Twelve statements: Difference between revisions

Line 504:

statements = [ (==12) . length,

3 ⊂ [length statements-6..],

3 ? [length statements-6..],

2 ⊂ [1,3..],

2 ? [1,3..],

4 → [4..6],

4 ? [4..6],

0 ⊂ [1..3],

0 ? [1..3],

4 ⊂ [0,2..],

4 ? [0,2..],

1 ⊂ [1,2],

1 ? [1,2],

6 → [4..6],

6 ? [4..6],

3 ⊂ [0..5],

3 ? [0..5],

2 ⊂ [10,11],

2 ? [10,11],

1 ⊂ [6,7,8],

1 ? [6,7,8],

4 ⊂ [0..10]

4 ? [0..10]

] where

(s ⊂ x) b = s == (sum . map (b!!) . takeWhile (< length b)) x

(s ? x) b = s == (sum . map (b!!) . takeWhile (< length b)) x

(a → x) b = (b!!a == 0) || all ((==1).(b!!)) x

(a ? x) b = (b!!a == 0) || all ((==1).(b!!)) x

testall s n = [(b, w) | b <- tf s, w <- [wrongness b s], length w == n]

Line 579:

'''All true'''

<lang j> (#~0=#@{::~&_1"1) testall S

+------------------------+

┌───────────────────────┬┐

│1 0 1 1 0 1 1 0 0 0 1 ~~0││~~

¦1 0 1 1 0 1 1 0 0 0 1 0¦¦

+------------------------+</lang>

└───────────────────────┴┘</lang>

'''Near misses'''

