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No. 2


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#1 rookie1ja

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Posted 31 March 2007 - 05:49 PM

No. 2 - Back to the Cryptograms and Algebra Puzzles
Replace the same characters by the same numerals so that the mathematical operations are correct.
IFIB - EBG = CEH
   -	 -	 +
CCE  /  GD =  FE
------------------------
EFF  + EED = CBA

This old topic is locked since solution is already provided in the Spoiler below.
Pls visit New Puzzles section to see always fresh brain teasers.


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#2 BoilingOil

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Posted 26 September 2007 - 09:49 PM

No. 2 - Back to the Cryptograms and Algebra Puzzles
Replace the same characters by the same numerals so that the mathematical operations are correct.
IFIB - EBG = CEH
- - +
CCE / GD = FE
------------------------
EFF + EED = CBA




From IFID - CCE = EFF follows that I = 1
From CCE / GD = FE follows that D x E must be xE, which limits the possibilities to E = 4 and D = 6, or E = 5 and D = 3, 7 or 9 (other options not possible, because 1 is already in use)
If we assume E to be 4, we get 4BG - G6 = 446, which would imply G = 2, and therefor B = 7, and because of 1F17 - 472 = C4H, H would become 5.
C45 + F4 = C7A would then imply that A = 9, and from 4FF + 446 = C79 would follow that F = 3 and C = 8

884 / 26 = 34, which covers the CCE / GD = FE line perfectly in accordance with all the above.

1317 - 472 = 845
- - +
884 / 26 = 34
----------------
433 + 446 = 879

A = 9, B = 7, C = 8, D = 6, E = 4, F = 3, G = 2, H = 5, I = 1

Since this solution fits perfectly, I see hardly a need to try the E = 5 option. Hardly reasonable to expect that there are two valid solutions to this type of puzzle.

Thanx for having this section, Rookie. I've always loved this kind of puzzles


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#3 lastinline2solve

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Posted 02 December 2010 - 07:38 PM

Hey Rookie...

I am new to the site as you know.. I love Crypto puzzles and ones with algebra in them as well but I am having a hard time understanding these puzzles. Why is there 3 layers of numbers and mutiple operations? Im not much of the math whiz here and certainly know nothing more than your basic algebra.. lol But I have never seen these kinds of equations before. Can you possibly explain a little about how to solve so I can get involved? If not I understand the reasoning... Thanks in advance though!
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#4 lastinline2solve

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Posted 02 December 2010 - 07:39 PM

Hey Rookie...

I am new to the site as you know.. I love Crypto puzzles and ones with algebra in them as well but I am having a hard time understanding these puzzles. Why is there 3 layers of numbers and mutiple operations? Im not much of the math whiz here and certainly know nothing more than your basic algebra.. lol But I have never seen these kinds of equations before. Can you possibly explain a little about how to solve so I can get involved? If not I understand the reasoning... Thanks in advance though!



I wanted to say as well.. I have figured part of it out.. but it doesnt seem to work for all puzzles.... if this helps.
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#5 LReese

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Posted 06 June 2011 - 11:39 PM

From IFID - CCE = EFF follows that I = 1
From CCE / GD = FE follows that D x E must be xE, which limits the possibilities to E = 4 and D = 6, or E = 5 and D = 3, 7 or 9 (other options not possible, because 1 is already in use)
If we assume E to be 4, we get 4BG - G6 = 446, which would imply G = 2, and therefor B = 7, and because of 1F17 - 472 = C4H, H would become 5.
C45 + F4 = C7A would then imply that A = 9, and from 4FF + 446 = C79 would follow that F = 3 and C = 8

884 / 26 = 34, which covers the CCE / GD = FE line perfectly in accordance with all the above.

1317 - 472 = 845
- - +
884 / 26 = 34
----------------
433 + 446 = 879

A = 9, B = 7, C = 8, D = 6, E = 4, F = 3, G = 2, H = 5, I = 1

Since this solution fits perfectly, I see hardly a need to try the E = 5 option. Hardly reasonable to expect that there are two valid solutions to this type of puzzle.

Thanx for having this section, Rookie. I've always loved this kind of puzzles <!-- s:D --><!-- s:D -->


BoilingOil



I know your solution works, but I'm curious in the line "From CCE / GD = FE follows that D x E must be xE" why are the only possibilities for this sentence only:
D=3, E=5
D=6, E=4
D=7, E=5
D=9, E=5

Why not also:
D=6, E=2
D=6, E=8
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