### 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?

# In Sum-mary

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

The sum of the first two numbers and the last two numbers is $1004+1005=2009$. This counts the middle number twice. But the sum of all three numbers is $2009$, so the middle number is $0$. Hence the product of all three numbers is $0$.

[Alternatively: Let the three numbers be a, b and c.

We have
$a+b=1004$
$b+c=1005$
and     $a+b+c=2009$

Adding the first two equations gives
$a+2b+c=2009$

and subtracting the third equationg from this gives
$b=0$

Thus the product $abc=0$.]

This problem is taken from the UKMT Mathematical Challenges.
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