Transmission from the moon radio-station
After a long time in space I started to forget what N and E stand for on Earth. Well, now it's clear to me: East and North are directions. The first time I tried to get through those Space Grids, I mixed them up and also tried to take clues from the spectrum... Oops, let me get the spoiler glasses on. I might talk ...
This puzzle is the Towers of Hanoi with three disks. A, B, and C are the pegs, and the positions from left to right are the disks; the lines connect positions that are valid to move between.
The initial puzzle is probably the Towers of Hanoi with more disks - the area needed to draw the diagram is quadrupled with every new disk added, so a larger diagram ...
This is something to do with
Specifically (with thanks to @GentlePurpleRain for help coming up with this):
This fits with most of what your rival is saying, as follows (with help from the OP for one or two lines):
Ah, interesting! But I don't get how this one is supposed to work; it obviously looks too short.
Hmm...a CD maybe?
Silence? What could mean ...
I have noticed that in the first image,
Solving picture 2 using the rules of the game yin-yang (suggested by @edderiofer) gives the unique solution
Now, adding shapes to the second image using the rule discovered in the first gives the new image
I actually think it is the number of sides of the shapes rather than the shapes themselves that matter - we ...
He was trying to answer:
total number of dead people
extra ear mutation
average number of cloudy days
exorcist scene rotating
child slavery laws
mt everest erosion
howitzer firing rate
pigeon water migration
average walking speed
If we assume that one of the puzzles is a sudoku, we are left with only four possible grid constructions because the last two pieces can not be next to each other and have to form the diagonal. I tried slitherlink as the second puzzle which gave a unique solution for only one of those grids. In that grid the three corners with numbers can be solved ...
rand al'thor points out that
the numbers are
but after the square marked 16, Robert's got this (image courtesy of OP)
and we can now see why Robert is distressed:
... which is a situation that always frustrates me, though I don't get quite as angry...
Your friend is in:
Handdrawn solutions (originals for reference, click on the links to see):
Prettified solutions, image by @TheGreatEscaper:
My initial set of rules:
That was close. Upon some solving, I realised that:
That solves all the outer puzzles, with a couple of tricks to help simplify:
To solve the centre puzzle:
It looks like a version of the Prisoner's Dilemma. You're player 2, and the choice is either to Cooperate or to Defect, after which player 1 will make their choice on the second level of the tree.
If you both cooperate, you get the best overall outcome ("only" 2 points lost total). But a defector to a cooperator gets a better outcome for themself (no points ...
Let me try a different approach.
There is one red square in each row and column (fact). That provides us with a free pairwise collocation on rows and columns, or: on the letters written one the up and on the left. This collocations for the first three images (yes, that is a lot of examples!) give you:
Drawing a line through letters is convenient, if we ...
Just to expand on @Deusovi's devious answer, you can convert the states described in the circle to a game state as follows:
Start with a set of empty pegs, labelled A, B, and C.
Place the biggest disk on the peg with the letter shown on the right.
Place the middle disk on the peg with the letter shown in the middle.
Place the smallest disk on the peg with ...