Tuesday, June 19, 2012
Okay, so maybe it isn't as complicated as this little machine... by a long shot... BUT using some of the same principals to develop the combinations needed from scratch.
Here is a link to the diagram I used to start writing the formula to go level by level calculating the potential 'touches' that a word could have.
For example, if the word I wanted to build started at position 5, the next possible position would be either a 6, 10, 9, 1, or a 2 (see prior post for the actual positions). Number 6 would be due east, 10 southeast and so on and so forth. I need to know this as we progress down the levels so I can follow the rules of Wordament - once I 'touch' the number 7, I can no longer touch it until I pick up my finger (z axis).
The diagram also tells me the number possible 1st choices I have for the formula - so the most being 6,7,10,11 - as they are in the middle of the board and the fewest being 1,4,13 & 16 since those areas are in the corners. Each combination of these gives me every potential position for 2 letter words. I'm sure there is a mathematical formula to prove the number I have (or prove that it is wrong) - closest I could get using the combination formula: however, this does not take into account the rules of not using a number again.
Nevertheless this get's me exactly 84 combinations for level 1 and level 2... now for the fun part.