Solutions for Act I Scene 4 - Recursive Puzzle

A quick attempt will show that all four puzzles are unsolvable as they are, although this is harder to see for the Sudoku. What is of note, though, is that for the bottom three puzzles:

  • The coloured squares match the colour of the name of the puzzle above it
  • The coloured squares look like they could be replaced with numbers to form a standard puzzle (i.e. Ripple Effect and Nurikabe usually have fewer given clues, and Fillomino usually has a lot - just like this puzzle)

Combining these observations with the title "Recursive puzzle", we realise that all four grids in fact form one giant puzzle, with each grid feeding into the next via the coloured squares. For example, the 6 in the top row of the Sudoku coincides with an orange square in the Ripple Effect, so that orange square must be a 6 also. Going further, we realise that it can also go the other way - the bottom right 4 in the Ripple Effect indicates that the bottom right corner of the Sudoku is also a 4.

Adding this new rule allows us to solve the grid.

Taking the circled numbers and converting them to letters spells IONA, which doesn't seem like a likely answer and doesn't anagram to give anything either. That's because there's one more thing which has yet to be used - the Nurikabe's solution!

The Nurikabe in this puzzle is unusual since it starts out with given black squares. Treating these squares as somehow "different" (e.g. by colouring them a different colour) gives the word EIGHT.

Adding the eighth letter to the letters so far gives IONAH. This still doesn't look like anything, and doesn't anagram to anything obvious, but reading it backwards (akin to returning after a recursive base case in programming) spells HANOI. This isn't a very thematic answer on its own though, but looking up "Hanoi puzzle" or noting that we are presented with a "tower" of puzzles gives the tower of Hanoi, a famous puzzle with a simple recursive solution.

Design notes:

Due to the intricate nature of this puzzle, it was hard to come up with a nice puzzle where you ping pong back and forth throughout all four puzzles passing along clues. As such most of the solving for this puzzle (unfortunately) happens on the top two grids, with the resulting numbers sifting downwards.

The crooked G in the Nurikabe is a result of an attempt to reduce the number of 4s within the puzzle. This is because the 4 would have propagated up to Ripple Effect, where it would become a problem for construction.

The given black squares of the Nurikabe were not originally there, but were added once the difficulty of deciphering the Nurikabe was realised through testing. The squares also served to draw attention to the fact that the Nurikabe's solution is important but unfortunately, based on the guesses of IONA by some teams, this does not seem to have been immediately obvious.

HANOI is spelt backwards in the puzzle solely as an attempt to deter teams from guessing before the whole puzzle was completed. Also, spelling out NINE does not look as pretty on a Nurikabe thanks to the Ns.

The answer is: towerofhanoi