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 Three Fractions II (Posted on 2012-10-01)
Each of the letters should be replaced by a different digit from 1 to 9 to satisfy this alphanumeric equation:

A     C     E
--- + --- + --- = 1, with A > C > E
B     D     F
Can you solve it, knowing that if I told you whether CA is a prime number or not, you would be able to tell me all the other letters?

Note: CA denotes the concatenation of the digits.

 No Solution Yet Submitted by K Sengupta Rating: 3.0000 (1 votes)

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 computer solution | Comment 3 of 4 |

DEFDBL A-Z
FOR e = 1 TO 7
used(e) = 1
FOR c = e + 1 TO 8
used(c) = 1
FOR a = c + 1 TO 9
used(a) = 1

FOR b = 1 TO 9
IF used(b) = 0 THEN
used(b) = 1
FOR d = 1 TO 9
IF used(d) = 0 THEN
used(d) = 1
FOR f = 1 TO 9
IF used(f) = 0 THEN
used(f) = 1

IF a * d * f + c * b * f + e * b * d = b * d * f THEN
PRINT STR\$(a); "/"; LTRIM\$(STR\$(b)); " +";
PRINT STR\$(c); "/"; LTRIM\$(STR\$(d)); " +";
PRINT STR\$(e); "/"; LTRIM\$(STR\$(f))
END IF

used(f) = 0
END IF
NEXT
used(d) = 0
END IF
NEXT
used(b) = 0
END IF
NEXT

used(a) = 0
NEXT
used(c) = 0
NEXT
used(e) = 0
NEXT

finds

3/6 + 2/8 + 1/4
3/9 + 2/4 + 1/6
4/8 + 3/9 + 1/6

CA = 23 in both of the first two, but 34 in the third. Only if told that it was not prime would we be able to determine the letters. So the letters, in alphabetic order, represent 4, 8, 3, 9, 1 and 6.

 Posted by Charlie on 2012-10-01 13:51:26

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