WINNER FOUND :
GenlyAi
Solution submitted at 10:44AM forum time
Runners up:
Irond Will - 12:00 PM
Nytewarrior - 12:09 PM
Thanks to everyone who participated!
The official explanation and solution will be posted in a spoiler below.
Alien Math Homework
ATTENTION CITIZEN,
I am Dr. S, lead investigator for NASA's Extraterrestrial Contact Taskforce. We have an urgent matter that requires the attention of all who might be of assistance. One of our researchers has intercepted what appears to be the math homework of a young extraterrestrial, vacationing with his family on Europa. Unfortunately, the youngster has failed to answer two of the questions on his assignment! Details from the transmission suggest that such omissions mean the little slacker will need immediate tutoring back on his home planet, cutting his family's vacation short and eliminating any chance we have to assemble a first contact mission.
We must decode this homework assignment, fill in the gaps, and retransmit before our chance to join the intergalactic community slips away!
The decoded transmission follows. Please help us. We will make it worth your while with a copy of L.A. Noire, the cinematic detective mystery game by Team Bondi and Rockstar Games. A $50 value!
Sincerely,
Dr. Jet Starman
NASA Extraterrestrial Task Force
BEGIN HOMEWORK ASSIGNMENT TRANSMISSIONPART 1: COMPLETED PROBLEMS
PART 2: INCOMPLETE PROBLEMSSUBMISSION:
Send me, Donkey Kong, your solutions to the two incomplete problems by
Private Message. If you are the first to provide the correct solutions, you will win a copy of L.A. Noire for XBox 360.
Limit: One solution PM per 8 hours (to prevent guessing, my box from filling up). If you send two in a row, the second will still count, but I'll pretend like I didn't get it for another 8 hours. Feel free to discuss the puzzle publicly in this thread but keep in mind that everyone reading is your competition.
Feel free to make an image solution or use text in a format like this, with dashes indicating blanks:
RG
-R
G-
RULES:
Offer valid only in the United States and Canada. (There may be a slight delay shipping to Canada) XBox 360 version. Item will be shipped as soon as possible. Puzzle may be adjusted if errors are found or the difficulty is too high.
Thousands of hot, local singles are waiting to play at
bubbulon.com.
Posts
I understand all the operations except this one. I think that if I can figure this piece out, I'll have the solution.
I'm not sure what happens when two red tiles in the same location are added. I see what happens when you add two green tiles when the green tiles are in a corner location, but not when they're in the middle of a column.
So this example is introducing two new operations simultaneously and it is befuddling me.
the "no true scotch man" fallacy.
the "no true scotch man" fallacy.
every conditional value i try just makes my head hurt and i'm guessing the solution's actually more difficult than the rules and methods i'm imagining
Pass
FIRST HINT:
Alien addition is commutative
A+B=B+A
Edit: I blame the schools. They should teach more alien math.
edit: I think we have to assume that the operators given are the correct operators, although we should note that they may function oddly. For example, when I add "foo" and "bar", should I get 6 charecters or 3 ("foobar" or whatever adding their numeric position in the alphabet generates for letters).
Does adding 3 lower left Greens equal one mid right green?
As far as I can tell, yes.
I figured it out, but I don't have enough time to figure it out.
Then it's math. We just have to decode what the symbols mean. I'm still thinking Roman numerals.
Each square represents a number. Green is positive, red is negative, white is null. Bottom left is 1, middle right is 3. Middle left is 3 times the value of upper right.
Cheers!
EDIT: Also, middle left is the highest number on the board.
That doesn't work for figure 7, which starts with all tiles as solid green.
All greens is the highest value, if you want to look at it that way. There is nothing wrong with solved example 7.
Thanks to everyone who participated. I didn't imagine it would be over in under 4 hours!
Would you post a key.... or explanation?
the "no true scotch man" fallacy.
Each position in the grid represents a value. Its color is its sign. White means zero. The number represented by each grid is the sum of its components. This is the official key:
However, given the nature of the problem, any multiple of these numbers will work. In fact, the whole problem is underdetermined by the number of clues given (as our winner noticed), so there are a very large number of possible solutions. The GenlyAI's winning solution wasn't even the official one:
It does, however, conform to every clue and properly resolve the relations in the final two unsolved questions.
Addendum: The official solution is actually wrong due to... and don't hit me, a problem with clue number 7. I've inserted a revised clue 7 into the OP for history's sake. Please note that Genly's solution works despite this flaw. I verified it independently. Note that for his to work, you must consider the original clue 7:
These aliens must have a very difficult time doing science.
Games: Ad Astra Per Phalla | Choose Your Own Phalla
Yes, you can locate my shame in an addendum to the solution. Genly's solution, however, does solve all the clues, 7 included, and resolve the problems.
Sentret:
A solution does exist (or at least should have if the original clue #7 had been correct) where the number system defines all integers in its range. Regardless, any solution that works would have been fine.
(I was a little surprised that my notes from this morning were suddenly incorrect.)
Games: Ad Astra Per Phalla | Choose Your Own Phalla
And more to Irond Will for not only coming up with the official solution but also pointing out exactly where clue 7 was broken.
I got to a similar point myself, but then decided "fuck it", and chose one arbitrarily. If it weren't for my well-developed sense of arbitraricity, I can't imagine where I'd be in this crazy life.
Looking at it as far as I can tell green is positive and red is negative, blank is 0? I have no idea.
Donkey Kong posted a solution on the previous page. For the steps to actually solve it:
Let's think of the values as variables:
ab
cd
ef
So you look at the completed problems and see
1. 0 + e = e <- Not particularly helpful, but it's a hint to the right direction
2. e + -e = 0 <- Again, just a hint
3. e + e = d-e <-Here's something that can actually help. Let's use a little math on this.
3. e+e+e=d
3. 3e=d <- So now we have the workings of a solution! I arbitrarily assigned the values e=1 and d=3 at this point. It turns out that that does work out and is part of the official solution. If I got stuck, I would've gone back and just continued using them as variables.
4. d-e + d-e = d+e <- Not very helpful if you've already figured out what's going on, but it helps to confirm the rules of the game. My first guess for how the game works (ternary, with green=n and red=2n) failed on this part.
4. 2d -2e = d+e
4. d = 3e
4. 3 = 3
And you basically go through each of the problems like that. I had to make another arbitrary choice for a (selected 9, since it looked like a ternary variant by that point). The thing that helped me come to the "official" solution rather than picking another arbitrary value was how much it reminded me of negabinary. It's not quite the same thing, but similar enough to really help me make the mental leap towards "weird negative ternary thing." This numbering system probably has an official name, but I've never heard of it before.
DK: Thanks! I unfortunately arrived at this way after the contest ended, but it was fun to figure out! I got it really quickly, but only because my second guess about how it worked was spot on.
To actually find that it's just algebra, yeah, lots of trial and error. That's how math proofs are made.
One thing a couple people have implied but nobody's said explicitly is that that the two numbers you need to represent for the answers can't necessarily be represented for a given valid solution of the "clue" equations. According to DK, what makes the official solution special is that it can represent every integer over its range. In that sense, I was lucky that I picked a solution where the answers could be represented.