<lang j> (#~1=#@{::~&_1"1) testall S

+--------------------------+

┌───────────────────────┬──┐

│0 0 0 0 1 0 0 1 0 0 1 ~~0│0~~ │

¦0 0 0 0 1 0 0 1 0 0 1 0¦0 ¦

+-----------------------+--¦

├───────────────────────┼──┤

│0 0 0 0 1 0 0 1 0 1 1 ~~1│0~~ │

¦0 0 0 0 1 0 0 1 0 1 1 1¦0 ¦

+-----------------------+--¦

├───────────────────────┼──┤

│0 0 0 1 0 0 0 1 0 1 1 ~~1│0~~ │

¦0 0 0 1 0 0 0 1 0 1 1 1¦0 ¦

+-----------------------+--¦

├───────────────────────┼──┤

│1 0 0 0 1 0 0 0 0 0 0 ~~0│7~~ │

¦1 0 0 0 1 0 0 0 0 0 0 0¦7 ¦

+-----------------------+--¦

├───────────────────────┼──┤

│1 0 0 0 1 0 0 1 0 0 0 ~~0│10│~~

¦1 0 0 0 1 0 0 1 0 0 0 0¦10¦

+-----------------------+--¦

├───────────────────────┼──┤

│1 0 0 0 1 0 0 1 0 0 1 ~~0│11│~~

¦1 0 0 0 1 0 0 1 0 0 1 0¦11¦

+-----------------------+--¦

├───────────────────────┼──┤

│1 0 0 0 1 0 0 1 0 1 1 ~~1│11│~~

¦1 0 0 0 1 0 0 1 0 1 1 1¦11¦

+-----------------------+--¦

├───────────────────────┼──┤

│1 0 0 0 1 1 0 0 1 0 1 ~~0│7~~ │

¦1 0 0 0 1 1 0 0 1 0 1 0¦7 ¦

+-----------------------+--¦

├───────────────────────┼──┤

│1 0 0 1 0 0 0 0 0 0 0 ~~0│7~~ │

¦1 0 0 1 0 0 0 0 0 0 0 0¦7 ¦

+-----------------------+--¦

├───────────────────────┼──┤

│1 0 0 1 0 0 0 1 0 1 1 ~~1│11│~~

¦1 0 0 1 0 0 0 1 0 1 1 1¦11¦

+-----------------------+--¦

├───────────────────────┼──┤

│1 0 0 1 0 1 0 1 1 0 0 ~~0│5~~ │

¦1 0 0 1 0 1 0 1 1 0 0 0¦5 ¦

+-----------------------+--¦

├───────────────────────┼──┤

│1 0 1 1 0 0 0 1 1 0 0 ~~0│6~~ │

¦1 0 1 1 0 0 0 1 1 0 0 0¦6 ¦

+-----------------------+--¦

├───────────────────────┼──┤

│1 0 1 1 0 1 1 0 1 0 0 ~~0│8~~ │

¦1 0 1 1 0 1 1 0 1 0 0 0¦8 ¦

+-----------------------+--¦

├───────────────────────┼──┤

│1 1 0 1 0 0 1 0 1 0 0 ~~1│11│~~

¦1 1 0 1 0 0 1 0 1 0 0 1¦11¦

+-----------------------+--¦

├───────────────────────┼──┤

│1 1 0 1 0 0 1 0 1 1 0 ~~0│9~~ │

¦1 1 0 1 0 0 1 0 1 1 0 0¦9 ¦

+-----------------------+--¦

├───────────────────────┼──┤

│1 1 0 1 0 0 1 1 1 0 0 ~~0│7~~ │

¦1 1 0 1 0 0 1 1 1 0 0 0¦7 ¦

+--------------------------+</lang>

└───────────────────────┴──┘</lang>

'''Iterative for all true'''

Line 622:

<lang j> (-N)&{. #: S <:@]^:((]-.@-:(apply&><)"1) (-N)&{.@#:@])^:(_) 2^N=.#S

1 0 1 1 0 1 1 0 0 0 1 0</lang>

=={{header|Java}}==

The following Java code uses brute force. It tries to translate the logical statements as naturally as possible. The run time is almost zero. --[[User:Mga010|Rene Grothmann]] 10:33, 28 October 2012 (UTC)

public class LogicPuzzle

{

boolean S[] = new boolean[13];

int Count = 0;

public boolean check2 ()

{

int count = 0;

for (int k = 7; k <= 12; k++)

if (S[k]) count++;

return S[2] == (count == 3);

}

public boolean check3 ()

{

int count = 0;

for (int k = 2; k <= 12; k += 2)

if (S[k]) count++;

return S[3] == (count == 2);

}

public boolean check4 ()

{

return S[4] == ( !S[5] || S[6] && S[7]);

}

public boolean check5 ()

{

return S[5] == ( !S[2] && !S[3] && !S[4]);

}

public boolean check6 ()

{

int count = 0;

for (int k = 1; k <= 11; k += 2)

if (S[k]) count++;

return S[6] == (count == 4);

}

public boolean check7 ()

{

return S[7] == ((S[2] || S[3]) && !(S[2] && S[3]));

}

public boolean check8 ()

{

return S[8] == ( !S[7] || S[5] && S[6]);

}

public boolean check9 ()

{

int count = 0;

for (int k = 1; k <= 6; k++)

if (S[k]) count++;

return S[9] == (count == 3);

}

public boolean check10 ()

{

return S[10] == (S[11] && S[12]);

}

public boolean check11 ()

{

int count = 0;

for (int k = 7; k <= 9; k++)

if (S[k]) count++;

return S[11] == (count == 1);

}

public boolean check12 ()

{

int count = 0;

for (int k = 1; k <= 11; k++)

if (S[k]) count++;

return S[12] == (count == 4);

}

public void check ()

{

if (check2() && check3() && check4() && check5() && check6()

&& check7() && check8() && check9() && check10() && check11()

&& check12())

{

for (int k = 1; k <= 12; k++)

if (S[k]) System.out.print(k + " ");

System.out.println();

Count++;

}

public void recurseAll (int k)

{

if (k == 13)

check();

else

{

S[k] = false;

recurseAll(k + 1);

S[k] = true;

recurseAll(k + 1);

}

public static void main (String args[])

{

LogicPuzzle P = new LogicPuzzle();

P.S[1] = true;

P.recurseAll(2);

System.out.println();

System.out.println(P.Count + " Solutions found.");

}

</lang>

<pre>

1 3 4 6 7 11

1 Solutions found.

</pre>

=={{header|Perl 6}}==

<lang perl6>sub infix:<→> ($protasis,$apodosis) { !$protasis or $apodosis }

<lang perl6>sub infix:<?> ($protasis,$apodosis) { !$protasis or $apodosis }

my @tests = { True }, # (there's no 0th statement)

Line 630:

Line 756:

