int count = Enumerable
.Range(0, 101)
.Where(n => n.ToString().Contains(”7″))
.Count();
Console.WriteLine(count);

If you treat each number as a series of Hundreds, Units and Tens you would have a 100 x 3 grid

001
002
003
.
.
.
099
100

You can discount the hundreds as that will be either 0 or 1, never 7. After that you can see that each column would have 7 ten times each; with one row that both the tens and the units would be 7.

Personally I find it very helpful thinking of sets of numbers with their leading zeros (or right aligned if you prefer).

You have 7, 17, 17 … 97 and also 70, 71 … 79.

The most common answer seems to be 10 and then second most common answer is 11. Some people also say 20, because they count 77 twice.