### 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?

# Fangs

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

Alternate angles BDF and DFG are equal, so lines BD and FG are parallel.
Therefore angle BCA = angle FGC = $80^{\circ}$ (corresponding angles).

Consider triangle ABC: $x + 70 + 80 = 180$ so $x=30$.

Alternatively, note that angle ACB = angle DCE, and therefore triangles ABC and CDE are similar, so angle DEC = $70^{\circ}$. Similarly, angle DCE is $80^{\circ}$, and therefore $x=30^{\circ}$.

This problem is taken from the UKMT Mathematical Challenges.
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