**************
SIMPLE SPLITTER (same as AND gate)
**************

Input map:
b*c
 *
 a

maximum tiles = 1
One possible layout:
AAA
 *
 *

Truth table with 3 variables:
abc [is max possible, with given squares removed]
000 1 //no squares removed (max always possible)
001 1
010 1
011 1
100 1
101 0
110 0
111 0


**************
4-WAY SPLITTER (it's just 3 SIMPLE SPLITTERs combined)
**************

Input map:
b c  d e
* *  * *
* *  * *
***  ***
 *    *
 ******
     *
     a

maximum tiles = 8
One possible layout:
A B  C D
A B  C D
A B  C D
EEE  FFF
 *    *
 GGGHHH
     *
     *

Truth table with 5 variables:
abcde [is max possible, with given squares removed]
00000 1 //no squares removed (max always possible)
00001 1
00010 1
00011 1
00100 1
00101 1
00110 1
00111 1
01000 1
01001 1
01010 1
01011 1
01100 1
01101 1
01110 1
01111 1
10000 1
10001 0
10010 0
10011 0
10100 0
10101 0
10110 0
10111 0
11000 0
11001 0
11010 0
11011 0
11100 0
11101 0
11110 0
11111 0




**************
(x | y | z) & (!x | y | !z) with splitter fixed
**************


    *******
    *     *
    *     *
 ****   ***
 *       *
***      ****
  *         *
  *         *
  * ******* *
  * *     * *
  * *     * *
 *z*x*   *****
   *       *
   *********
       *
       y


Input map:

    *******
    *     *
    *     *
 ****   ***
 *       *
***      ****
  *         *
  *         *
  * ******* *
  * *     * *
  * *     * *
 *z*x*   *****
   *       *
   *********
       *
       y

maximum tiles = 21
One possible layout: (y=false, x=true, z=false)

    AAABBBC
    D     C
    D     C
 EEED   FFF
 *       *
GGG      HHHI
  J         I
  J         I
  J KLLLMMM N
  O K     P N
  O K     P N
 *OQQQ   *PRRR
   *       *
   SSSTTTUUU
       *
       *

Truth table with 3 variables: (not too meaningful)
xyz [is max possible, with given squares remove
000 1 //no squares removed (max always possible
001 1
010 1
011 0
100 1
101 1
110 0
111 0




**************
crossover, with splitter fixed
**************
Input map:
             ********** *******
             *        * *     *
             *        * *     *
            ***       * *    ***
              *       ***    *
           ****        *     ****
           *           *        *
           *        ****        *
          ***       *          ***
            *      ***         *
         ****      * *         ****
    y    *         * *            *    x
    *    *         * *            *    *
    * ****         ***            **** *
    ***            ***               ***
      *************X*Y****************

maximum tiles = 45
One possible layout: (usable X allows usable x, covered Y forces covered y)
             AAABBBCCCD EEEFFFG
             H        D I     G
             H        D I     G
            *HJ       * I    KKK
              J       LLL    *
           MMMJ        N     OOOP
           Q           N        P
           Q        RRRN        P
          *QS       *          TTT
            S      UUU         *
         VVVS      W X         YYYZ
    [    \         W X            Z    *
    [    \         W X            Z    ]
    [ ^^^\         ___            ```a ]
    bbb            ccc               a*]
      dddeeefffggghhh*iiijjjkkklllmmma


Truth table with 4 variables:
XYxy [is max possible, with given squares removed]
0000 1 //no squares removed (max always possible)
0001 1
0010 1
0011 1
0100 1
0101 0
0110 1
0111 0
1000 1
1001 1
1010 0
1011 0
1100 0  <-- problem! (no solution if X & Y are covered)
1101 0
1110 0
1111 0