Each of the ID numbers issued to Mr.Cooper and Mr. Duncan is of the form ABCDEFGHIJ, with each of the letters representing a different digit from 0 to 9 inclusively, such that:
(i) BCD is divisible by 2.
(ii) CDE is divisible by 3.
(iii) DEF is divisible by 5.
(iv) EFG is divisible by 7.
(v) FGH is divisible by 11.
(vi) GHI is divisible by 13.
(vii) HIJ is divisible by 17.
Determine the ID numbers issued to each of the gentlemen, given that the ID number of Mr. Cooper is greater than that of Mr. Duncan.
Note: A is not 0, and C is greater than D.
*** While a solution may be trivial with the aid of a computer program, show how to derive it without one.
I might be missing something but I get four possible ID numbers:
4 1 3 0 9 5 2 8 6 7
4 1 6 0 3 5 7 2 8 9
1 4 3 0 9 5 2 8 6 7
1 4 6 0 3 5 7 2 8 9
and don't know a way of eliminating two.
Yes, I used a program:
CLS
FOR b = 0 TO 9
used(b) = 1
FOR c = 0 TO 9
IF used(c) = 0 THEN
used(c) = 1
FOR d = 0 TO 8 STEP 2
IF used(d) = 0 AND c > d THEN
used(d) = 1
FOR e = 0 TO 9
IF used(e) = 0 THEN
IF (c + d + e) MOD 3 = 0 THEN
used(e) = 1
FOR f = 0 TO 5 STEP 5
IF used(f) = 0 THEN
used(f) = 1
FOR g = 0 TO 9
IF used(g) = 0 THEN
IF (100 * e + 10 * f + g) MOD 7 = 0 THEN
used(g) = 1
FOR h = 0 TO 9
IF used(h) = 0 THEN
IF (100 * f + 10 * g + h) MOD 11 = 0 THEN
used(h) = 1
FOR i = 0 TO 9
IF used(i) = 0 THEN
IF (100 * g + 10 * h + i) MOD 13 = 0 THEN
used(i) = 1
FOR j = 0 TO 9
IF used(j) = 0 THEN
IF (100 * h + 10 * i + j) MOD 17 = 0 THEN
used(j) = 1
FOR a = 0 TO 9
IF used(a) = 0 THEN EXIT FOR
NEXT a
PRINT a; b; c; d; e; f; g; h; i; j
used(j) = 0
END IF
END IF
NEXT j
used(i) = 0
END IF
END IF
NEXT i
used(h) = 0
END IF
END IF
NEXT h
used(g) = 0
END IF
END IF
NEXT g
used(f) = 0
END IF
NEXT f
used(e) = 0
END IF
END IF
NEXT e
used(d) = 0
END IF
NEXT d
used(c) = 0
END IF
NEXT c
used(b) = 0
NEXT b
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Posted by Charlie
on 2008-08-19 12:39:09 |
Hmmmmm.... (spoilers)
