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Age Ascertainment III (Posted on 2013-03-19) Difficulty: 3 of 5
  1. When completed, this crossnumber puzzle has exactly one digit in each box.
  2. None of the a,b,c or d boxes (whether down or across) can contain any leading zero.
  3. Both concatenations ab and cd consist of nonzero digits.
       +-----+-----+
       |  a  |  b  |
 +-----+-----+-----+
 |  c  |     |     |
 +-----+-----+-----+
 |  d  |     |      
 +-----+-----+


    ACROSS                                         DOWN                

a. Abigail's age                           a. Sum of three of the ages
                                             in c "across".
c. Sum of Abigail's age, 
Blanche's age, Cynthia's                   b. Cynthia's age.
age, and Darlene's age.                    
                                           c. Darlene's age.
d. Blanche's age                            
Whose age was omitted in a "down" category?

No Solution Yet Submitted by K Sengupta    
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Solution Better late than never Comment 2 of 2 |
Blanche's age was omitted from a 'down'.

Computer solution (Python) found a unique solution:
count=0
missingAge = ''
for A in range(1,3):
    for B in range(1,10):
        for C in range(1,4):
            for D in range(1,10):
                for E in range(0,10):
                    for F in range(0,10):
                        for G in range(0,10):
                            Abigail = 10*A+B
                            Blanche = 10*D+G
                            Cynthia = 10*B+F
                            Darlene = 10*C+D
                            cAcross = Abigail+Blanche+Cynthia+Darlene
                            if cAcross == 100*C+10*E+F:
                                if 100*A+10*E+G == Abigail+Blanche+Cynthia or \
                                100*A+10*E+G == Abigail+Blanche+Darlene or \
                                100*A+10*E+G == Abigail+Cynthia+Darlene or \
                                100*A+10*E+G == Blanche+Cynthia+Darlene:
                                    print(A,B,C,D,E,F,G)
                                    print('Abigail: ', Abigail)
                                    print('Blanche: ', Blanche)
                                    print('Cynthia: ', Cynthia)
                                    print('Darlene: ', Darlene)
                                    print('The age not included in A Down is ', cAcross - (100*A+10*E+G) )
                                   
                                    if cAcross - (100*A+10*E+G) == Abigail:
                                        missingAge='Abigail'
                                    elif cAcross - (100*A+10*E+G) == Blanche:
                                        missingAge='Blanche'
                                    elif cAcross - (100*A+10*E+G) == Cynthia:
                                        missingAge='Cynthia'
                                    elif cAcross - (100*A+10*E+G) == Darlene:
                                        missingAge='Darlene'
                                    else:
                                        print('error')
                                    print('The person whose age is not included in A Down is', missingAge)
                                    count += 1
                           
print('The program found',count, 'solution.')

----------
Results:
1 6 2 9 0 0 5
Abigail:  16
Blanche:  95
Cynthia:  60
Darlene:  29
The age not included in A Down is  95
The person whose age is not included in A Down is Blanche
The program found 1 solution.

  Posted by Larry on 2019-11-17 11:26:02
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