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14 Divisors

What is the smallest number with exactly 14 divisors?

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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?

Writ Large

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Suppose you had to begin the never ending task of writing out the natural numbers: 1, 2, 3, 4, 5.... and so on.

What would be the 1000th digit you would write down. In what number would it occur?

What number would contain the millionth digit?

When would you have written six for the 6000th time?