Why do you add +1 in counting test questions?

Solution 1:

If you don't add 1, then you're saying "take the first 201 customers, but then exclude the first 149 ones." That would give you the number of customers in the list from 150-201.

The way I think of it is this: The number of customers from #149 to #201 is $201-148=53$, because it's the first 148 customers we're trying to exclude.

Does that help?

Solution 2:

There's a Wikipedia article about this question:

http://en.wikipedia.org/wiki/Off-by-one_error#Fencepost_error

Solution 3:

Here's one way of thinking about it.

The numbering of customers is pretty inconvenient. It would be much better if the first customer was customer number $1$, the second customer was customer number $2$, and so on. That way, the total number of customers would be the customer number of the last customer. So I am going to change the numbering of customers to suit my needs. How am I going to do this? Well, to change the first customer's number from $149$ to $1$, I subtract $148$. Likewise, for each customer, their new customer number is their old one minus $148$. This gives the desired numbering and the final customer's new customer number is $201 - 148 = 53$. Therefore $53$ people were waited on.

Note $201 - 148 = 201 - (149 - 1) = 201 - 149 + 1$; that's where the one comes from. If you didn't add the one, the first customer's number would be zero, not one.