Time for an 2014 update…
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265
Task/Twelve-statements/Bracmat/twelve-statements.bracmat
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265
Task/Twelve-statements/Bracmat/twelve-statements.bracmat
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@ -0,0 +1,265 @@
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(
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( number
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= n done ntest oldFT
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. !arg:(?done.(=?ntest).?oldFT)
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& 0:?n
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& ( !done
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: ?
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( !ntest
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. !oldFT&1+!n:?n&~
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)
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?
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| !n
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)
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)
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& ( STATEMENTS
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= ( (1."This is a numbered list of twelve statements.")
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. 1
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. (
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= n nr done toDo
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. !arg:(?done.?toDo)
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& 0:?n
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& whl
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' ( !done:(?nr.?) ?done
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& 1+!n:!nr:?n
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)
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& whl
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' ( !toDo:((?nr.?).?) ?toDo
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& 1+!n:!nr:?n
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)
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& (!n:12&true|false)
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)
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)
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( (2."Exactly 3 of the last 6 statements are true.")
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. end
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. (
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= done toDo lastSix
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. !arg:(?done.?toDo)
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& !done:? [-7 ?lastSix
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& ( number$(!lastSix.(=?).true):3
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& true
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| false
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)
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)
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)
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( (3."Exactly 2 of the even-numbered statements are true.")
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. end
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. (
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= done toDo ii
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. !arg:(?done.?toDo)
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& ( number
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$ ( !done
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. (=?ii&!ii*1/2:~/)
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. true
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)
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: 2
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& true
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| false
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)
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)
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)
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( (4."If statement 5 is true, then statements 6 and 7 are both true.")
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. 7
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. (
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= done toDo
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. !arg:(?done.?toDo)
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& ( !done
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: ( ? (5.false) ?
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| ? (6.true) ?
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: ? (7.true) ?
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)
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& true
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| false
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)
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)
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)
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( (5."The 3 preceding statements are all false.")
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. 5
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. (
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= done toDo
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. !arg:(?done.?toDo)
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& ( !done
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: ?
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(?.false)
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(?.false)
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(?.false)
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(?.?)
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& true
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| false
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)
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)
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)
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( (6."Exactly 4 of the odd-numbered statements are true.")
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. end
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. (
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= done toDo i
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. !arg:(?done.?toDo)
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& ( number
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$ ( !done
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. (=?i&!i*1/2:/)
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. true
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)
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: 4
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& true
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| false
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)
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)
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)
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( (7."Either statement 2 or 3 is true, but not both.")
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. 7
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. (
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= done toDo
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. !arg:(?done.?toDo)
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& ( number
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$ (!done.(=2|3).true)
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: 1
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& true
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| false
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)
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)
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)
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( (8."If statement 7 is true, then 5 and 6 are both true.")
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. 8
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. (
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= done toDo
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. !arg:(?done.?toDo)
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& ( !done
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: ( ? (7.false) ?
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| ? (5.true) ?
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: ? (6.true) ?
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)
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& true
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| false
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)
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)
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)
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( (9."Exactly 3 of the first 6 statements are true.")
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. 9
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. (
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= done toDo firstSix
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. !arg:(?done.?toDo)
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& !done:?firstSix [6 ?
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& ( number$(!firstSix.(=?).true):3
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& true
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| false
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)
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)
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)
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( (10."The next two statements are both true.")
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. 12
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. (
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= done toDo
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. !arg:(?done.?toDo)
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& ( !done:? (?.true) (?.true)
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& true
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| false
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)
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)
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)
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( (11."Exactly 1 of statements 7, 8 and 9 are true.")
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. 11
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. (
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= done toDo
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. !arg:(?done.?toDo)
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& ( number
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$ ( !done
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. (=7|8|9)
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. true
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)
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: 1
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& true
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| false
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)
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)
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)
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( (12."Exactly 4 of the preceding statements are true.")
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. 12
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. (
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= done toDo preceding
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. !arg:(?done.?toDo)
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& !done:?preceding (?.?)
