About a month ago I was watching a YouTube video where YouTuber Drew Gooden was struggling with a “weird” puzzle:
This is what the puzzle looks like:
It has 10 pieces that can be flipped/rotated and placed on a calendar. They claim there is a solution for each day/month/weekday combination. In the YouTube video Drew is struggling and says:
The problem is, I’ll never be able to prove that
But… what if we can?
As a programmer this sounds like a perfect little puzzle to solve.
Solving the puzzle
To solve this, I first encoded all the puzzle pieces, this is relatively easy to do because it’s just a 2D grid.
Next I wrote the code to generate all the possible rotations of a certain puzzle piece (and eliminated duplicates). Some pieces have more rotations than others because some are the same after a 180 degree rotation, others are not.
Next I blocked the target puzzle solutions on the board, for example “2nd June Monday”, placing three markers.
After that I just go through all possible piece/location combinations, placing the first puzzle piece in the top position and continuing down.
This was fast enough to solve the first puzzle after a couple of minutes.
But… not fast enough to generate all: 12 (months) x 31 (days) x 7 (weekdays) = 2.604 solutions
Example output: The image above has a solution for Thursday 8th of April. The code outputs this as:
Solution for: 8/4 : 0 0 0 X 1 1 X 2 2 0 0 4 1 X 2 2 3 3 4 1 1 X 2 3 4 4 5 5 7 6 3 3 5 5 9 7 6 6 6 6 8 9 7 7 7 8 8 8 9 X X X X X 8 9
Each number 0-9 stands for a certain puzzle piece. The X’s are blocked off (solution and edge).
Improve solving speed
To improve the speed of the solver I decided to do a small flood fill after placing each puzzle piece. If we’ve created a spot where there are just 4 places left (a small island) I stopped looking further, because no puzzle piece will ever fill this spot.
This small algorithmic improvement was enough to make it fast enough to generate a puzzle solution for every single combination.
Solutions: If you’re just looking for all the solutions: solutions.txt.
Code: If you want to take a look at the (Java) code, check out PuzzleADaySolver.java.