and I shoot one, how many are left in the tree?

None, because all the others flew away at the sound of the shot?

[Kieran Child]

Hey hey hey wooah. What are all these accusations flying about?
Speaking about flying, there are 10 birds in a tree and I shoot one, how many are left in the tree?

None, because all the others flew away at the sound of the shot?

Full marks for working. Half marks for conclusion. My answer is 1 because the one you shoot stays there.

[Michael Wallace]

Raccoon is sacked as moderator. Zef assumes the position immediately.

I can't really argue with that

[Derek Hazell]

Hey hey hey wooah. What are all these accusations flying about?
Speaking about flying, there are 10 birds in a tree and I shoot one, how many are left in the tree?

None, because all the others flew away at the sound of the shot?

Full marks for working. Half marks for conclusion. My answer is 1 because the one you shoot stays there.

Oops. That's what comes of trying to get in first in such a clever forum!

Although, it could be argued that the dead bird would fall out of the tree.

[Matt Morrison]

Full marks for working. Half marks for conclusion. My answer is 1 because the one you shoot stays there.

Although, it could be argued that the dead bird would fall out of the tree.

Or it could be argued that you only grazed its wing with the bullet, so it survived, and flew off.
Or it could be argued that you shot one tree rather than one bird, and either all ten birds flew off, or the tree you shot was twenty miles from the one with the birds in and they never noticed.
Or it could be argued that you actually loaded your gun with digestive biscuits, it got blocked, and never fired.
Or it could be argued that Kieran's puzzles are just annoying.

[Derek Hazell]

If that's you MWM, that's very clever.

If it's someone else posing as you, it's shit.


ps I didn't know that moderators can access our passwords. I still have my insulting one from when I thought this forum was going to be a bad idea . . .

[Charlie Reams]

ps I didn't know that moderators can access our passwords.

We can't.