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& ( number$(!preceding.(=?).true):4
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& true
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| false
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)
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)
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)
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)
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& ( TestTruth
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= done toDo postponedTests testToBePostponed
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, n when test FT oldFT A Z text
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, postponedTest testNow
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. !arg:(?done.?toDo.?postponedTests)
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& ( !toDo:
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& "We have come to the end of the list of tests.
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Perform any tests that had to be postponed until now."
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& whl
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' ( !postponedTests
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: (?.?oldFT.(=?postponedTest)) ?A
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& postponedTest$(!done.):!oldFT
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& !A:?postponedTests
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)
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& !postponedTests:
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& out$("Solution:" !done)
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& ~
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| !toDo
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: ((?n.?text).?when.(=?test)) ?toDo
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& "'false' and 'true' are just two symbols, not 'boolean values'.
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You can choose other symbols if you like.
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The program first guesses the first symbol and assigns it to the variable FT.
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After backtracking, the second symbol is guessed and assigned to FT.
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This is done for each statement."
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& false true
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: ?
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%@?FT
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( ?
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& 1+!guesses:?guesses
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& (!n.!FT):?testNow
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& "Do all tests that had to be postponed until now, unless one of those tests
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fails. Remove the successful tests from the list of postponed tests."
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& whl
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' ( !postponedTests
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: ?A
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(!n.?oldFT.(=?postponedTest))
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?Z
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& postponedTest$(!done !testNow.!toDo)
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: !oldFT
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& !A !Z:?postponedTests
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)
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& "Check that all tests that had to be postponed until now are removed from
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the list of postponed tests. Only then go on with looking at testing
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the current statement. Backtrack if a test failed."
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& !postponedTests:~(? (!n.?) ?)
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& ( !when:>!n
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& "The current statement cannot be tested right now. Postpone it to
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the earliest coming statement where the current statement can be
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tested.
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(The earliest statement, denoted by 'when', is computed manually.)"
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& (!when.!FT.'$test):?testToBePostponed
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| "No need to postpone. Test the current statement now."
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& :?testToBePostponed
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& "If the test fails, backtrack. If it succeeds, go on to the next
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statement."
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& test$(!done !testNow.!toDo):!FT
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)
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& "So far so good. Test the next statements. (recursively)"
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& TestTruth
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$ ( !done !testNow
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. !toDo
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. !testToBePostponed !postponedTests
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)
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)
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)
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)
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& 0:?guesses
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& TestTruth$(.!STATEMENTS.)
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| out
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$ ( str
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$ ( "That's it. I made "
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!guesses
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" true/false guesses in all. (A brute force method needs 2^12="
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2^12
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" guesses."
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)
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)
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);
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43
Task/Twelve-statements/Forth/twelve-statements.fth
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43
Task/Twelve-statements/Forth/twelve-statements.fth
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: lastbit ( n1 -- n2)
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dup if 1 swap begin dup 1 <> while swap 1+ swap 1 rshift repeat drop then
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;
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: bit 1 swap lshift and 0<> ; ( n1 n2 -- f)
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: bitcount 0 swap begin dup while dup 1- and swap 1+ swap repeat drop ;
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12 constant #stat \ number of statements
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\ encoding of the statements
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: s1 >r #stat 12 = r> 0 bit = ; \ heavy use of binary
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: s2 >r r@ 4032 and bitcount 3 = r> 1 bit = ;
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: s3 >r r@ 2730 and bitcount 2 = r> 2 bit = ;
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: s4 >r r@ 4 bit 0= 96 r@ over and = or r> 3 bit = ;
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: s5 >r r@ 14 and 0= r> 4 bit = ;
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: s6 >r r@ 1365 and bitcount 4 = r> 5 bit = ;
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: s7 >r r@ 1 bit r@ 2 bit xor r> 6 bit = ;
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: s8 >r r@ 6 bit 0= 48 r@ over and = or r> 7 bit = ;
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: s9 >r r@ 63 and bitcount 3 = r> 8 bit = ;
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: s10 >r 3072 r@ over and = r> 9 bit = ;
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: s11 >r r@ 448 and bitcount 1 = r> 10 bit = ;
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: s12 >r r@ 2047 and bitcount 4 = r> 11 bit = ;
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: list #stat 0 do dup i bit if i 1+ . then loop drop ;
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: nearmiss? \ do we have a near miss?
