A university uses student numbers consisting of 6 digits plus a check digit in the 7th position. The check digit is found by taking the number formed by the first 6 digits modulo 7. A transposition in this setup is a switch of two adjacent digits - check digit excluded. Which transpositions of a student number (a6,a5,a4,a3,a2,a1,a0) (here written as a vector, with check digit a0) will not be detected by the check digit? Explain your answer in full and show any calculations you do. Hint: Note that the value of any ai in the number is ai×10i and consider the difference between the values of the correct and incorrect numbers modulo 7.

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Array

The simplest way to start thinking about an array is as a collection, or a set of elements. In programming, these elements may be constants, variables, functions and pointers.