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Counting Factors

Is there an efficient way to work out how many factors a large number has?

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Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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Helen's Conjecture

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

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.