Twelve statements: Difference between revisions
(→{{header|Haskell}}: using unicode operators. Might not be a terribly smart thing to do, those who know haskell, feel free to change it) |
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Extra credit: also print out a table of near misses, that is, solutions that are contradicted by only a single statement. |
Extra credit: also print out a table of near misses, that is, solutions that are contradicted by only a single statement. |
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=={{header|Haskell}}== |
=={{header|Haskell}}== |
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<lang haskell>tf |
<lang haskell>tf = mapM (\_ -> [True, False]) |
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tf (x:xs) = map (True:) s ++ map (False:) s where s = tf xs |
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sumbool = length . filter id |
sumbool = length . filter id |
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wrongness b = sumbool . zipWith (/=) b . map ( |
wrongness b = sumbool . zipWith (/=) b . map ($ b) |
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statements = [ (==12) . length, |
statements = [ (==12) . length, |
Revision as of 06:44, 20 September 2012
This puzzle is borrowed from here.
Given the following twelve statements, which of them are true?
1. This is a numbered list of twelve statements. 2. Exactly 3 of the last 6 statements are true. 3. Exactly 2 of the even-numbered statements are true. 4. If statement 5 is true, then statements 6 and 7 are both true. 5. The 3 preceding statements are all false. 6. Exactly 4 of the odd-numbered statements are true. 7. Either statement 2 or 3 is true, but not both. 8. If statement 7 is true, then 5 and 6 are both true. 9. Exactly 3 of the first 6 statements are true. 10. The next two statements are both true. 11. Exactly 1 of statements 7, 8 and 9 are true. 12. Exactly 4 of the preceding statements are true.
When you get tired of trying to figure it out in your head, write a program to solve it, and print the correct answer or answers.
Extra credit: also print out a table of near misses, that is, solutions that are contradicted by only a single statement.
Haskell
<lang haskell>tf = mapM (\_ -> [True, False])
sumbool = length . filter id wrongness b = sumbool . zipWith (/=) b . map ($ b)
statements = [ (==12) . length, 3 ⊂ [length statements-6..], 2 ⊂ [1,3..], 4 → [4..6], 0 ⊂ [2..4], 4 ⊂ [0,2..], 1 ⊂ [1,2], 6 → [4..6], 3 ⊂ [0..5], 2 ⊂ [10,11], 1 ⊂ [6,7,8], 4 ⊂ [0..10] ] where (⊂) s x = \b -> s == (sumbool . map (b!!) . takeWhile (< length b)) x (→) a x = \b -> not (b!!a) || all (b!!) x
main = let t n s = filter ((==n).fst) [(wrongness b s, b) | b <- tf s] in do putStrLn "Answer" mapM_ print $ t 0 statements putStrLn "Near misses" mapM_ print $ t 1 statements</lang>
- Output:
Answer (0,[True,False,True,True,False,True,True,False,False,False,True,False]) Near misses (1,[True,True,False,True,False,False,True,True,True,False,False,False]) (1,[True,True,False,True,False,False,True,False,True,True,False,False]) (1,[True,True,False,True,False,False,True,False,True,False,False,True]) (1,[True,False,True,True,False,True,True,False,True,False,False,False]) (1,[True,False,True,True,False,False,False,True,True,False,False,False]) (1,[True,False,False,True,False,True,False,True,True,False,False,False]) (1,[True,False,False,True,False,False,False,True,False,True,True,True]) (1,[True,False,False,True,False,False,False,False,False,False,False,False]) (1,[False,False,False,True,False,False,False,True,False,True,True,True])
Perl 6
<lang perl6>sub infix:<→> ($protasis,$apodosis) { !$protasis or $apodosis }
my @tests = { True }, # (there's no 0th statement)
{ all(.[1..12]) === any(True, False) }, { 3 == [+] .[7..12] }, { 2 == [+] .[2,4...12] }, { .[5] → all .[6,7] }, { none .[2,3,4] }, { 4 == [+] .[1,3...11] }, { one .[2,3] }, { .[7] → all .[5,6] }, { 3 == [+] .[1..6] }, { all .[11,12] }, { one .[7,8,9] }, { 4 == [+] .[1..11] };
my @good; my @bad; my @ugly;
for reverse 0 ..^ 2**12 -> $i {
my @b = $i.fmt("%012b").comb; my @assert = True, @b.map: { .so } my @result = @tests.map: { .(@assert).so } my @s = ( $_ if $_ and @assert[$_] for 1..12 ); if @result eqv @assert {
push @good, "<{@s}> is consistent.";
} else {
my @cons = gather for 1..12 { if @assert[$_] !eqv @result[$_] { take @result[$_] ?? $_ !! "¬$_"; } } my $mess = "<{@s}> implies {@cons}."; if @cons == 1 { push @bad, $mess } else { push @ugly, $mess }
}
}
.say for @good; say "\nNear misses:"; .say for @bad;</lang>
- Output:
<1 3 4 6 7 11> is consistent. Near misses: <1 2 4 7 8 9> implies ¬8. <1 2 4 7 9 10> implies ¬10. <1 2 4 7 9 12> implies ¬12. <1 3 4 6 7 9> implies ¬9. <1 3 4 8 9> implies 7. <1 4 6 8 9> implies ¬6. <1 4 8 10 11 12> implies ¬12. <1 4> implies 8. <1 5 6 9 11> implies 8. <1 5 8 10 11 12> implies ¬12. <1 5 8 11> implies 12. <1 5 8> implies 11. <1 5> implies 8. <4 8 10 11 12> implies 1. <5 8 10 11 12> implies 1. <5 8 11> implies 1.