Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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?

Don't Be Late

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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