I found someone who shared a formula that would produce permutations of a factorial up to 10 without VBA. Fortunately I just needed it to go to 9. That's 362,880 permutations. Once I had that, I produced all the sums (answers) for my Circuit Board Square (there are 8 sums per puzzle). I then concatenated those as a single string and did a =countif across all those entires.
This =countif calculation took ~3 hours to complete since it had to do it against all 362,880 entires. Once that was done I was able to see how many unique entires there were with these permutations for solving the puzzle. Out of 362,880 permutations, there were 213,248 entries with a count of 1.
It was important for me to determine these individual permutations because I'd hate to be in a position where I randomly inserted numbers, got sums, and realized there were multiple answers. An answer key that had a different answer than yours, which may also be valid, is a bad puzzle experience.
Now I have 213,248 puzzles to choose from. I think that's pretty good for a 100 page starter book!
I took the standard "fill the 3x3 with numbers 1-9" and started messing around with the sums of different blocks. Sujiko puzzles add circles on the four main intersections and provide those as sums to help you figure out how to place 1-9 inside. I decided to see what would happen if you add other portions together instead.
The result was a rather pretty looking circuit board looking puzzle. Maybe I'll call it a Circuit Board Square?
I have to run some calculations to see if the permutations in the 3x3 can create the 9! unique answers.
I'm entering a new chapter in my design career, so it's worth mentioning here. Appetizer games, baby.
What are they? Here are the rules.
- Fast play: All players must be able to play at the same time
- Fast action: All players share the same result, but have a choice on what to do with it
- Inclusive: All games can be played by 1+ players and quick to learn (i.e. can I teach this to my 5 year old)
- Affordable: Have limited components and a print-and-play version is already available
My newest Kickstarter, Blankout, is another example of this. I'll be working on games like this for a while. I'll leave all that heavy cardboard stuff to the pros.
Kickstarter Link: Blankout on Kickstarter
That's the family's feet. Made this for Josie's grandma. More like FEEThearts, amirite?