### 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?

# Weekly Problem 13 - 2010

##### Stage: 2 and 3 Short Challenge Level:
Suppose the youngest dwarf is $x$ years old. The sum of the ages of the youngest three is $x+(x+1)+(x+2)=3x+3$, and the sum of the ages of the oldest three is $(x+4)+(x+5)+(x+6)=3x+15$.

We know that $3x+3=42$, so $3x+15=42+12=54$.

This problem is taken from the UKMT Mathematical Challenges.

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