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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?

How Many Miles to Go?

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

A car's milometer reads $4631$ miles and the trip meter has $173.3$ on it:

Milometer: 4631, trip distance 173.3

How many more miles must the car travel before the two numbers contain the same digits in the same order?

Can you find some other starting numbers that will lead to matching pairs?

What is the relationship between two starting numbers that will work?

If the milometer and trip meters had the following exact readings ($4632$ and $173.3$) then the two numbers will not contain the same digits in the same order before the milometer reaches $99999$ miles. Why is this?

Milometer: 4632, trip distance 173.3

If the milometer 'loops the clock' back to $00000$ again at $100,000$ miles and the trip meter loops the clock back to $000.0$ at $1000$ miles, will the two numbers ever contain the same digits in the same order?