Twelve statements: Difference between revisions
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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}}== |
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<lang haskell>tf [x] = [[True], [False]] |
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tf (x:xs) = map (True:) s ++ map (False:) s where s = tf xs |
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sumbool = sum . map fromEnum |
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wrongness b = sumbool . zipWith (/=) b . map (\f -> f b) |
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statements = [ (==12) . length, |
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sumto 3 [len - 6..], |
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sumto 2 [1,3..], |
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\b -> not (b!!4) || all (b!!) [5,6], |
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\b -> not $ any (b!!) [2..4], |
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sumto 4 [0,2..], |
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sumto 1 [1,2], |
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\b -> not (b!!6) || all (b!!) [4,5], |
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sumto 3 [0..5], |
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sumto 2 [10,11], |
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sumto 1 [6,7,8], |
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sumto 4 [0..10] |
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] where |
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len = length statements |
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sumto s x b = s == (sumbool . map (b!!) . takeWhile (< length b)) x |
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main = let t n s = filter ((==n).fst) [(wrongness b s, b) | b <- tf s] in do |
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putStrLn "Answer" |
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mapM_ print $ t 0 statements |
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putStrLn "Near misses" |
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mapM_ print $ t 1 statements</lang> |
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{{out}} |
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<pre> |
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Answer |
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(0,[True,False,True,True,False,True,True,False,False,False,True,False]) |
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Near misses |
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(1,[True,True,False,True,False,False,True,True,True,False,False,False]) |
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(1,[True,True,False,True,False,False,True,False,True,True,False,False]) |
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(1,[True,True,False,True,False,False,True,False,True,False,False,True]) |
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(1,[True,False,True,True,False,True,True,False,True,False,False,False]) |
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(1,[True,False,True,True,False,False,False,True,True,False,False,False]) |
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(1,[True,False,False,True,False,True,False,True,True,False,False,False]) |
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(1,[True,False,False,True,False,False,False,True,False,True,True,True]) |
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(1,[True,False,False,True,False,False,False,False,False,False,False,False]) |
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(1,[False,False,False,True,False,False,False,True,False,True,True,True]) |
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</pre> |
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=={{header|Perl 6}}== |
=={{header|Perl 6}}== |
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<lang perl6>sub infix:<→> ($protasis,$apodosis) { !$protasis or $apodosis } |
<lang perl6>sub infix:<→> ($protasis,$apodosis) { !$protasis or $apodosis } |
Revision as of 02:57, 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 [x] = [[True], [False]] tf (x:xs) = map (True:) s ++ map (False:) s where s = tf xs
sumbool = sum . map fromEnum wrongness b = sumbool . zipWith (/=) b . map (\f -> f b)
statements = [ (==12) . length, sumto 3 [len - 6..], sumto 2 [1,3..], \b -> not (b!!4) || all (b!!) [5,6], \b -> not $ any (b!!) [2..4], sumto 4 [0,2..], sumto 1 [1,2], \b -> not (b!!6) || all (b!!) [4,5], sumto 3 [0..5], sumto 2 [10,11], sumto 1 [6,7,8], sumto 4 [0..10] ] where len = length statements sumto s x b = s == (sumbool . map (b!!) . takeWhile (< length 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.