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 The omitted age (Posted on 2005-10-20)
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.

 Subject Author Date Answer K Sengupta 2009-03-06 03:19:33 re: my solution pcbouhid 2005-10-30 06:24:08 my solution Mindy Rodriguez 2005-10-30 01:28:55 re: The Solution pcbouhid 2005-10-27 14:02:12 re(2): Solution pcbouhid 2005-10-27 13:57:32 The Solution dopey915 2005-10-27 13:56:29 re(2): Solution pcbouhid 2005-10-23 19:54:56 re: Solution BRIAN 2005-10-23 19:17:05 Solution BRIAN 2005-10-23 18:48:34 re(9): Re: Solution by hand*****remark - I forgot pcbouhid 2005-10-22 07:25:25 re(8): Re: Solution by hand*****remark Ady TZIDON 2005-10-22 04:00:18 re(7): Re: Solution by hand pcbouhid 2005-10-21 15:59:12 re(6): Re: Solution by hand Mike 2005-10-21 15:35:41 re(5): Re: Solution by hand pcbouhid 2005-10-21 15:12:12 re(4): Re: Solution by hand Mike 2005-10-21 14:53:09 re(3): Re: Solution by hand pcbouhid 2005-10-21 09:47:03 re(2): Re: Solution by hand Mike 2005-10-21 09:38:19 a program which gives the result is (soln repeated) Charlie 2005-10-20 22:54:40 re: Re: Solution by hand pcbouhid 2005-10-20 19:21:13 Re: Solution by hand Mike 2005-10-20 17:18:23 Solution by hand Mike 2005-10-20 17:04:59

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