{ 3 == [+] .[7..12] },

{ 2 == [+] .[2,4...12] },

{ .[5] → all .[6,7] },

{ .[5] ? all .[6,7] },

{ none .[2,3,4] },

{ 4 == [+] .[1,3...11] },

{ one .[2,3] },

{ .[7] → all .[5,6] },

{ .[7] ? all .[5,6] },

{ 3 == [+] .[1..6] },

{ all .[11,12] },

Line 827:

Line 953:

Missed by one statement: 8, If statement 7 is true, then 5 and 6 are both true:

1:T, 2:T, 3:F, 4:T, 5:F, 6:F, 7:T, 8:T, 9:T, 10:F, 11:F, 12:F</pre>

=={{header|Java}}==

The following Java code uses brute force. It tries to translate the logical statements as naturally as possible. The run time is almost zero. --[[User:Mga010|Rene Grothmann]] 10:33, 28 October 2012 (UTC)

public class LogicPuzzle

{

boolean S[] = new boolean[13];

int Count = 0;

public boolean check2 ()

{

int count = 0;

for (int k = 7; k <= 12; k++)

if (S[k]) count++;

return S[2] == (count == 3);

}

public boolean check3 ()

{

int count = 0;

for (int k = 2; k <= 12; k += 2)

if (S[k]) count++;

return S[3] == (count == 2);

}

public boolean check4 ()

{

return S[4] == ( !S[5] || S[6] && S[7]);

}

public boolean check5 ()

{

return S[5] == ( !S[2] && !S[3] && !S[4]);

}

public boolean check6 ()

{

int count = 0;

for (int k = 1; k <= 11; k += 2)

if (S[k]) count++;

return S[6] == (count == 4);

}

public boolean check7 ()

{

return S[7] == ((S[2] || S[3]) && !(S[2] && S[3]));

}

public boolean check8 ()

{

return S[8] == ( !S[7] || S[5] && S[6]);

}

public boolean check9 ()

{

int count = 0;

for (int k = 1; k <= 6; k++)

if (S[k]) count++;

return S[9] == (count == 3);

}

public boolean check10 ()

{

return S[10] == (S[11] && S[12]);

}

public boolean check11 ()

{

int count = 0;

for (int k = 7; k <= 9; k++)

if (S[k]) count++;

return S[11] == (count == 1);

}

public boolean check12 ()

{

int count = 0;

for (int k = 1; k <= 11; k++)

if (S[k]) count++;

return S[12] == (count == 4);

}

public void check ()

{

if (check2() && check3() && check4() && check5() && check6()

&& check7() && check8() && check9() && check10() && check11()

&& check12())

{

for (int k = 1; k <= 12; k++)

if (S[k]) System.out.print(k + " ");

System.out.println();

Count++;

}

public void recurseAll (int k)

{

if (k == 13)

check();

else

{

S[k] = false;

recurseAll(k + 1);

S[k] = true;

recurseAll(k + 1);

}

public static void main (String args[])

{

LogicPuzzle P = new LogicPuzzle();

P.S[1] = true;

P.recurseAll(2);

System.out.println();

System.out.println(P.Count + " Solutions found.");

}

</lang>

<pre>

1 3 4 6 7 11

1 Solutions found.

</pre>

=={{header|REXX}}==

Line 989:

end /*pass*/

exit /*stick a fork in it, we're done.*/

/*----------------------------------YESES subroutine--------------------*/

/*──────────────────────────────────YESES subroutine────────────────────*/

yeses: parse arg L,H,B; #=0

do i=L to H by word(B 1,1); #=#+@.i; end /*i*/

Line 1,049:

do e=0 for 2**(q-1); n='1'right(x2b(d2x(e)), q-1, 0)

parse var n @1 2 @2 3 @3 4 @4 5 @5 6 @6 7 @7 8 @8 9 @9 10 @10 11 @11 12 @12

/*~~███~~ if @1 then if \ @1 then iterate ~~███~~*/

/*¦¦¦ if @1 then if \ @1 then iterate ¦¦¦*/

if @2 then if @7+@8+@9+@10+@11+@12 \==3 then iterate

if @3 then if @2+@4+@6+@8+@10+@12 \==2 then iterate

Line 1,152:

