How can they guess my number just by knowing which rows it appears in? I've saw this "trick" many times in math club, I'm just wondering if it's real that they know ESP, or is it just a scam?
We're given 5 rows: $\newcommand{\tsf}[1]{\mathsf{\text{#1}}}$
$$\begin{array}{c|cccccccccccccccc}
\tsf{Row 1} & \sf 1 & \sf 3 & \sf 5 & \sf 7 & \sf 9 & \sf 11 & \sf 13 & \sf 15 & \sf 17 & \sf 19 & \sf 21 & \sf 23 & \sf 25 & \sf 27 & \sf 29 & \sf 31\\[0.1in]
\tsf{Row 2} & \sf 2 & \sf 3 & \sf 6 & \sf 7 & \sf 10 & \sf 11 & \sf 14 & \sf 15 & \sf 18 & \sf 19 & \sf 22 & \sf 23 & \sf 26 & \sf 27 & \sf 30 & \sf 31\\[0.1in]
\tsf{Row 3} & \sf 4 & \sf 5 & \sf 6 & \sf 7 & \sf 12 & \sf 13 & \sf 14 & \sf 15 & \sf 20 & \sf 21 & \sf 22 & \sf 23 & \sf 28 & \sf 29 & \sf 30 & \sf 31\\[0.1in]
\tsf{Row 4} & \sf 8 & \sf 9 & \sf 10 & \sf 11 & \sf 12 & \sf 13 & \sf 14 & \sf 15 & \sf 24 & \sf 25 & \sf 26 & \sf 27 & \sf 28 & \sf 29 & \sf 30 & \sf 31\\[0.1in]
\tsf{Row 5} & \sf 16 & \sf 17 & \sf 18 & \sf 19 & \sf 20 & \sf 21 & \sf 22 & \sf 23 & \sf 24 & \sf 25 & \sf 26 & \sf 27 & \sf 28 & \sf 29 & \sf 30 & \sf 31
\end{array}$$
Then I pick a number, and they ask me what rows did my number show up in.  I answered honestly, and they were able to guess my number correctly every time!
Is this a scam or, what's the truth behind this?  Every time I asked they said it's mathemagics.

Note that 1 only appears in row 1, and nothing else only shows up in row 1. Likewise, 2 only shows up in row 2, and nothing else lies only in row 2. So if you answer "Only row 1," then they can see that the number is 1.
22, on the other hand, is the unique number appearing in rows 2, 3 and 5 alone. 
You can check that, in fact, all the numbers from 1 to 31 have this uniqueness property.
