Caveat: my answer violates the rules because I solved it using a computer.
My script reads in the input in a list of rows, each of which is a list of cells, each of which is a two-element tuple containing an integer (the count of filled neighbours for that cell, or 99 if the count is unknown) and a "#" (filled), " " (blank), or "?" (unresolved) character. ...
I found an answer im satisfied with :
Reasoning and variations :
This puzzle was fun to solve, I really enjoyed it. I still don't know if this is the best solution. With less pieces, checkmating gets really hard.
PS : My solution is computer-free, and im not good enough at programming to be able to verify my solution. If I missed something or if there is ...
On the bounty challenge:
Here is a secret bounty recipe that uses one operation and 74 ingredients.
How I got this solution:
On the general question:
Here is a secret recipe with 61 57 ingredients.
(The answer survived a triple check of the logic, mostly by pure luck. The readability of my explanation didn't survive; so here's is a rewrite.)
The house has two repeating runs of 27 consecutive rooms: the first one starts at room 20 and repeats at room 50, and the other one starts at room 128 and repeats at room 170. However, it's still possible to ...
For a General Case solution (i.e. an guaranteed solve, starting from any room), I'm going to go with an Upper Bound of
This is because
So, you add 1 more room to make the sequence unique
As a bonus, here is a practical implementation on how to apply this:
Edit : my first answer no longer works because i assumed re-visiting a room that we already explored doesn't count. I deleted that part and went back to solving it. As @DEEM stated, revisiting counts.
With these changes, i found :
The different starting positions i found for this number are :
It turns out the answer is way higher than what I excepted. If i ...
My color scheme is: yellow for "empty", dark gray for "human", red for "vampire", light red for "no human, maybe vampire", and light gray for "no vampire, maybe human".
Start with the basic deductions on the 0s:
A similar strategy can be used
We can also attack the top left in a similar way.
And another pair can be attacked:
Some miscellaneous ...
Step by step deduction
Firstly, note that MASTERING is a full nine-letter word so it takes up a whole row, and EMIGRANT is an eight-letter word so the column is either EMIGRANTS or SEMIGRANT. Also note that ARTEMIS must begin from either the 1st or 3rd place in its row, because otherwise the A will clash with MASTERING; and the remaining ...
The last episode was difficult, with a few twists and turns, but this selfmate left little doubt: the answer is 18 moves.
It's clear that we must manipulate Black's pawn structure somehow, because there's no way a mate can come out of the current structure. The fact that such a manipulation must be forced, i.e. Black's only legal move, ...
A few basic facts I notice:
The breakthrough threat of ...b4, cxb4, and ...c3 prevents the White
king from leaving the square a1-d4, namely we must rule out a winning plan of running to the kingside and gobbling up the black pawns on g4 etc.
The a6-b7 structure keeps Black's king confined, both spatially and temporally, to b8-a7 (or c7).