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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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Dozens

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Inspector Remorse

Stage: 3 Short Challenge Level: Challenge Level:1

Inspector Remorse estimates that he can solve the average murder in $x$ hours, a bank robbery in half that time, and a car theft in one third of the time he takes to solve a bank robbery.

How much time would he expect to take in solving two murders, six car thefts and four bank robberies?
 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.

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