Here's this week's collection. Answers & extensions tomorrow. Why not discuss the problems on Twitter using #SundayAfternoonMaths or on Reddit. This Tuesday is Maths Jam, make sure you're there!

#### Three Squares

The diagram shows three squares with diagonals drawn on and three angles labelled.

What is the value of \(\alpha+\beta+\gamma\)?

#### Equal Opportunity

Can two (six-sided) dice be weighted so that the probability of each of the numbers 2, 3, …, 12 is the same?

#### Double Derivative

What is

$$\frac{d}{dy}\left(\frac{dy}{dx}\right)$$
when:

(i) \(y=x\)

(ii) \(y=x^2\)

(iii) \(y=x^3\)

(iv) \(y=x^n\)

(v) \(y=e^x\)

(vi) \(y=\sin(x)\)?

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