This number is self-verifying, in that it is picked in such a way that summing up a function of the digits yields a total divisible by 11.
Suppose we index the digits of the number starting from 1 on the right:
| Index i | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
| Digit di | 0 | 2 | 6 | 2 | 0 | 1 | 0 | 7 | 7 | 1 |
Let f(i,di) = i × di
Now compute the sum of the f(i,di) for 1 ≤ i ≤ 10:
| f(1,d1) + f(2,d2) + ... + f(10,d10) | = |
| 1×1 + 2×7 + 3×7 + ... + 9×2 + 10×0 | = |
| 121 |
Since 121 is divisible by 11, 0-262-01077-1 is a valid ISBN number.