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BRIAN = LINDA = LEVIK = CORAL (Posted on 2006-12-08) Difficulty: 4 of 5
Can you find a five-figure number, with distinct digits between 1 and 9, which satisfies all of the following encoded equations?

BRIAN x 2 = CONGA
LINDA x 3 = NAILER
LEVIK x 4 = VARIED
CORAL x 6 = NESTED

Repeated letters within an equation indicate the replication of digits. However, the same letter in different equations does not necessarily refer to the same digit.

See The Solution Submitted by Josie Faulkner    
Rating: 4.3750 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution the programmatic way | Comment 2 of 8 |

DECLARE FUNCTION checkPat! (a$, b$)
FOR n = 12345 TO 98765
  n$ = LTRIM$(STR$(n))
  IF checkPat(n$, "brian") THEN

    a$ = LTRIM$(STR$(n * 2))
    IF checkPat(n$ + a$, "brianconga") THEN

      b$ = LTRIM$(STR$(n * 3))
      IF checkPat(n$ + b$, "lindanailer") THEN

    c$ = LTRIM$(STR$(n * 4))
    IF checkPat(n$ + c$, "levikvaried") THEN

      d$ = LTRIM$(STR$(n * 6))
      IF checkPat(n$ + d$, "coralnested") THEN

        PRINT n; "* 2 ="; n * 2
        PRINT n; "* 3 ="; n * 3
        PRINT n; "* 4 ="; n * 4
        PRINT n; "* 6 ="; n * 6

      END IF

    END IF

      END IF

    END IF

  END IF
NEXT n

FUNCTION checkPat (a$, b$)
 d$ = SPACE$(10)
 IF LEN(a$) <> LEN(b$) THEN checkPat = 0: EXIT FUNCTION
 FOR i = 1 TO LEN(b$)
   l$ = MID$(b$, i, 1)
   p = VAL(MID$(a$, i, 1)) + 1
   IF MID$(d$, p, 1) = " " THEN
     IF INSTR(d$, l$) > 0 THEN checkPat = 0: EXIT FUNCTION
     MID$(d$, p, 1) = l$
   ELSEIF MID$(d$, p, 1) <> l$ THEN
     checkPat = 0: EXIT FUNCTION
   END IF
 NEXT i
 checkPat = 1
END FUNCTION

finds

45163 * 2 = 90326
45163 * 3 = 135489
45163 * 4 = 180652
45163 * 6 = 270978


  Posted by Charlie on 2006-12-08 11:02:45
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