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 Unknown Digits (Posted on 2004-08-11)
In this cryptarithm, each letter above the line represents a digit differing by 1 from the digit represented by the same letter below the line. For example, if A=3 above the line, then A=2 or A=4 below the line. All occurrences of a letter on the same side of a line represent the same digit. It is also known that there are total of five digits in the solution.
``` ADABA
+CACBA
------
DBABC
```

 See The Solution Submitted by Brian Smith Rating: 3.6667 (3 votes)

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 brute force -- spoiler | Comment 1 of 8

FOR a = 1 TO 9
FOR b = 0 TO 9
IF b <> a THEN
FOR c = 1 TO 9
IF c <> a AND c <> b THEN
FOR d = 0 TO 9
IF d <> c AND d <> b AND d <> a THEN

top = a * 10101 + d * 1000 + b * 10
bottom = c * 10100 + a * 1001 + b * 10
tot = top + bottom
t\$ = LTRIM\$(STR\$(tot))
IF LEN(t\$) = 5 THEN
IF MID\$(t\$, 2, 1) = MID\$(t\$, 4, 1) THEN
IF ABS(VAL(MID\$(t\$, 3, 1)) - a) = 1 THEN
IF ABS(VAL(MID\$(t\$, 2, 1)) - b) = 1 THEN
IF ABS(VAL(MID\$(t\$, 5, 1)) - c) = 1 THEN
IF ABS(VAL(MID\$(t\$, 1, 1)) - d) = 1 THEN
PRINT top: PRINT bottom: PRINT tot
END IF
END IF
END IF
END IF
END IF
END IF

END IF
NEXT d
END IF
NEXT c
END IF
NEXT b
NEXT a

finds

56505
15105

71610

 Posted by Charlie on 2004-08-11 13:24:39
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