25 Sep 2009
Can you fill the 4x4 Checker Board with set of L-Shaped Trominoes???
Watch this File
1. Use L-Shaped Trominoes to fill 4x4 Checker Board.
2. Use directions for [Linear] or (Angular) movements.
1. The inspiration of this game is from Mathematical Problem/Puzzle.
2. This Math Problem is very famous and mostly used in Mathematical Induction and also in Algorithm Lectures (hence Number Theory).
3. The choosen board is 4x4 as it is very critical/important step in Mathematical Induction.
4. Other higher levels of the Puzzle will be repetition of 4x4 levels and hence not much of fun.
5. The intention of the game is to appreciate the capability of Mathematical Induction (not GUI of the game) for problems that look very complicated but results in simple solution.
6. The solution using Congruence Modulo is, for generalized 2^k x 2^k case (= 4^k), the congruence modulo division by 3 (L-Shaped Tromino has 3 unit squares) is always 1^k (= 1).
MATLAB 7.4 (R2007a)