I thought I'd try my hand at writing a program for Mobius sudoku. I used the Z3 SMT solver (Python wrapper) for this. There isn't much of a "solution path" to describe: most of the constraints translate fairly directly, even the wrapping around of the columns. The main difficulty was
The other constraint which required some care was:
Here's the ...
I'm going to propose the answer as:
First, take notice of:
Secondly, take notice of:
Additionally, it can be seen that:
This leads me to believe that all of the aforementioned points would remain true in the blank square, and as such our only logical options are:
Also, notice that:
With this, we can conclude that:
Note: I tried making sense with sides ...
Say I'm one of the residents of this island, and the Guru hasn't shown up yet. I'm a perfect logician, like all the rest of the residents... but I'm very forgetful. So, to help me remember things, I make little scale models of the island in my hut!
Whenever I'm unsure of something, I make two models of the island, and then see how the other perfect ...
Your "parallel induction" is already happening in the generally accepted solution
When the solution says "A considers that B considers that ...", B, C, and so on are all arbitrary people. So it does indeed extend to "A knows that everybody knows that...". However, you seem to be failing to take some uncertainty into account.
What new ...
This puzzle is easier than it looks.
First you have to realise that
We then simply look at the row and column sums:
Now that we know which cells have to change, it is simple matter to change them to make the sums equal to 246. These changes indeed happen to be a permutation of those six numbers.
For all of these questions, the real key is to look at the possible answers.
Many times, the testers have one real solution in mind with 3 fake solutions that are adjacent by one thing to the real one.
So, looking for majorities gives the following results:
3 times the right column is occupied, only 1 time the left => right column is correct
3 times the ...
Completion of proof:
Observe that because of parity there actually have to be two bridging dominoes for every pair of adjacent rows/columns. Now count them: 5x2 horizontal + 5x2 vertical: That's more than we have at our disposal.
You are given four statements; let's rewrite them in more basic/formal notation.
SUNNY implies WET.
RAINCOAT implies SWEAT.
RAINY implies (DRY and NOT SUNNY).
(WINDY and NOT SUNNY) implies SWEAT EVAPORATES.
In the given situation, it is RAINY and WINDY and you wear a RAINCOAT. By 2, you SWEAT. By 3, you are DRY and it is NOT SUNNY. By 4, your SWEAT ...