98
Solutions to Exercises
7. (a) [BB] The given rule is w· a = 0 (mod 11) for a =
(al,a2,
... , alO)
and
w = (1,1,1,1,1,1,1,1,1,1).
(b) Suppose an error is made in the ith digit of an ISBN number so that instead of
ala2
...
ai
...
alO,
the number appears
as
ala2'
..
a~
...
alO,
with
a~
:F
ai.
Then 0 =
at
+
a2
... +
ai
+
... +
alO
¢
at
+
a2
+
... +
a~
+
... +
alO
because
[at
+
a2
+
... +
ai
+
... + alOl 
[at
+
a2
+
... +
a~
+
... + alOl
=
ai

a~
¢ 0
(mod 11)
since
ai
and
a~
are
digits between 0 and 9.
(c) Suppose
ata2
... alO is a correct ISBN number. The transposition of
ai
and aHt cannot be
detected because when we apply our test to the incorrect number
at
... aH
t
ai
...
alO,
we compute
at
+
... +
aiH
+
ai
+
... + alO which is, of course, congruent to 0 (mod 11) because it's the
exactly the same as
at
+
... +
ai
+ aHt +
... +
alO.
8.
(a)[BB]
113579024688;
(d)
[BB]
063042006355;
(b)
102468135796;
(e)
063000164257;
(c) 062608393496;
(0 8294471 04931 .
9. (a) [BB] Not valid: 3(0 + 2 + 4 + 6 + 8 + 0) + (1 + 3 + 5 + 7 + 9 + 1) = 60 + 26 = 86 ¢ 0
This is the end of the preview.
Sign up
to
access the rest of the document.
 Summer '10
 any
 Graph Theory, Numerical digit, Prime number, International Standard Book Number, check digit

Click to edit the document details