Solution

156613

First name
Zaia Kawagoe
School
Little Bowden
Country
Age
9

2 digit numbers that belong in 2 of the sets are, 10,15,21,30,42,45,50,55,60,66,70,75,78,90

2 digit numbers that belong in 3 of the sets are, 10,15,30,66,78,

Smallest number that belongs in all 4 sets is, 210

The pattern that satisfies Alison's and Sam's statements is, after 10 add 20 each time.

The pattern that satisfies Alison's and Matt's statements is, after 15, add 15 then add 30 then add 15 etc

There is a pattern with Alison and Becky's numbers, 4th and 5th triangular numbers, then 9th and 10th triangular numbers, then 14th and 15th triangular numbers and so on.