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over #stat 1- = if ( true-pattern #true stat-pattern)
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." Near miss with statements " dup list ." true (failed "
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>r over invert 1 #stat lshift 1- and lastbit 0 .r ." )" cr r>
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then \ extract the failed statement
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;
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\ have we found a solution?
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: solution? ( true-pattern #true stat-pattern)
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over #stat = if ." Solution! with statements " dup list ." true." cr then
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;
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: 12statements \ test the twelve patterns
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1 #stat lshift 0 do \ create another bit pattern
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i s12 2* i s11 + 2* i s10 + 2* i s9 + 2* i s8 + 2* i s7 + 2*
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i s6 + 2* i s5 + 2* i s4 + 2* i s3 + 2* i s2 + 2* i s1 +
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abs dup bitcount i solution? nearmiss? drop drop drop
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loop \ count number of bytes and evaluate
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;
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12statements
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@ -5,20 +5,20 @@ tf = mapM (\_ -> [1,0])
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wrongness b = findIndices id . zipWith (/=) b . map (fromEnum . ($ b))
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statements = [ (==12) . length,
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3 ? [length statements-6..],
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2 ? [1,3..],
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4 ? [4..6],
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0 ? [1..3],
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4 ? [0,2..],
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1 ? [1,2],
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6 ? [4..6],
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3 ? [0..5],
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2 ? [10,11],
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1 ? [6,7,8],
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4 ? [0..10]
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3 ⊂ [length statements-6..],
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2 ⊂ [1,3..],
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4 → [4..6],
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0 ⊂ [1..3],
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4 ⊂ [0,2..],
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1 ⊂ [1,2],
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6 → [4..6],
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3 ⊂ [0..5],
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2 ⊂ [10,11],
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1 ⊂ [6,7,8],
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4 ⊂ [0..10]
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] where
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(s ? x) b = s == (sum . map (b!!) . takeWhile (< length b)) x
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(a ? x) b = (b!!a == 0) || all ((==1).(b!!)) x
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(s ⊂ x) b = s == (sum . map (b!!) . takeWhile (< length b)) x
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(a → x) b = (b!!a == 0) || all ((==1).(b!!)) x
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testall s n = [(b, w) | b <- tf s, w <- [wrongness b s], length w == n]
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@ -1,4 +1,4 @@
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(#~0=#@{::~&_1"1) testall S
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+------------------------+
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¦1 0 1 1 0 1 1 0 0 0 1 0¦¦
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+------------------------+
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┌───────────────────────┬┐
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│1 0 1 1 0 1 1 0 0 0 1 0││
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└───────────────────────┴┘
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@ -1,34 +1,34 @@
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(#~1=#@{::~&_1"1) testall S
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+--------------------------+
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¦0 0 0 0 1 0 0 1 0 0 1 0¦0 ¦
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+-----------------------+--¦
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¦0 0 0 0 1 0 0 1 0 1 1 1¦0 ¦
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+-----------------------+--¦
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¦0 0 0 1 0 0 0 1 0 1 1 1¦0 ¦
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+-----------------------+--¦
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¦1 0 0 0 1 0 0 0 0 0 0 0¦7 ¦
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+-----------------------+--¦
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¦1 0 0 0 1 0 0 1 0 0 0 0¦10¦
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+-----------------------+--¦
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¦1 0 0 0 1 0 0 1 0 0 1 0¦11¦
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+-----------------------+--¦
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¦1 0 0 0 1 0 0 1 0 1 1 1¦11¦
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+-----------------------+--¦
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¦1 0 0 0 1 1 0 0 1 0 1 0¦7 ¦
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+-----------------------+--¦
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¦1 0 0 1 0 0 0 0 0 0 0 0¦7 ¦
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+-----------------------+--¦
