Alex from Elm Park Primary School in New Zealand sent in the following:

The rule is the number must be divisible by 5.
Because 5 and 15 are both divisible by 5 and 18 and 22 are not.


Haima from Tempo School in Canada sent in this work:

 

Gwenny who is home-schooled in the United Kingdom wrote:

I think the rules could be:
1) He only likes numbers with 5 in them
2) He only likes odd numbers
3) He only likes numbers in the 5 times table
4) He only likes numbers that have a 5 in the units

To test the rule, I would ask him if he likes the number 53.  If he put it in the "don't like" column, we would know it wasn't rule 1 or 2. If he put it in the "like" box, we would know it wasn't rule 3 or 4. My next number to ask would be 50. This way, I would find out if it was odd numbers or numbers with 5 in that he liked.

Elie from The International School of Brussels sent this in: 

      click to see full size
and from Lumina:

      click to see full size

Thank you for these observations and thoughts.