The Hotel Problem

After a presentation on web analytics in one of my classes where I was discussing the different types of unique visitors a website can have. A particular part of the presentation seemed to receive a particularly good response, it was when I broke down a common problem for beginners to analytics, known as the Hotel Problem. I decided to show this problem here. This is taken from it's posting on Wikipedia.

Say you have a hotel that offers 2 different rooms. We will look at who uses which room over a 3 day period and how many unique 'visitors' you had.

• The first day, room A is rented by John and room B is rented by Mark. Thus 2 Unique visitors for the day.
• The second day, room A is rented by John and room B is rented by Jane, again 2 unique visitors for the day.
• The third day, room A is rented by Jane and room B is rented by Mark. For the last time, 2 unique visitors came to the hotel that day.

So in summary, each day we had 2 unique visitors, or to look at it another way, each room had 2 unique visitors.

Now for the easy question: How many unique visitors came to the hotel?

To help answer the question, here is a table showing what just happened:

Do you see the problem?

So how many did we have? 3? 4? 6? The numbers and logic support each of these answers.

Actually each of these numbers are correct, it just depends on what metric is being used.

• Based on days, there were 6 unique visitors, or 2 unique users each day
• Based on rooms, there were 4 unique visitors, or 2 unique users in each room
• Based on individual people, there were only 3 different visitors total over the 3 day period.

It is important to be remembered that unique visitors can be interpreted different ways. Depending on the business, one particular metric may be the best.