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The omitted age (Posted on 2005-10-20) Difficulty: 2 of 5
When completed, the cross-number below will have one digit (from 0-9) in each cell, and no zeros in row (a) and in column (a).
         (a) (b) (c) 
            +---+---+
    (a)     |   |   |
        +---+---+---+
    (b) |   |   |   |
        +---+---+---+
    (c) |   |   |    
        +---+---+

ACROSS : (a) Abigail´s age.
         (b) Sum of Abigail´s age,
                    Blanche´s age,
                    Cynthia´s age, and
                    Darlene´s age.
         (c) Blanche´s age.

DOWN   : (a) Darlene´s age
         (b) Sum of three of the ages in (b) across.
         (c) Cynthia´s age.
Whose age was omitted from (b) down, and what are the ages of the 4 women ?

Note: this can be solved by hand. Those who will use the computer, give the others some time before posting the solution obtained this way. Tk you.

  Submitted by pcbouhid    
Rating: 3.0000 (3 votes)
Solution: (Hide)
Let´s identify the cells:
         (a) (b) (c) 
            +---+---+
    (a)     | A | B |
        +---+---+---+
    (b) | C | D | E |
        +---+---+---+
    (c) | F | G |    
        +---+---+
There are 4 possible cases (the name between parentheses is the name of the woman whose age was omitted):
       CASE I     CASE II     CASE III     CASE IV
     (Abigail)   (Cynthia)   (Darlene)    (Blanche) 

        ADG         ADG         ADG          ADG
       + AB        + BE        + CF         + FG
       ----         ---         ---          ---
        CDE         CDE         CDE          CDE
CASE I: In the middle column, A is 9 or 0, and since A is in row (a) where there is no zero, A = 9. Then C is more than 9 in the sum. So this case is impossible.

CASE II: B is 9 or 0, so B = 9 (B is in row (a)). Then 1 was carried from the right column. But G must be 0, so 1 could not be carried from the right column. This situation is impossible. So Case II is not a correct case.

CASE III: In the middle column, C is 9 or 0. Then, C = 9. But AB + BE + CF + FG = CDE. So C in CDE could not be greater than 3. This situation is impossible. So Case III is not a correct case, too.

CASE IV: This must be the correct case, and Blanche´age was omitted from (b) down.

F is 0 or 9, so F = 9. Then 1 was carried from the right column and 1 was carried from the middle column. Because 1 was carried from the right column, G is greater than 4. Because 1 was carried from the middle column, C is 1 more than A.

Because this is the correct case and once AB + BE + CF = ADG, then A = 1 and C = 2, or A = 2 and C = 3.

But, if A = 2 and C = 3 in the middle column, then A cannot be 2 in ADG. So A = 1 and C = 2.

Because F = 9 and G is greater than 4, (B + F + G) in the right column of AB + BE + CF + FG must be 20 (B + F + G must end in 0).

Then, because F = 9, (B + G) = 11. Because (B + G) = 11 and G is greater than 4, B is 6 or less.

Because A = 1 and C = 2 and F = 9, (A + B + C + F) is at least 18; so B is 6 or more. Thus B = 6. So G = 5.

D = 0 in AB + BE + CF + FG = CDE, and E = 0 in ADG + FG = CDE.

The complete grid is:
         (a) (b) (c) 
            +---+---+
    (a)     | 1 | 6 |
        +---+---+---+
    (b) | 2 | 0 | 0 |
        +---+---+---+
    (c) | 9 | 5 |    
        +---+---+
The ages: Abigail - 16, Blanche - 95, Cynthia - 60, and Darlene - 29.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
AnswerK Sengupta2009-03-06 03:19:33
re: my solutionpcbouhid2005-10-30 06:24:08
Solutionmy solutionMindy Rodriguez2005-10-30 01:28:55
re: The Solutionpcbouhid2005-10-27 14:02:12
re(2): Solutionpcbouhid2005-10-27 13:57:32
SolutionThe Solutiondopey9152005-10-27 13:56:29
re(2): Solutionpcbouhid2005-10-23 19:54:56
re: SolutionBRIAN2005-10-23 19:17:05
SolutionSolutionBRIAN2005-10-23 18:48:34
re(9): Re: Solution by hand*****remark - I forgotpcbouhid2005-10-22 07:25:25
re(8): Re: Solution by hand*****remarkAdy TZIDON2005-10-22 04:00:18
re(7): Re: Solution by handpcbouhid2005-10-21 15:59:12
re(6): Re: Solution by handMike2005-10-21 15:35:41
re(5): Re: Solution by handpcbouhid2005-10-21 15:12:12
re(4): Re: Solution by handMike2005-10-21 14:53:09
re(3): Re: Solution by handpcbouhid2005-10-21 09:47:03
re(2): Re: Solution by handMike2005-10-21 09:38:19
Solutiona program which gives the result is (soln repeated)Charlie2005-10-20 22:54:40
re: Re: Solution by handpcbouhid2005-10-20 19:21:13
Re: Solution by handMike2005-10-20 17:18:23
Solution by handMike2005-10-20 17:04:59
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