<pre>

exact match (S(1)⋀¬S(2)⋀S(3)⋀S(4)⋀¬S(5)⋀S(6)⋀S(7)⋀¬S(8)⋀¬S(9)⋀¬S(10)⋀S(11)⋀¬S(12))

exact match (S(1)?¬S(2)?S(3)?S(4)?¬S(5)?S(6)?S(7)?¬S(8)?¬S(9)?¬S(10)?S(11)?¬S(12))

almost found (¬S(1)⋀¬S(2)⋀¬S(3)⋀¬S(4)⋀S(5)⋀¬S(6)⋀¬S(7)⋀S(8)⋀¬S(9)⋀¬S(10)⋀S(11)⋀¬S(12)) ⇒ S(1)

almost found (¬S(1)?¬S(2)?¬S(3)?¬S(4)?S(5)?¬S(6)?¬S(7)?S(8)?¬S(9)?¬S(10)?S(11)?¬S(12)) ? S(1)

almost found (¬S(1)⋀¬S(2)⋀¬S(3)⋀¬S(4)⋀S(5)⋀¬S(6)⋀¬S(7)⋀S(8)⋀¬S(9)⋀S(10)⋀S(11)⋀S(12)) ⇒ S(1)

almost found (¬S(1)?¬S(2)?¬S(3)?¬S(4)?S(5)?¬S(6)?¬S(7)?S(8)?¬S(9)?S(10)?S(11)?S(12)) ? S(1)

almost found (¬S(1)⋀¬S(2)⋀¬S(3)⋀S(4)⋀¬S(5)⋀¬S(6)⋀¬S(7)⋀S(8)⋀¬S(9)⋀S(10)⋀S(11)⋀S(12)) ⇒ S(1)

almost found (¬S(1)?¬S(2)?¬S(3)?S(4)?¬S(5)?¬S(6)?¬S(7)?S(8)?¬S(9)?S(10)?S(11)?S(12)) ? S(1)

almost found (S(1)⋀¬S(2)⋀¬S(3)⋀¬S(4)⋀S(5)⋀¬S(6)⋀¬S(7)⋀¬S(8)⋀¬S(9)⋀¬S(10)⋀¬S(11)⋀¬S(12)) ⇒ S(8)

almost found (S(1)?¬S(2)?¬S(3)?¬S(4)?S(5)?¬S(6)?¬S(7)?¬S(8)?¬S(9)?¬S(10)?¬S(11)?¬S(12)) ? S(8)

almost found (S(1)⋀¬S(2)⋀¬S(3)⋀¬S(4)⋀S(5)⋀¬S(6)⋀¬S(7)⋀S(8)⋀¬S(9)⋀¬S(10)⋀¬S(11)⋀¬S(12)) ⇒ S(11)

almost found (S(1)?¬S(2)?¬S(3)?¬S(4)?S(5)?¬S(6)?¬S(7)?S(8)?¬S(9)?¬S(10)?¬S(11)?¬S(12)) ? S(11)

almost found (S(1)⋀¬S(2)⋀¬S(3)⋀¬S(4)⋀S(5)⋀¬S(6)⋀¬S(7)⋀S(8)⋀¬S(9)⋀¬S(10)⋀S(11)⋀¬S(12)) ⇒ S(12)

almost found (S(1)?¬S(2)?¬S(3)?¬S(4)?S(5)?¬S(6)?¬S(7)?S(8)?¬S(9)?¬S(10)?S(11)?¬S(12)) ? S(12)

almost found (S(1)⋀¬S(2)⋀¬S(3)⋀¬S(4)⋀S(5)⋀¬S(6)⋀¬S(7)⋀S(8)⋀¬S(9)⋀S(10)⋀S(11)⋀S(12)) ⇒ ¬S(12)

almost found (S(1)?¬S(2)?¬S(3)?¬S(4)?S(5)?¬S(6)?¬S(7)?S(8)?¬S(9)?S(10)?S(11)?S(12)) ? ¬S(12)

almost found (S(1)⋀¬S(2)⋀¬S(3)⋀¬S(4)⋀S(5)⋀S(6)⋀¬S(7)⋀¬S(8)⋀S(9)⋀¬S(10)⋀S(11)⋀¬S(12)) ⇒ S(8)

