How does the use of a variable instead of a value help to reduce detail and focus?

Answer 1

We try to generalise our code as much as we can. We cannot avoid using values completely, however a value is a literal constant and if we use the same constant over and over it makes sense to use a named constant variable rather than a value, if only to make it much easier to change the value throughout our code.
To use a real world example, suppose we are writing a Sudoku solving program. The value 9 crops up quite a lot because there are 9 rows, 9 columns, 9 boxes and 9 digits, one of which is the digit 9. However, Sudoku is not a number puzzle, we just use digits for notational convenience. Any 9 unique symbols would do, so using variables instead of values would give us the ability to change symbols.

Moreover, Sudoku puzzles are not just limited to 9 rows, columns and boxes, we can use any number that is a square. 9 is the square of 3 thus a standard Sudoku has order 3. We can also use order 2 (a 4x4 Sudoku), order 4 (a 16x16 Sudoku) and so on. The size of the Sudoku does not change the logic of solving it, so by using a variable to keep track of the order we can cater for any size Sudoku without changing the code. Our code becomes more generalised (less detailed) because it no longer focuses on a standard Sudoku.