Determine the maximum value of a (base ten) positive integer N (with non leading zeroes) such that each of the digits of N, with the exception of the first digit and the last digit, is less than the harmonic mean of the two neighboring digits.

*** For an extra challenge, solve this puzzle without the aid of a computer program.

DECLARE SUB build (n#)
DEFDBL A-Z
CLEAR , , 25000

CLS
DIM SHARED h(50), maxv, v

maxv = 1
FOR st = 1 TO 9
  h(1) = st: v = st
  build 2
NEXT

SUB build (n)
  FOR tr = 1 TO 9
    IF n = 2 THEN
      h(n) = tr: vsave = v: v = v * 10 + tr
      IF v > maxv THEN
        maxv = v
        FOR i = 1 TO n
          PRINT h(i);
        NEXT
        PRINT
      END IF
      build n + 1
      v = vsave
    ELSE
      IF h(n - 1) < 2 / (1 / h(n - 2) + 1 / tr) THEN
        h(n) = tr: vsave = v: v = v * 10 + tr
        IF v > maxv THEN
          maxv = v
          FOR i = 1 TO n
            PRINT h(i);
          NEXT
          PRINT "   "; v
        END IF
        build n + 1
        v = vsave
      END IF
    END IF
  NEXT
END SUB

finds as the highest:

976679

Posted by Charlie on 2013-12-28 16:00:13