**************
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