Most books have an ISBN number. For example, the ISBN number of
Recreations in the
Theory of Numbers
is
0486210960
. Let's multiply these digits by the numbers ten to
one. 10*
0
+9*
4
+8*
8
+7*
6
+6*
2
+5*
1
+4*
0
+3*
9
+2*
6
+1*
0
= 198 = 18*11. The sum is
divisible by 11. Two of the Martin Gardner books are 0879752823 and 0226282546.
Using this same method, we get the sums 286 (26*11) and 165 (15*11). So far, all of the
sums have been divisible by 11. But how about the ISBN number of
The Book of
Numbers
-- 038797993X ? We'll let the X represent 10, and we obtain the sum 308
(28*11). For any book you pick, this method will yield a number divisible by 11. Makes
a great bar bet in bars with books. The ISBN's are designed that way. The final digit (or
X) is a
checksum
. The number 0100000001 cannot be an ISBN number. If we know
that only one digit is wrong, then the correct ISBN number might be 0600000001,
0170000001, 0108000001, 0100200001, 0100090001, 0100003001, 0100000401,
0100000061, or 0100000002.
William Ivey, Greg Bensimon, Derrick Schneider and Rod Bogart pointed out that my
previous mentions of ISDN should be ISBN. Claude Chaunier and Joe DeVinctentis
solved my puzzle about ISBN's. 123456789X is the only valid starting ISBN for the
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- Fall '10
- Dr. Yaan
- ISBN, check digit, Error detection and correction, Parity bit, golay code, Binary Golay Code
-
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