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 ABCD's Of Greatest Divisor (Posted on 2009-09-24)
The greatest common divisor of five positive integers ABCD, 1920CD41, 496BC3, 872AB76 and 10A25D8 is ≥ 2, where each of A, B, C and D represents a different base 10 digit from 0 to 9.

Determine all possible quadruplet(s) (A, B, C, D) that satisfy the given conditions.

 See The Solution Submitted by K Sengupta No Rating

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 QB version Comment 3 of 3 |

` A  B  C  D      the Numbers------------------- 8  5  2  4    8524  19202441  496523  8728576  1082548 GCD: 2131 only 1 solution`

DECLARE FUNCTION gcd# (a#, b#)
DEFDBL A-Z

FOR a = 0 TO 9
used(a) = 1
FOR b = 0 TO 9
IF used(b) = 0 THEN
used(b) = 1
FOR c = 0 TO 9
IF used(c) = 0 THEN
used(c) = 1
FOR d = 0 TO 9
IF used(d) = 0 THEN
used(d) = 1

abcd = a * 1000 + b * 100 + c * 10 + d
cd = (19200 + c) * 1000 + d * 100 + 41
bc = (4960 + b) * 100 + c * 10 + 3
ab = (8720 + a) * 1000 + b * 100 + 76
ad = (100 + a) * 10000 + (250 + d) * 10 + 8

g = gcd(abcd, cd)
g = gcd(g, bc)
g = gcd(g, ab)
IF g >= 2 THEN
PRINT a; b; c; d, abcd; cd; bc; ab; ad, g: ct = ct + 1

END IF

used(d) = 0
END IF
NEXT
used(c) = 0
END IF
NEXT
used(b) = 0
END IF
NEXT
used(a) = 0
NEXT

PRINT ct

FUNCTION gcd (a, b)
dnd = a: dvr = b
DO
q = INT(dnd / dvr): r = dnd - q * dvr
dnd = dvr: dvr = r
LOOP UNTIL dvr = 0
gcd = dnd
END FUNCTION

 Posted by Charlie on 2009-09-24 14:28:03

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