Solve this set of simultaneous alphametic equations, where HUIT and NEUF are respectively positive integers in base 8 and base 9 notation. Each of the letters in bold represents a different digit, and none of the numbers contains any leading zero.

(HUIT)₈ = (NEUF)₉ - 1, and:
sod(HUIT) = sod(NEUF) - 1

Extra Challenge: A non computer program aided solution.

*** sod(x) denotes the numeric value of the sum of the digits of x.

FOR h = 1 TO 7
  used(h) = 1
FOR u = 0 TO 7
  IF used(u) = 0 THEN
    used(u) = 1
FOR i = 0 TO 7
  IF used(i) = 0 THEN
    used(i) = 1
FOR t = 0 TO 7
  IF used(t) = 0 THEN
    used(t) = 1
    sod1 = h + u + i + t
    huit = t + 8 * (i + 8 * (u + 8 * h))
FOR n = 1 TO 8
  IF used(n) = 0 THEN
    used(n) = 1
FOR e = 0 TO 8
  IF used(e) = 0 THEN
    used(e) = 1
FOR f = 0 TO 8
  IF used(f) = 0 THEN
    used(f) = 1
    sod2 = n + e + u + f
    neuf = f + 9 * (u + 9 * (e + 9 * n))
    IF huit = neuf - 1 AND sod1 = sod2 - 1 THEN
      PRINT h; u; i; t, n; e; u; f, huit, neuf
    END IF
    used(f) = 0
  END IF
NEXT
    used(e) = 0
  END IF
NEXT
    used(n) = 0
  END IF
NEXT
    used(t) = 0
  END IF
NEXT
    used(i) = 0
  END IF
NEXT
    used(u) = 0
  END IF
NEXT
  used(h) = 0
NEXT

finds

                                   as
                                 decimal
H  U  I  T    N  E  U  F    huit          neuf
                            value         value

5  4  7  0    3  8  4  2    2872          2873

Posted by Charlie on 2013-12-27 17:29:39