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Sunday Afternoon Maths LI

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Posted on 2016-04-03

What is the Sum

What is $$\displaystyle\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{15}+\sqrt{16}}$$?

Two Semicircles

The diagram shows two semicircles.
$$CD$$ is a chord of the larger circle and is parallel to $$AB$$. The length of $$CD$$ is 8m. What is the area of the shaded region (in terms of $$\pi$$)?

Doubling Cribbage

Brendan and Adam are playing high stakes cribbage: whoever loses each game must double the other players money. For example, if Brendan has £3 and Adam has £4 then Brendan wins, they will have £6 and £1 respectively.
Adam wins the first game then loses the second game. They then notice that they each have £180. How much did each player start with?
If you enjoyed these puzzles, check out Sunday Afternoon Maths LXI,
puzzles about number, or a random puzzle.