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## Sunday, 29 June 2014

### Sunday Afternoon Maths XIX

Here's this week's collection. Answers & extensions tomorrow. Why not discuss the problems on Twitter using #SundayAfternoonMaths or on Reddit.

#### Dartboard

Concentric circles with radii 1, $$\frac{1}{2}$$, $$\frac{1}{3}$$, $$\frac{1}{4}$$, ... are drawn. Alternate donut-shaped regions are shaded.
What is the total shaded area?

#### Multiples of Three

If the digits of a number add up to a multiple of three, then the number is a multiple of three. Therefore if a two digit number, $$AB$$ (first digit $$A$$, second digit $$B$$; not $$A\times B$$), is a multiple of three, then $$A0B$$ is also a multiple of three.
If $$AB\div 3=n$$, then what is $$A0B\div 3$$?