This puzzle is borrowed from   math-frolic.blogspot.



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.



Task

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

Print out a table of near misses, that is, solutions that are contradicted by only a single statement.




 
from itertools import product
#from pprint import pprint as pp
 
constraintinfo = (  
  (lambda st: len(st) == 12                 ,(1, 'This is a numbered list of twelve statements')),
  (lambda st: sum(st[-6:]) == 3             ,(2, 'Exactly 3 of the last 6 statements are true')),
  (lambda st: sum(st[1::2]) == 2            ,(3, 'Exactly 2 of the even-numbered statements are true')),
  (lambda st: (st[5]&st[6]) if st[4] else 1 ,(4, 'If statement 5 is true, then statements 6 and 7 are both true')),
  (lambda st: sum(st[1:4]) == 0             ,(5, 'The 3 preceding statements are all false')),
  (lambda st: sum(st[0::2]) == 4            ,(6, 'Exactly 4 of the odd-numbered statements are true')),
  (lambda st: sum(st[1:3]) == 1             ,(7, 'Either statement 2 or 3 is true, but not both')),
  (lambda st: (st[4]&st[5]) if st[6] else 1 ,(8, 'If statement 7 is true, then 5 and 6 are both true')),
  (lambda st: sum(st[:6]) == 3              ,(9, 'Exactly 3 of the first 6 statements are true')),
  (lambda st: (st[10]&st[11])               ,(10, 'The next two statements are both true')),
  (lambda st: sum(st[6:9]) == 1             ,(11, 'Exactly 1 of statements 7, 8 and 9 are true')),
  (lambda st: sum(st[0:11]) == 4            ,(12, 'Exactly 4 of the preceding statements are true')),
)  
 
def printer(st, matches):
    if False in matches:
        print('Missed by one statement: %i, %s' % docs[matches.index(False)])
    else:
        print('Full match:')
    print('  ' + ', '.join('%i:%s' % (i, 'T' if t else 'F') for i, t in enumerate(st, 1)))
 
funcs, docs = zip(*constraintinfo)
 
full, partial = [], []
 
for st in product( *([(False, True)] * 12) ):
    truths = [bool(func(st)) for func in funcs]
    matches = [s == t for s,t in zip(st, truths)]
    mcount = sum(matches)
    if mcount == 12:
        full.append((st, matches))
    elif mcount == 11:
        partial.append((st, matches))
 
for stm in full + partial:
    printer(*stm)