All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Going Cyclic With Geometric II (Posted on 2009-07-04)
Three 3-digit non leading zero positive base N integers P, Q and R, with P > Q > R, are such that:

• Q is the geometric mean of P and R, and:
• P, Q and R can be derived from one another by cyclic permutation of digits.

Determine all possible positive integer values of N < 30 for which this is possible.

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: computer solution for N<=100 -- the program Comment 4 of 4 |
(In reply to computer solution for N<=100 by Charlie)

DEFDBL A-Z
CLS
FOR n = 2 TO 100
n2 = n * n
FOR a = 1 TO n - 1
FOR b = 1 TO n - 1
FOR c = 1 TO n - 1
p = a * n2 + b * n + c
q = b * n2 + c * n + a
r = c * n2 + a * n + b
IF p > q AND q > r THEN
a2 = b: b2 = c: c2 = a
a3 = c: b3 = a: c3 = b
GOSUB report
END IF
SWAP q, r
IF p > q AND q > r THEN
a2 = c: b2 = a: c2 = b
a3 = b: b3 = c: b3 = a
GOSUB report
END IF
NEXT
NEXT
NEXT
NEXT n
END

report:
IF q * q = p * r THEN
PRINT USING "###  ##  ##  ##    ##  ##  ##    ##  ##  ##    ######## ######## ########"; n; a; b; c; a2; b2; c2; a3; b3; c3; p; q; r
ct = ct + 1
IF ct MOD 40 = 0 THEN DO: LOOP UNTIL INKEY\$ > "": PRINT
END IF
RETURN

 Posted by Charlie on 2009-07-04 16:05:28

 Search: Search body:
Forums (0)