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# View of /trunk/NationalProblemLibrary/Rochester/setDiscrete6Integers/ur_dis_6_9.pg

Tue Jun 26 21:45:47 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1839 byte(s)
Updated tags. --JJH


    1 ## DESCRIPTION
2 ##   Modular Arithmetic Application
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Mod', 'Modular', 'ISBN')
6 ## Tagged by nhamblet
7
8 ## DBsubject('Discrete Mathematics')
9 ## DBchapter('Number Theory')
10 ## DBsection('Modular Arithmetic')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
14 ## TitleText1('Discrete Mathematics')
15 ## EditionText1('')
16 ## AuthorText1('Rosen')
17 ## Section1('2.3')
18 ## Problem1('47,48')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23 "PG.pl",
24 "PGbasicmacros.pl",
26 );
27
28 TEXT(beginproblem());
29 $showPartialCorrectAnswers=1; 30 31 32 do { 33$sum = 0;
34  $sumb = 0; 35 for ($i = 0; $i < 9;$i++) {
36   $a[$i] = random(0,9);
37   $sum =$sum + ($i+1)*$a[$i]; 38$b[$i] = random(0,9); 39$sumb = $sumb + ($i+1)*$b[$i];
40  }
41
42  $q =$sum % 11;
43  $qb =$sumb % 11;
44 } until (($q < 10) and ($qb < 10));
45
46 BEGIN_TEXT
47 Books are identified by an International Standard Book Number (ISBN), a
48 10-digit code $$x_1x_2\dots x_{10}$$, assigned by the publisher. These
49 10 digits consist of blocks identifying the language, the publisher,
50 the number assigned to the book by its publishing company, and
51 finally, a 1-digit check digit that is either a digit or the letter X
52 (used to represent 10). This check digit is selected so that
53 $$\sum_{i=1}^{10} ix_i \equiv 0 \text{ mod } 11$$ and is used
54 to detect errors in individual digits and transposition of digits.
55 $BR 56$BR
57 (a) The ISBN for a book is $$a[0]-a[1]a[2]-a[3]a[4]a[5]a[6]a[7]a[8]- 58 \text{Q}$$
59  where Q is the check digit.
60 What is Q?
61 \{ ans_rule(30) \}
62 $PAR 63 (b) The ISBN of another book is 64 $$b[0]-b[1]b[2]b[3]-b[4]b[5]\text{M}b[7]b[8]-qb$$. Find the digit M. 65 \{ ans_rule(30) \} 66 END_TEXT 67 68 ANS(num_cmp($q) );
69 ANS(num_cmp(\$b[6]) );
70
71
72 ENDDOCUMENT();        # This should be the last executable line in the problem.;