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 arithmetic mean of the two neighboring digits.

Note: Try to solve this problem analytically, although computer program/ spreadsheet solutions are welcome.

DECLARE SUB addOn ()
DEFDBL A-Z
CLEAR , , 25000
DIM SHARED s$, maxV
FOR n = 10 TO 99
  s$ = LTRIM$(STR$(n))
  addOn
NEXT
PRINT maxV

SUB addOn
  p2 = VAL(MID$(s$, LEN(s$) - 1, 1))
  p1 = VAL(MID$(s$, LEN(s$), 1))
  i = 2 * p1 - p2 + 1
  DO WHILE i <= 9 AND i > -1
    s$ = s$ + LTRIM$(STR$(i))
    IF LEN(s$) > 10 THEN PRINT s$: STOP
    IF VAL(s$) > maxV THEN maxV = VAL(s$): PRINT maxV
    addOn
    s$ = LEFT$(s$, LEN(s$) - 1)
    i = i + 1
  LOOP
END SUB

finds

96433469

Posted by Charlie on 2008-09-27 16:40:32