 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Going Maximum With Harmonic (Posted on 2013-12-28) 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.

 No Solution Yet Submitted by K Sengupta No Rating Comments: ( Back to comment list | You must be logged in to post comments.) computer solution | Comment 1 of 2

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 Please log in:
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