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?

Handy Angles

Stage: 3 Short Challenge Level:

Let $x$ denote the angle between the hour hand and the vertical, and $y$ the angle between the minute hand and the vertical.

$\frac{360}{12}=30$ so we calculate that $x = \left( 4+\frac{2}{3} \right) \times 30 =140^\circ$ and $y = 8 \times 30 = 240^\circ$.

The angle between the hands is $y - x = 240^\circ - 140^\circ = 100^\circ$.

This problem is taken from the UKMT Mathematical Challenges.
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