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¦1 0 0 1 0 0 0 1 0 1 1 1¦11¦
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+-----------------------+--¦
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¦1 0 0 1 0 1 0 1 1 0 0 0¦5 ¦
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+-----------------------+--¦
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¦1 0 1 1 0 0 0 1 1 0 0 0¦6 ¦
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+-----------------------+--¦
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¦1 0 1 1 0 1 1 0 1 0 0 0¦8 ¦
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+-----------------------+--¦
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¦1 1 0 1 0 0 1 0 1 0 0 1¦11¦
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+-----------------------+--¦
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¦1 1 0 1 0 0 1 0 1 1 0 0¦9 ¦
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+-----------------------+--¦
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¦1 1 0 1 0 0 1 1 1 0 0 0¦7 ¦
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+--------------------------+
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┌───────────────────────┬──┐
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│0 0 0 0 1 0 0 1 0 0 1 0│0 │
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├───────────────────────┼──┤
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│0 0 0 0 1 0 0 1 0 1 1 1│0 │
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├───────────────────────┼──┤
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│0 0 0 1 0 0 0 1 0 1 1 1│0 │
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├───────────────────────┼──┤
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│1 0 0 0 1 0 0 0 0 0 0 0│7 │
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├───────────────────────┼──┤
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│1 0 0 0 1 0 0 1 0 0 0 0│10│
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├───────────────────────┼──┤
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│1 0 0 0 1 0 0 1 0 0 1 0│11│
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├───────────────────────┼──┤
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│1 0 0 0 1 0 0 1 0 1 1 1│11│
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├───────────────────────┼──┤
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│1 0 0 0 1 1 0 0 1 0 1 0│7 │
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├───────────────────────┼──┤
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│1 0 0 1 0 0 0 0 0 0 0 0│7 │
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├───────────────────────┼──┤
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│1 0 0 1 0 0 0 1 0 1 1 1│11│
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├───────────────────────┼──┤
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│1 0 0 1 0 1 0 1 1 0 0 0│5 │
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├───────────────────────┼──┤
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│1 0 1 1 0 0 0 1 1 0 0 0│6 │
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├───────────────────────┼──┤
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│1 0 1 1 0 1 1 0 1 0 0 0│8 │
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├───────────────────────┼──┤
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│1 1 0 1 0 0 1 0 1 0 0 1│11│
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├───────────────────────┼──┤
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│1 1 0 1 0 0 1 0 1 1 0 0│9 │
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├───────────────────────┼──┤
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│1 1 0 1 0 0 1 1 1 0 0 0│7 │
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└───────────────────────┴──┘
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|
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28
Task/Twelve-statements/Perl/twelve-statements.pl
Normal file
28
Task/Twelve-statements/Perl/twelve-statements.pl
Normal file
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@ -0,0 +1,28 @@
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use List::Util 'sum';
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my @condition = (
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sub { 0 }, # dummy sub for index 0
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sub { 13==@_ },
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sub { 3==sum @_[7..12] },
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sub { 2==sum @_[2,4,6,8,10,12] },
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sub { $_[5] ? ($_[6] and $_[7]) : 1 },
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sub { !$_[2] and !$_[3] and !$_[4] },
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sub { 4==sum @_[1,3,5,7,9,11] },
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sub { $_[2]==1-$_[3] },
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sub { $_[7] ? ($_[5] and $_[6]) : 1 },
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sub { 3==sum @_[1..6] },
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sub { 2==sum @_[11..12] },
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sub { 1==sum @_[7,8,9] },
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sub { 4==sum @_[1..11] },
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);
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sub miss {
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return grep { $condition[$_]->(@_) != $_[$_] } 1..12;
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}
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for (0..2**12-1) {
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my @truth = split //, sprintf "0%012b", $_;
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my @no = miss @truth;
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print "Solution: true statements are ", join( " ", grep { $truth[$_] } 1..12), "\n" if 0 == @no;
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print "1 miss (",$no[0],"): true statements are ", join( " ", grep { $truth[$_] } 1..12), "\n" if 1 == @no;
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}
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