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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?


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

Consider all two digit numbers ($10$, $11$, . . . ,$99$). In writing down all these numbers, which digits occur least often, and which occur most often ?

What about three digit numbers, four digit numbers and so on?