Issue #23 Feedback

Post by **Midnight Synergy** » Sat Dec 31, 2011 5:24 pm

Have pigs started to fly? Has heck frozen over?

No, but a new issue of the Midnight Post came out!

http://midnightsynergy.com/newsletter/issue023/

Post by **Sammy_P** » Sat Dec 31, 2011 5:25 pm

UNEXPECTED!

Emerald141 · Post by **Emerald141** » Sat Dec 31, 2011 5:25 pm

dig 222 · Post by **dig 222** » Sat Dec 31, 2011 5:28 pm

YES!
Thanks Patrick!

Post by **Sammy_P** » Sat Dec 31, 2011 5:29 pm

[no, there's nothing here]

[go away]

Emerald141 · Post by **Emerald141** » Sat Dec 31, 2011 5:38 pm

Post by **|Cookie|** » Sat Dec 31, 2011 5:51 pm

YAY !

Thanks Patrick!
This is the first time i post here !

And i solve one puzzle !

Post by **Sammy_P** » Sat Dec 31, 2011 5:52 pm

You could've atleast featured the tennis WAE levels, just saying.

Post by **Sammy_P** » Sat Dec 31, 2011 5:53 pm

message from Sammy_Bro

Well, in the second puzzle,

Spoiler wrote:There are 6 Z-Bots and 3 rows, and since 2 Z-Bots are moved, that means 6 divided by 3 equals 2, right?

And there are 120 Z-Bots and maybe 15 rows, 120 divided by 15 is 8.

Sammy_Bro · Post by **Sammy_Bro** » Sat Dec 31, 2011 5:55 pm

also I have a picture of the first puzzle's answer

SPOLIER ALERT

StinkerSquad01 · Post by **StinkerSquad01** » Sat Dec 31, 2011 5:58 pm

I was expecting this.

TheThaumaturge · Post by **TheThaumaturge** » Sat Dec 31, 2011 6:03 pm

Awesome! Thank you Patrick!

DARIUSH2001 · Post by **DARIUSH2001** » Sat Dec 31, 2011 6:04 pm

Thanks!

Muzozavr · Post by **Muzozavr** » Sat Dec 31, 2011 6:17 pm

Awesome.

Got the 1st puzzle, too. Haven't tried the second yet.

Technos72 · Post by **Technos72** » Sat Dec 31, 2011 6:20 pm

Wow, talk about a post for the new year.

I also see my glyphs from long ago

Master Wonder Mage · Post by **Master Wonder Mage** » Sat Dec 31, 2011 6:38 pm

Nice to have any news about POTZ, even if it's not progress.

I wish Patrick would bring back Community Spotlight though, and focus more on the Custom Adventures section than he has been in the past.

Website · Post by **jdl** » Sat Dec 31, 2011 6:41 pm

Wow I really wasn't expecting this either, thank you Patrick!

I also got the first puzzle, but the second is going to be very tricky.

The information for WA3 is really cool, I'm glad you added it! It gives us more to think about.

I think I'll give Hyper Princess Pitch a try.

- jdl

Edit: I just noticed that Hyper Princess Pitch is made by the same person who made Castle of Elite! http://remar.se/daniel/castle.php

maxnick · Post by **maxnick** » Sat Dec 31, 2011 7:57 pm

StinkerSquad01 wrote:I was expecting this.

Indeed.

MyNameIsKooky · Post by **MyNameIsKooky** » Sat Dec 31, 2011 8:23 pm

whoa, newspaper explosion

I'm glad to hear new stuff about POTZ. I'm especially interested in the planet Uo!

Sammy_P wrote:You could've atleast featured the tennis WAE levels, just saying.

The tennis adventures aren't all that impressive compared to people's main adventures.

Marinus · Post by **Marinus** » Sun Jan 01, 2012 4:42 pm

Best wishes everyone!

I think I have the answer to the second Peegue puzzle, (which is not the answer Sammy P gave) but perhaps it's a bit too early to spoil the fun.

Anyone who's interested may PM me.

yot yot5 · Post by **yot yot5** » Sun Jan 01, 2012 5:10 pm

YESSSSSSSS!!!!!!!!!!!!!!!!
Reading it now!!

yot yot5 · Post by **yot yot5** » Sun Jan 01, 2012 5:25 pm

Righty ho, answer to puzzle 2 is:

15 rows of z-bots, and it will take 45 moves (I think...)

Marinus · Post by **Marinus** » Sun Jan 01, 2012 5:31 pm

Yot:

45 moves is not very far from my solution, but I can do it with less moves.

