H.M.S. Relentless Puzzler

Thanks :)

With these light puzzles, the simplest way is often to just bruteforce it, unfortunately. A slight optimisation is to write down the patterns that you can toggle so that you can at least spot when you are one move away from the solution.

If you are into maths and computer science, this type of puzzle has a more systematic way to think about it (and to solve it). The state of the system is the 7 windows, on or off. Clicking any window toggles 3 windows, in a predetermined pattern. You can encode the entire puzzle as a linear equation in GF(2). The toggling patterns become a 7x7 matrix, with each column representing one possible move. The goal is to find a set of moves that results in all lights on, or in other words, to find a vector which, when multiplied with the matrix, results in a vector of all ones. In sagemath (free online version at cocalc.com), which can solve GF(2) linear equations:

# the puzzle
#
# we number the windows 1 - 7 in some order,
# here: left to right
#
# every column represents what happens
# when a window is clicked
#
# for example, column 1 shows that clicking
# window 1 makes windows 1, 3, and 4 toggle
A = matrix(GF(2), 7, 7, [
  1, 1, 0, 0, 0, 1, 0,
  0, 1, 0, 1, 0, 0, 1,
  1, 0, 1, 0, 0, 0, 1,
  1, 0, 1, 1, 1, 1, 0,
  0, 0, 0, 0, 1, 0, 0,
  0, 0, 0, 0, 1, 1, 0,
  0, 1, 1, 1, 0, 0, 1,
])
# our target is all lights on
b = vector(GF(2), [
  1, 1, 1, 1, 1, 1, 1,
])
# solve the linear equation
x = A.solve_right(b)
print(x)
# >>> (1, 0, 0, 1, 1, 0, 0)
# so the solution is:
# click windows 1, 4, and 5
# (just to verify, does `x` really produce
#  `b` in our puzzle?)
print(A * x)
# >>> (1, 1, 1, 1, 1, 1, 1)

See my reply to KNGDAVD Game Team below :)

Haha, sorry, the "exciting ending" is something to take with a grain of salt ;)

There is! I don't really like pixel hunting, so I am not super happy about it being in my game, but I ran out of time for the gamejam. What you need to click happens to be very close to the back-most chimney that just went down.

Maybe the jump to that puzzle was too sudden, or I should have added at least some subtle feedback! If you'd like a hint …

(spoilers incoming)

The only two relevant elements in that puzzle are the 4 windows and the chimney that just came up. Can you see anything similar about the two? You do need to press the windows in some order.