almost found (S(1)?¬S(2)?¬S(3)?¬S(4)?S(5)?S(6)?¬S(7)?¬S(8)?S(9)?¬S(10)?S(11)?¬S(12)) ? S(8)

almost found (S(1)⋀¬S(2)⋀¬S(3)⋀S(4)⋀¬S(5)⋀¬S(6)⋀¬S(7)⋀¬S(8)⋀¬S(9)⋀¬S(10)⋀¬S(11)⋀¬S(12)) ⇒ S(8)

almost found (S(1)?¬S(2)?¬S(3)?S(4)?¬S(5)?¬S(6)?¬S(7)?¬S(8)?¬S(9)?¬S(10)?¬S(11)?¬S(12)) ? S(8)

almost found (S(1)⋀¬S(2)⋀¬S(3)⋀S(4)⋀¬S(5)⋀¬S(6)⋀¬S(7)⋀S(8)⋀¬S(9)⋀S(10)⋀S(11)⋀S(12)) ⇒ ¬S(12)

almost found (S(1)?¬S(2)?¬S(3)?S(4)?¬S(5)?¬S(6)?¬S(7)?S(8)?¬S(9)?S(10)?S(11)?S(12)) ? ¬S(12)

almost found (S(1)⋀¬S(2)⋀¬S(3)⋀S(4)⋀¬S(5)⋀S(6)⋀¬S(7)⋀S(8)⋀S(9)⋀¬S(10)⋀¬S(11)⋀¬S(12)) ⇒ ¬S(6)

almost found (S(1)?¬S(2)?¬S(3)?S(4)?¬S(5)?S(6)?¬S(7)?S(8)?S(9)?¬S(10)?¬S(11)?¬S(12)) ? ¬S(6)

almost found (S(1)⋀¬S(2)⋀S(3)⋀S(4)⋀¬S(5)⋀¬S(6)⋀¬S(7)⋀S(8)⋀S(9)⋀¬S(10)⋀¬S(11)⋀¬S(12)) ⇒ S(7)

almost found (S(1)?¬S(2)?S(3)?S(4)?¬S(5)?¬S(6)?¬S(7)?S(8)?S(9)?¬S(10)?¬S(11)?¬S(12)) ? S(7)

almost found (S(1)⋀¬S(2)⋀S(3)⋀S(4)⋀¬S(5)⋀S(6)⋀S(7)⋀¬S(8)⋀S(9)⋀¬S(10)⋀¬S(11)⋀¬S(12)) ⇒ ¬S(9)

almost found (S(1)?¬S(2)?S(3)?S(4)?¬S(5)?S(6)?S(7)?¬S(8)?S(9)?¬S(10)?¬S(11)?¬S(12)) ? ¬S(9)

almost found (S(1)⋀S(2)⋀¬S(3)⋀S(4)⋀¬S(5)⋀¬S(6)⋀S(7)⋀¬S(8)⋀S(9)⋀¬S(10)⋀¬S(11)⋀S(12)) ⇒ ¬S(12)

almost found (S(1)?S(2)?¬S(3)?S(4)?¬S(5)?¬S(6)?S(7)?¬S(8)?S(9)?¬S(10)?¬S(11)?S(12)) ? ¬S(12)

almost found (S(1)⋀S(2)⋀¬S(3)⋀S(4)⋀¬S(5)⋀¬S(6)⋀S(7)⋀¬S(8)⋀S(9)⋀S(10)⋀¬S(11)⋀¬S(12)) ⇒ ¬S(10)

almost found (S(1)?S(2)?¬S(3)?S(4)?¬S(5)?¬S(6)?S(7)?¬S(8)?S(9)?S(10)?¬S(11)?¬S(12)) ? ¬S(10)

almost found (S(1)⋀S(2)⋀¬S(3)⋀S(4)⋀¬S(5)⋀¬S(6)⋀S(7)⋀S(8)⋀S(9)⋀¬S(10)⋀¬S(11)⋀¬S(12)) ⇒ ¬S(8)

almost found (S(1)?S(2)?¬S(3)?S(4)?¬S(5)?¬S(6)?S(7)?S(8)?S(9)?¬S(10)?¬S(11)?¬S(12)) ? ¬S(8)

</pre>