Challenge Level

Alison, Becky, Sam and Matt are playing a game.

Each of them writes down a statement that describes a set of numbers.

Alison writes "Multiples of five".

Becky writes "Triangular numbers".

Sam writes "Even, but not multiples of four".

Matt writes "Multiples of three but not multiples of nine".

Can you find some two-digit numbers that belong in three sets?

What is the smallest number that belongs in all four sets?

How could you describe the pattern of the numbers that satisfy both Alison's and Sam's statements?

How about the numbers that satisfy both Alison's and Matt's statements?

Can you describe patterns for other pairs of statements?