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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 two of the sets?
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?
You might now like to play the game Statement Snap and then have a go at Charlie's Delightful Machine.
Satisfying Statements
Age 11 to 14
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 two of the sets?
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?
You might now like to play the game Statement Snap and then have a go at Charlie's Delightful Machine.
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Adding All Nine
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!
