### 14 Divisors

What is the smallest number with exactly 14 divisors?

### 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?

### Dozens

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

# Weekly Problem 31 - 2010

##### Stage: 3 Short Challenge Level:

Let the time for which Mary drove at $70$ mph be $t$ hours. Then the total distance covered was$55 \times 2 + 70 \times t$ miles. Also, as her average speed over $2 +t$ hours was $60$ mph, so the total distance travelled was $60(2+t)$ miles.
Therefore $110 +70 t = 120 + 60 t$, that is $10 t = 10$, that is $t=1$.
So in total Mary's journey took $3$ hours.

This problem is taken from the UKMT Mathematical Challenges.

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