Muzozavr · Post by **Muzozavr** » Sun Jan 01, 2012 7:52 pm

2nd puzzle:

I was able to get it in 41 move and I'm not going to try any further. EDIT: Marinus has beaten me, not only solving it in 40 moves but also finding out it's the minimum number of moves.

Marinus · Post by **Marinus** » Mon Jan 02, 2012 1:21 am

People who are not going to try further, I will send the link to my solution, if they are interested.

People who want to keep trying, but need a hint: click here

professor_k · Post by **professor_k** » Mon Jan 02, 2012 11:37 am

Puzzle 2 (solution with proof):

It involves some math, but can there be proof without it, right?

To find minimal number of z-bots to move, we must minimize area (special "z-bot" area) of three triangles that are outside of overlapping zone of two triangles with side 15 (it's easy to find, as number of z-bots is sum of arithmetical progression, so n(n+1)/2=120 and n=15 (also -16, but obviously it can't be negative)), when one of them is turned upside down.
First of all, it's obvious that biggest coverage we'll receive when at least one height of that triangles coincide (we'll definitely got more bots outside if shift it aside). So we'll have three small triangles who's area we need to calculate, and we already have formula for z-bots count in them: n(n+1)/2.
We'll have two same symmetric triangles on bottom - left and right. And we'll have one triangle on top. Another observation: we have to increase size of top triangle each time by 2 to have bottom triangles same. On one edge we'll have one huge triangle with side 14, and two small were reduced to 0, and on other edge - two with side 7, and that that was big - reduced to 0 too. It's easy to see that if size of bottom triangle is n, then the size of top triangle is m=k-2n. (k=14-constant restriction based on original triangle size) Now as we have n and m we can easily calculate what is number of z-bots outside overlapping zone:
s=2n(n+1)/2+m(m+1)/2=n(n+1)+(k-2n)(k-2n+1)/2=3n^2-2kn+(k^2+k)/2.
This is quadratic function (on n) and it will have it's minimum in point k/3.
When this point isn't integer, we'll have to round it to closest integer. Function is parabolic, so it we be okay (I can also prove this is someone don't believe, but I'm too lazy to do it now).
When k=14:
s=3n^2-28n+105 and minimum is 14/3=4.(6), and closest integer point is 5. And in point 5 there will be minimal value of function: s=40. This value consists of three triangles, two with side 5 (15 bots each) and one with side 4 (10 bots). Substituting other close points, we'll receive other solutions listed up here:
n=p=4, m=6, s=41
n=p=6, m=2, s=45

p.s. After thinking a bit more, it's not so obvious that heights have to coincide. Let's prove that too. So we can have three different triangles with the rule that restricts their sized: m+n+p=k and we have to minimize function m(m+1)/2+n(n+1)/2+p(p+1)/2. To do calculations we can drop divisions by two as they don't impact the point of minimum (function is always positive), and also drop +1s after opening brackets as they will always gave us k in sum, that also don't change the result. So the function is equivalent to the m^2+n^2+p^2. It will have absolute minimum when all of the m n and p are same and equal to k/3 (suspicious similar result, huh?:)). But when k/3 isn't integer, we need to find closes integer point that satisfies minimum condition. Let's assume that in solution none of heights coincide, so we have three different small triangles m!=n, m!=p and n!=p. Function is parabolic, so the further we go from optimum point, the bigger difference is, so we can assume that difference between m, n and p will not exceed 1. The only possible case when all that inequalities for this is when m+1=n=p-1 (or similar with different order). But in this case k=m+n+p=3n, so m+1=n=p-1 isn't optimal solution as m=n=p is better. As a result we have that at least two of the m, n and p coincide, so overlapping is symmetrical and this means that one height of triangles must coincide.

Marinus, is you solution similar?

StinkerSquad01 · Post by **StinkerSquad01** » Mon Jan 02, 2012 4:37 pm

Welcome to the forums, professor_k.

Marinus · Post by **Marinus** » Mon Jan 02, 2012 7:30 pm

Marinus, is you solution similar?

No, actually my solution is by trying things out: https://docs.google.com/spreadsheet/ccc ... l=nl#gid=1

Blast!10 · Post by **Blast!10** » Mon Jan 02, 2012 8:15 pm

A little bird whispered in my ear that this is going to be good

...to say the least

professor_k · Post by **professor_k** » Tue Jan 03, 2012 2:07 pm

StinkerSquad01 wrote:Welcome to the forums, professor_k.

Thank you, actually I'm not completely new, as I had around dozen post time ago. But it seems that now I have one again

Marinus, huge work! Respect for that!